{"data":[{"id":5,"title":"A First Course in Linear Algebra","edition_statement":null,"volume":null,"copyright_year":2015,"ISBN10":null,"ISBN13":"9780984417551","license":"Free Documentation License (GNU)","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled \"Chapter V\" and the theorem that elementary matrices are nonsingular is labeled \"Theorem EMN.\" Another feature of this book is that it is designed to integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minute video tutorial on SAGE and teaching linear algebra. This textbook has been used in classes at: Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.","contributors":[{"id":3623,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Robert","middle_name":"A.","last_name":"Beezer","location":"University of Puget Sound","background_text":"Robert A. Beezer is a Professor of Mathematics at the University of Puget Sound, where he has been on the faculty since 1984. He received a B.S. in Mathematics from the University of Santa Clara in 1978, a M.S. in Statistics from the University of Illinois at Urbana-Champaign in 1982 and a Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign in 1984. He teaches calculus, linear algebra and abstract algebra regularly, while his research interests include the applications of linear algebra to graph theory."}],"subjects":[{"id":83,"name":"Algebra","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":29,"url":"https://open.umn.edu/opentextbooks/subjects/algebra?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":103,"url":"http://linear.ups.edu/","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2020-08-17T09:47:04.000-05:00","name":"Robert Beezer"}],"formats":[{"id":143,"type":"Online","url":"http://linear.pugetsound.edu/html/fcla.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":144,"type":"PDF","url":"https://citeseerx.ist.psu.edu/document?repid=rep1\u0026type=pdf\u0026doi=2d126254474e43b7d300ef5e60752d5e19f287c3","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":145,"type":"Hardcopy","url":"https://www.amazon.com/First-Course-Linear-Algebra/dp/0984417559","price":{"cents":3300,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":11,"reviews":[{"id":188,"first_name":"Barry","last_name":"Minemyer","position":"Ross Visiting Assistant Professor","institution_name":"The Ohio State University","comprehensiveness_rating":5,"comprehensiveness_review":"This book covers a tiny bit more than I would normally cover in an introductory linear algebra class (due to its use of the complex numbers throughout), and omits nothing that I would normally cover.  All subject areas address in the Table of Contents are covered thoroughly.","accuracy_rating":5,"accuracy_review":"I found no accuracy issues in the text.  Examples are worked out in full detail throughout the text, and at a first reading appeared to be error-free.","relevance_rating":5,"relevance_review":"The content is as up-to-date as any introductory linear algebra textbook can reasonably be.  The text includes some guidance on how to use Sage to help with calculations, but the book is written in such a way that it can be easily used without implementing Sage into the course.","clarity_rating":5,"clarity_review":"I think that the text in this book is extremely clear, which is great for a first course in linear algebra.  The book includes a few \"one-liners\" to help keep students engaged while reading, and I think that this is done really well!","consistency_rating":5,"consistency_review":"This text is consistent in its terminology, both internally and globally.","modularity_rating":5,"modularity_review":"The text is subdivided into small digestible chunks for students to read.  The text is pretty self-referential, but the book is hyperlinked throughout.  So it just takes one click for the reader to be directed to the definition, example, or section being referenced.","organization_rating":4,"organization_review":"All of the material in the text follows from what has preceded it, so in that sense it is structured well.  But my only very minor issue with this book is that some of the material is covered in what I would consider an \"unusual order\".  Two big examples are:\r\n\r\n- eigenvalues and eigenvectors are covered before the notion of a linear transformation is defined.\r\n- The Gram-Schmidt procedure is introduced incredibly early in the text, before basic concepts like matrix operations, bases, dimension, or determinants.\r\n\r\nThis is, of course, an opinionated issue though.  Others may certainly like the ordering in this book better than what I would recommend.  But the key is that the book is written so that one could easily \"jump around\" these parts without causing much confusion for the students.  And due to the hyperlinks in the text, it is easy to navigate to the relevant sections.\r\n\r\nAlso, a really nice touch is that there are 24 recurring examples throughout the text that the author calls \"archetypes\".  These archetypes are all listed together at the end of the book, along with their description.  I feel that this is great tool for students to easily be able to compare and contrast different types of examples.","interface_rating":5,"interface_review":"I had no interface issues with this book.  One interesting thing of note is that items are indexed using acronyms instead of numerically.  For example, the fourth chapter is labeled \"Chapter VS\" instead of \"Chapter 4\" (and where VS is for vector spaces).  I am not sure whether I like acronyms or numbers better, but it is all a moot point because of the hyperlinks used in the text.  There is also a list of all acronyms used for definitions and theorems at the end of the book.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors in this textbook.  It is very well written.","cultural_rating":5,"cultural_review":"No portion of this text appeared to me to be culturally insensitive or offensive in any way, shape, or form.","overall_rating":10,"overall_review":"Overall, I think that this textbook provides a great introduction to linear algebra!  With such a great resource available to students for free, I do not see why I would ever force my students to purchase a different textbook in the future.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":201,"first_name":"James","last_name":"Fowler","position":"Assistant Professor","institution_name":"The Ohio State University","comprehensiveness_rating":5,"comprehensiveness_review":"Beezer's book includes all the expected topics in a first corse in linear algebra, and it also provides some review sections on set theory and complex numbers.\r\n\r\nTo place it in the broader world of linear algebra textbooks, this text is generally more algebraic and numeric than it is geometric: the section on Vector Operations, for instance, mentions that a vector might be thought of as \"representing a point in three dimensions\" and that one \"can construct an arrow,\" but then finishes by saying \"we will stick with the idea that a vector is just a list of numbers, in some particular order.\"  The student gets early exposure to the axioms for vector spaces, which then link to the Proof Techniques section.\r\n\r\nThe reference section at the end provides a list of notation, definitions, theorems.  The online format does a nice job of providing an overall perspective on the course.  The use of knols, for instance, lets a learner follow a reference without losing his/her place in the online text.","accuracy_rating":5,"accuracy_review":"The book is mathematically accurate as far as I can tell, but there are also wonderul structural features of this book that ensure such accuracy.  The content resides in a GitHub repo at https://github.com/rbeezer/fcla which makes it easy to submit edits (and indeed, to submit pull requests).  The examples are supported by Sage code, which also makes mechanical errors unlikely in the presentation.  As a globally-editable machine-assisted textbook, there are good reasons to believe it will remain accurate in future editions.","relevance_rating":5,"relevance_review":"The incorporation of Sage certainly makes the content especially timely, especally with the tremendous excitement around https://cloud.sagemath.com/\r\n\r\nIn terms of longevity, the fact that the text of the book is stored in LaTeX and XML ensures that the text will be useful for a long time to come.  Updates will be straightforward to implement.\r\n\r\nThe book includes a lot of exercises.","clarity_rating":5,"clarity_review":"In a definition, the word being defined is highlighted in bold.  Examples are distinguished by a different background color.  Sage code is supported with explanations (e.g., when thinking about Row Operations, the author explains that \"[t]he copy() function, which is a general-purpose command, is a way to make a copy of a matrix before you make changes to it. \"  This sort of documentation is critical for guiding a student---perhaps without much python experince---to successly using the Sage environment to learn some mathematics).\r\n\r\nWhen making an argument, the author both names the property, and briefly recalls what it says in English: e.g., the author writes that \"[s]ince every vector space must have a zero vector (Property Z), we always have a zero vector at our disposal.\"  The text is friendly  (literally about friends: the author writes \"These will bring us back to the beginning of the course and our old friend, row operations.\") without sacrificing rigor.","consistency_rating":5,"consistency_review":"The book is consistent.  Notation is presented at the end of the text, and used throughout.  Objects are labeled with short acronyms and referred to throughout the book.\r\n\r\nPerhaps most important for consistency, the book uses a list of \"archetypes\" which are \"typical examples of systems of equations, matrices and linear transformations\" that have been crafted to \"demonstrate the range of possibilities.\"  By  building the narrative around this small number of great examples, the book is pedagogically consistent.\r\n","modularity_rating":4,"modularity_review":"The use of knols and \"folding\" does provide a degree of modularity: a student can be exploring one section and need not \"open up\" an example until they want to pursue that example.  This format makes it very clear how the text is structured.\r\n\r\nI expect that instructors using this book would be using the material in the presented order, though, with the exception of perhaps pointing some students to the review sections at the end on complex numbers and sets.","organization_rating":5,"organization_review":"Sections and theorems and the like are labeled with short acronyms instead of numbers; this appears a bit idiosyncratic at first, but it actually makes the text easier to read: the learner is more likely to assign meaning to \"Theorem TSS\" than they would \"Theorem 17.42.\"  As a grader, I much prefer it when my students provide clear names for the theorems they are invoking in their write-ups.\r\n\r\nIn terms of organization, the book begins with concrete examples (e.g., column vectors) and then sections later provides \"a formal definition of a vector space\" which leads \"to an extra increment of abstraction.\"  This is a good way to provide a scaffold to more theoretical concerns, and is indicative of the thoughtful structure of the book overall.","interface_rating":5,"interface_review":"The HTML interface is fantastic: the use of Knols lets a learner follow a link without losing the broader context.  The math is rendered beautifully by MathJax.  Examples and the like are \"folded\" so they do not distact the reader until he/she is ready to dig into the example.\r\n\r\nOne thing that makes the book very useable is its use of the Sage cell server---the learner can use the interactive components of the textbook without having to install a local copy of Sage, which should make this book accessible by a broader number of people.","grammatical_rating":5,"grammatical_review":"I have not noticed any grammatical errors.  In terms of style, I would say that it is colloquial, friendly English.  The material is certainly technical but there is a consultative, invitating tone behind the technical discussion.\r\n\r\nThere is some concern to warn the reader about technical terms: e.g., the author wrtes \"A final reminder: the terms [...] used in reference to vectors or matrices with real number entries are special cases of the terms.\"","cultural_rating":5,"cultural_review":"There is a lot of great mathematical culture in the book, but perhaps not too many places where the book touches on \"real-world examples\" which might provide other places to touch on cultural issues.\r\n","overall_rating":10,"overall_review":null,"created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":475,"first_name":"Christopher","last_name":"Phan","position":"Assistant Professor","institution_name":"Winona State University","comprehensiveness_rating":5,"comprehensiveness_review":"This book includes a good selection of topics for a semester-long linear algebra course.","accuracy_rating":5,"accuracy_review":"I did not notice any errors. The open-source model allows any errors to be corrected promptly.","relevance_rating":5,"relevance_review":"Most of the material is basically timeless. The book does include computer code that can be used with SageMath, an open-source computer algebra system. Because SageMath is open-source, it should be possible to obtain a copy indefinitely.","clarity_rating":5,"clarity_review":"The book is easy to read, with practical examples sprinkled throughout. In addition, in the electronic version, the interface makes it easy to refer to previous theorems or examples.","consistency_rating":5,"consistency_review":"The author uses consistent terminology and notation throughout.","modularity_rating":5,"modularity_review":"The book is more modular than most other math texts. For example, theorems are not numbered, but given abbreviations, so that they would not need to be renumbered should you choose to adopt and incorporate sections into another text. Of course, some sections depend on results or material from others, which cannot be avoided in a math text. (But even then, the interface makes referring to the previous material easy.)","organization_rating":5,"organization_review":"The book is organized well. The author moves from concrete to more abstract concepts, starting with matrices and column vectors before moving on to abstract vector spaces and linear transformations. For example, eigenvectors are described before linear transformations. This organization is pleasant to follow.","interface_rating":5,"interface_review":"The interface in the electronic version is a selling point of the book. Every time a previous theorem or definition is invoked, the reader can click a link and view that previous theorem or definition without actually navigating to that page. Likewise, the book includes instruction on using the SageMath computer algebra system. The electronic version includes a direct interface to SageMath (through the SageMath Cell Server) which allows code to be run directly from the book.","grammatical_rating":5,"grammatical_review":"I did not notice any grammatical or spelling errors.","cultural_rating":5,"cultural_review":"I did not notice anything that was culturally insensitive or offensive.","overall_rating":10,"overall_review":null,"created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":595,"first_name":"Angela","last_name":"Martinek","position":"Instructor","institution_name":"Lane Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers all the topics of a first course in linear algebra. There is discussion on set theory, complex numbers and proof techniques. Complex number are mentioned very early in the text although not used. Very little emphasis on the geometric approach and more leaning to operations research.","accuracy_rating":4,"accuracy_review":"I found an error early on in the reading under Proof Techniques D  \"A definition is usually written as some form of an implication, such as “If something-nice-happens, then blatzo.” However, this also means that “If blatzo, then something-nice-happens,” even though this may not be formally stated.\"  I did not come across any other errors, although I didn't edit the entire book.\nSage is used and there is a section that calls out a video that was not accessible. There were other issues with the Sage tutorial, the \"blue line\" did not appear for instance.","relevance_rating":5,"relevance_review":"The book is written using Sage which we do not use t this time.  The Sage Cell Server is nice and allows students to use Sage without downloading it. The book is such that Sage is not required.\nSince the book is editable and Sage is also an open resource I see no problem with the longevity of this OER. The examples used in the text are relevant and up to date.","clarity_rating":5,"clarity_review":"The writing in the book is very clear. Many examples help put the mathematics in context in each section.","consistency_rating":5,"consistency_review":"The book is very consistent in terminology and structure. Each section has subsections with a description,  example(s), reading questions and exercises. The reading questions are designed to be completed by the student before class on the topic with most of the exercises having worked out solutions.","modularity_rating":4,"modularity_review":"The text is modular and could be reorganized but it flows by topic in such a way as not to be necessary. The proofs and their descriptions could be left out for a very early course in matrices. The online version has so many hyperlinks that it became a bit confusing where I had left off and how to get back.","organization_rating":3,"organization_review":"The flow and structure was ok as long as I didn't click on too many hyperlinks. I found the hyperlinks lead to good examples and definitions but with no chapter/section numbers it was difficult to go back. Seemed like a lot of jumping around leading me to get a bit lost and having to reopen sections I'd already read. Because of the acronym section names O could come after V. I found that experience a bit frustrating and decided bypass this feature.","interface_rating":4,"interface_review":"The displays and charts came across just fine. As far as navigation, it may be the operator but see my answer to number 7. Some of the links opened up a window that allowed the user to continue reading. This was true for most examples but not when directed to another section.","grammatical_rating":5,"grammatical_review":"The grammar was fine, easy to read.","cultural_rating":5,"cultural_review":"I did not fine anything insensitive or offensive in this book.","overall_rating":9,"overall_review":"I liked the book overall. \nI like the printable flash cards for students in the supplemental section. \nThe use of archetypes is also very useful and aides in understanding.\n\nI did not do well with all the acronyms, SLE vs SSLE vs SSSLE, section CNO with subsections CNE or CNA. Too many of these for me, I would suggest numbers. Like Section 2: Vectors, Section 2.1: Vector Operations.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":828,"first_name":"Michael","last_name":"Kirby","position":"Professor","institution_name":"Colorado State University","comprehensiveness_rating":3,"comprehensiveness_review":"There is a lot of great basic material here.  However, there are several topics missing that I would consider part of a standard first course in linear algebra.  Matrix factorizations, such as the Cholesky factorization, or decompositions, such as the LUD decomposition, do not appear to be treated.  The singular value decomposition has achieved an important status in linear algebra and it should be found even in first courses.  Strang's Linear Algebra did not have principal component analysis in 1984, but it does now for example. There is no index in this book that I can find.  ","accuracy_rating":5,"accuracy_review":"The book appears very carefully written and accurate.","relevance_rating":3,"relevance_review":"The basic material will not change and as such this text could be used a 100 years from now.   However, it is missing more applied ideas, such as linear algebra in image processing, that are becoming increasingly popular and serve to decrease its relevance.","clarity_rating":3,"clarity_review":"The writing style is very clear.  However, the use of abbreviations such as Theorem SLEMM, and Definition NM, make the book harder to read.  They also not very suggestive as a mnemonic device.","consistency_rating":5,"consistency_review":"Yes, the book appears very consistent.","modularity_rating":4,"modularity_review":"The topics are very nicely modular, but I would probably rearrange the order in which they are taught.","organization_rating":3,"organization_review":"The topics are presented in a carefully thought out manner and the structure is reasonable.  I would probably want matrix multiplication defined before introducing the solution of linear systems.","interface_rating":5,"interface_review":"The hypertext links are great.  Navigating the text is a pleasure.  The inclusion of Sage is also a huge addition.","grammatical_rating":5,"grammatical_review":"The grammar is fine.","cultural_rating":5,"cultural_review":"The text is culturally relevant and not offensive.  Unless you happen to not like matrices ;-)","overall_rating":8,"overall_review":"Nice addition to the available resources that I am sure will be attractive for a lot of instructors.","created_at":"2016-12-05T18:00:00.000-06:00","updated_at":"2016-12-05T18:00:00.000-06:00"},{"id":927,"first_name":"Richard","last_name":"Hammack","position":"Professor","institution_name":"Virginia Commonwealth University","comprehensiveness_rating":4,"comprehensiveness_review":"I examined this book carefully last semester while searching for a good inexpensive (or free) textbook to adopt for a sophomore-level linear algebra course. This book contains all the topics that I'd normally cover in such a course, plus more. The prose is often conversational, but ultimately accurate, unambiguous and lucid. \n\nThe book does have some quirks, the most noticeable of which is an extensive reliance on acronyms. Chapters are not numbered, but rather tagged with sometimes cryptic abbreviations. For example, the book begins with Chapter SLE (Systems of Linear Equations), followed by Chapter V (Vectors), then Chapter M (Matrices), etc. Even theorems, definitions, examples and diagrams are designated in this way. For instance, Definition ROLT is for the rank of a linear transformation. (Why not just call it \"Definition RANK\"?) All this takes some getting used to, but such brevity may have a place in classroom exposition.\n\nIf there is a serious omission, it is that the book has scarcely any figures at all, which is surprising given the geometric nature of linear algebra. And I felt that the occasional figures fell short of really illuminating the ideas that they were supposed to convey. For example, Diagram NILT (non-injective linear transformation) is identical to Diagram NSLT (non-surjective linear transformation), except for labeling. So by themselves they don't clearly differentiate the two ideas. Further, these illustrations show generic point sets, not vector spaces. I'd be more comfortable seeing (say) non-surjectivity illustrated by a map from 2-D space to a plane in 3-D space, etc.\n\nI had trouble locating an index in the on-line version of the book. ","accuracy_rating":5,"accuracy_review":"I found no mistakes at all. ","relevance_rating":5,"relevance_review":"I believe the book is very up to date. Some instructors may want to see a little more on matrix decompositions, but this is not an issue with me. Regardless, because of the non-numeric labeling of chapters and definitions, it would be very easy for the author to add material without affecting the numbering of subsequent sections. For this reason, I rank the book's longevity as high.","clarity_rating":4,"clarity_review":"The prose is very clear, and one feels that it has been informed by many years of teaching the subject. As mentioned above, I believe that it would be even clearer with the addition of well-crafted figures. ","consistency_rating":5,"consistency_review":"The author has done an excellent job here. The book is remarkably uniform in tone and format, and is uniquely Beezer's work from beginning to end. He has created his own brand of textbook.  ","modularity_rating":5,"modularity_review":"The book is broken into sections and subsections, and theorems, proofs, definitions and examples are clearly delineated. The acronym labeling scheme makes the book feel especially modular, possibly at the expense of emphasizing the interdependency among the various topics. ","organization_rating":5,"organization_review":"The sequencing is perfectly logical and natural, and l would see no reason to do anything in a different order. This is one instance where the acronyms seem out of place, as a simple numeric labeling of the chapters would underscore the importance of the flow of ideas in a way that the acronyms do not.","interface_rating":5,"interface_review":"I read the online version, which I thought was pretty good. I did find some aspects of the experience to be slightly disconcerting. For example, it's hard to gauge how long a section will be when clicking on an example can suddenly expand a simple phrase to an entire page, or more.  But whatever problems I had may have been due to my own preference for thumbing through paper books. ","grammatical_rating":5,"grammatical_review":"I found no problems with the grammar. ","cultural_rating":5,"cultural_review":"It is difficult to imagine how linear algebra could be culturally insensitive. At any rate, I can't imagine that the author has offended anyone.","overall_rating":10,"overall_review":null,"created_at":"2017-02-08T18:00:00.000-06:00","updated_at":"2017-02-08T18:00:00.000-06:00"},{"id":1978,"first_name":"Emese","last_name":"Kennedy","position":"Visiting Assistant Professor","institution_name":"Hollins University","comprehensiveness_rating":4,"comprehensiveness_review":"This is a great book that covers most topics that should be included in an introductory linear algebra course. In fact, many of the topics are discussed in more depth than what is necessary for an intro course. The Reading Questions at the end of each section make this book easy to use for a flipped style course. The sections on complex number operations, set theory are nice additions that help students gain a better understanding of these topics. The section on proof writing techniques is especially useful for students who have not had much exposure to proof writing. However, some topics that I usually cover in intro linear algebra like LU decomposition and applications to computer graphics are not included in the book.","accuracy_rating":5,"accuracy_review":"The book is well-written and very accurate.","relevance_rating":4,"relevance_review":"The content is very relevant and up-to-date. However, I think that more applications should be addressed, especially relating to the use of linear algebra in image processing and computer graphics.","clarity_rating":5,"clarity_review":"The book is very clearly written and the style is easy to read.","consistency_rating":5,"consistency_review":"The text is internally consistent in terms of terminology and framework.","modularity_rating":5,"modularity_review":"The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course. Each section can be covered in an hour long class if the students do the reading and complete the Reading Questions in advance.","organization_rating":4,"organization_review":"The book is well organized and the topics are presented in a logical manner. I wish that the acronyms used were more suggestive to make it easier to remember what they stand for. I like that the exercises have a letter indicating their type (e.g. T for theoretical), but don’t quite understand how they are numbered. For example, one section has exercise T12 immediately followed by exercise T20.","interface_rating":3,"interface_review":"I find the online version the easiest to navigate followed by the pdf version. I like that the electronic and online versions have hyperlinks that make it easy to find references. However, the use of acronyms for the names of chapters, sections, examples, definitions, and theorems makes navigation more challenging. For example, it is difficult to go back to where you were after clicking on a hyperlink in the pdf because the sections are not numbered, so one can easily get lost. The frequent referencing using acronyms only (instead of pages numbers) makes it very difficult to use the print version.","grammatical_rating":5,"grammatical_review":"I have not found any grammatical errors.","cultural_rating":5,"cultural_review":"I have not found anything that is culturally insensitive or offensive in the text.","overall_rating":9,"overall_review":"This is a high quality open source textbook that I would strongly recommend to any instructor teaching an introductory linear algebra course. The website corresponding to the book has plenty of supplementary resources for both students and instructors. The solution manual includes detailed answers for almost all the exercises. As an instructor, I wish that there were more exercises for which the students could not download the answers for to make assigning homework easier.","created_at":"2018-05-21T19:00:00.000-05:00","updated_at":"2018-05-21T19:00:00.000-05:00"},{"id":2157,"first_name":"Gabriel","last_name":"Tapia","position":"Teaching Instructor","institution_name":"West Virginia University","comprehensiveness_rating":5,"comprehensiveness_review":"If anything, this textbook is too comprehensive: it exhaustively covers all linear algebra canon.","accuracy_rating":5,"accuracy_review":"I found no errors after a month of teaching out of the book.","relevance_rating":5,"relevance_review":"This book attempts to balance its relevance among three audiences: general engineers, mathematics majors, and computer science students. At times it seems to swing too far in the direction of math major, but it remains a valuable resource for all audiences.","clarity_rating":4,"clarity_review":"Many of the examples were large systems meant to be presented on a computer rather than a blackboard. This emphasizes the material's applicability but at the expense of efficiency.","consistency_rating":5,"consistency_review":"It is consistent.","modularity_rating":5,"modularity_review":"I taught only portions of this book as part of a multivariable calculus course, and the book's modularity held up very well.","organization_rating":4,"organization_review":"The topics were clear for me as an instructor who already knew the material, but I don't know if my students were able to follow the text. However, reading mathematics texts is an acquired still and there are very few fully accessible to undergraduates.","interface_rating":4,"interface_review":"The only feature I was missing were bookmarks in the pdf of the solutions manual, but that was a big one.","grammatical_rating":5,"grammatical_review":"I found no errors.","cultural_rating":5,"cultural_review":"Is math a culture?","overall_rating":9,"overall_review":"As a resource for a multivariable calculus class, this book fit my needs perfectly. I would consider using it for a full-semester linear algebra course after my experience.","created_at":"2018-06-19T19:00:00.000-05:00","updated_at":"2018-06-19T19:00:00.000-05:00"},{"id":2261,"first_name":"Jason","last_name":"Gaddis","position":"Assistant Professor","institution_name":"Miami University","comprehensiveness_rating":4,"comprehensiveness_review":"This book contains a standard set of topics one would expect to see in a first semester Linear Algebra course, beginning with systems of linear equations and transitioning into vectors and matrices. Abstract vector spaces appear in the middle of the book once students are well-equipped to make the transition from real or complex vector spaces. The appendix provides a good review of complex numbers and basic set theory.\n\nThe book essentially ends with orthonormal diagonalization. I rank among those that would consider quadratic forms and singular value decomposition as unfortunate omissions from the text.\n\nAs other reviewers have pointed out, the acronym-labeling style for theorems is odd. Proofs and examples are usually done in sufficient detail, but the labeling system makes it more difficult than necessary to find references to other theorems. There is a list in the appendix of where to find theorems but using this seems like an unnecessary step for students. In addition, the index of definitions in the appendix is sorted by section, rather than alphabetically, making finding definitions cumbersome.","accuracy_rating":5,"accuracy_review":"I found no major errors in the text.","relevance_rating":5,"relevance_review":"This book can certainly compete with other standard Linear Algebra texts, such as Lay’s “Linear Algebra and its Applications”. The Sage supplement makes it especially relevant for instructors who wish to implement computation/programming into their course.","clarity_rating":4,"clarity_review":"The book seems relatively easy to read for students. Proofs are generally given with great detail and references that students can use to understand individual steps. Sometimes, the author includes elements in a proof that belong more in the discussion before or after. For example, the proof that the inverse of a matrix product is the product of the inverses in the opposite order begins with an analogy to dating services. It is a cute analogy, but does not give students a good example for how formal proofs should be written.","consistency_rating":5,"consistency_review":"The author does a good job of maintaining style throughout.","modularity_rating":4,"modularity_review":"While there is some natural dependence between topics, I saw no reason that many of the chapters could be moved around at will. Of course, it would make no sense to move the discussion of determinants after that of eigenvalues/eigenvectors.\n\nThe author introduces the idea of a basis in the chapter on vectors and even uses the term without fully defining it. This is saved until the chapter on abstract vector spaces but does prevent that chapter from being moved until later in the book, presenting some modularity problems for those that choose to focus primarily on R^n.","organization_rating":5,"organization_review":"The structure of this book is what I would expect in an introductory Linear Algebra text.","interface_rating":3,"interface_review":"There is a complete lack of figures/diagrams in this text. Not only does this obscure geometric concepts related to Linear Algebra, it also makes the text less inviting for students.","grammatical_rating":5,"grammatical_review":"I found no major grammatical issues in the text.","cultural_rating":4,"cultural_review":"This text does not heavily emphasize applications and therefore it is hard to judge the cultural relevance of the text. In fact, Linear Algebra is such an important part of modern mathematics/computer science/engineering that the text does some students a disservice by not focusing on these.","overall_rating":9,"overall_review":"Because this book is open source, I would consider using this in a future Linear Algebra course, possibly supplemented with my own notes or other resources.","created_at":"2018-08-02T19:00:00.000-05:00","updated_at":"2018-08-02T19:00:00.000-05:00"},{"id":2698,"first_name":"Teena","last_name":"Carroll","position":"Associate Professor of Mathematics","institution_name":"Emory and Henry College","comprehensiveness_rating":5,"comprehensiveness_review":"The standard set of topics is covered with many additional topics interspersed.  Review topics such as proof techniques and properties of complex numbers are included as supplements.  There are many nonstandard ways to navigate this book, but a standard index is not one of them.   (For instance I was trying to find all of the mentions of the word \"partition\" in the text and was unable to do that from something labelled an index; perhaps it is unnecessary because you can use the search feature on the pdf, but again that is not available from the online or printed source.)  \r\n\r\nOne place this text is missing a viewpoint is in the visualization of matrices and vectors in the geometry of 3 space.  Perhaps integrating the IOLA materials would fill in that hole (Inquiry Oriented Linear Algebra at iola.math.vt.edu/).","accuracy_rating":5,"accuracy_review":"Content is accurate, definitions are carefully stated.","relevance_rating":4,"relevance_review":"As long as SAGE stays compatible with online display and continues to be relevant this book will have staying power.  The context is written so updates will be straightforward.  ","clarity_rating":3,"clarity_review":"The book's writing is often quite dense.  For instance a single example covers approximately 4 pages; variables are assigned based on a comment in the first paragraph which requires the reader to scroll back to figure out why the variables are being named that way and what they represent (where a quick reminder would have taken a few words).  In the same example, there is lots of text which seems superfluous.  \r\n\r\nUsing 3-6 letter acronyms to name theorems and definitions is quixotic and nonstandard enough to be off-putting.   I think only a small number of students will respond well to it.  Although the linking available in the online formats certainly helps students overcome this, that is not available in a printed version of the text.\r\n","consistency_rating":3,"consistency_review":"There is some consistency issues in terms of what level ideas a reviewed.  Some words like \"partition\" or \"equivalence relation\" which might still be a fresh concepts for a new linear algebra students are just tossed into the text, whereas the author spends at least a page reviewing how to read function diagrams, which seems an equivalent level of background.\r\n\r\nNotation use seems consistent throughout.","modularity_rating":4,"modularity_review":"It would help to have a list of chapter dependencies.  ","organization_rating":4,"organization_review":"The organization is clear.","interface_rating":4,"interface_review":"The interface is clearly well thought out and takes advantage of many of the best features of the setting (be it online or pdf).  The text often appears as a big block of text or a list of theorems.  In the online interface having to click on the examples and proofs to display them in some ways is helpful for scanning, but also makes the text appear very dense.","grammatical_rating":5,"grammatical_review":"Grammar is fine.  Generally well written.","cultural_rating":5,"cultural_review":"The book focused mostly on mathematical examples, so there is not much room for cultural inclusivity or insensitivity. ","overall_rating":8,"overall_review":"If you take advantage of all of the additional features, teaching a course from this text is going to feel significantly different from using a standard paper text.  The use of the online/pdf interfaces are well thought out.  There are some features, like the examples which continue through the whole book (called archetypes) which set this book apart, but might also make it hard to use if you are used to a standard chapter model.  ","created_at":"2019-03-26T10:14:53.000-05:00","updated_at":"2019-03-26T10:14:53.000-05:00"},{"id":3000,"first_name":"Jessica","last_name":"Giglio","position":"Assistant Professor II","institution_name":"Central Oregon Community College","comprehensiveness_rating":4,"comprehensiveness_review":"The course covers all the topics I would expect to see in an introductory linear algebra course, plus more, and at an appropriate depth.  However, there are very few figures and little discussion of a geometric perspective (which admittedly the author notes in the first chapter, saying \"While much of our intuition will come from examples in two and three dimensions, we will maintain an algebraic approach to the subject, with the geometry being secondary. Others may wish to switch this emphasis around, and that can lead to a very fruitful and beneficial course, but here and now we are laying our bias bare.\") However, when dealing with certain topics like linear transformations, I really feel its lack.  There isn't really something I'd call an index or glossary, in the sense of being an alphabetized reference.","accuracy_rating":5,"accuracy_review":"I did not find any errors.","relevance_rating":4,"relevance_review":"Most of the material in a course like this is fairly static. The text is arranged in such a way that updates would be easy to add.  Since linear algebra is so important in computer animation, the lack of examples dealing with this application makes the book feel a little out-of-date.","clarity_rating":4,"clarity_review":"The language used in the book is clear, as conversational as is appropriate, and quite accessible.  However, as other reviewers have noted, the unique acronym-based way of naming chapters, theorems, examples, etc., is distracting and doesn't seem to serve any real purpose. ","consistency_rating":5,"consistency_review":"The text is internally consistent in terms of style, terminology, and approach.","modularity_rating":5,"modularity_review":"The text is written in nice bite-size portions--as the author notes, the material in each section can be covered in about an hour.  I teach a 2-credit, very introductory, Intro to Linear Algebra course so I started by reading through only the sections I would cover in that course, and I found that that didn't present much disruption to the flow.  I like the way that examples require the reader to click on their titles, so that the titles serve to break up the \"wall of text\" while the amount of information presented initially isn't overwhelming.","organization_rating":5,"organization_review":"There are a few organizational choices I'd disagree with (e.g. determinants show up later than I'd expect), but that's bound to happen with any text. The given organization of topics is clear and logical.  The idiosyncratic chapter naming convention does make navigating via hyperlinks a little confusing, though.","interface_rating":5,"interface_review":"There weren't any navigation issues or problems with distracting display features. I liked the choices of what to have visible when a section is opened and what requires an additional click.","grammatical_rating":5,"grammatical_review":"I did not notice any grammatical errors.","cultural_rating":5,"cultural_review":"There are few practical examples, but in them, there is no evidence of cultural insensitivity.","overall_rating":9,"overall_review":"A couple of features that I really liked about this text but haven't had a chance to mention yet were:\r\n--The Reading Questions at the end of each section (3 questions--often but not always 2 computational problems and one that is more critical-thinking based) are great and could serve as a starting point for a \"flipped classroom\" approach.\r\n--The Archetypes, 24 examples that are each touched on several times, from different perspectives, throughout the text provide a nice sense of continuity.","created_at":"2019-06-19T17:09:28.000-05:00","updated_at":"2019-06-19T17:09:28.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/a-first-course-in-linear-algebra?locale=es","updated_at":"2026-05-18T12:03:48.000-05:00"},{"id":7,"title":"Book of Proof","edition_statement":"Third Edition","volume":null,"copyright_year":2018,"ISBN10":null,"ISBN13":"9780989472128","license":"Attribution-NoDerivs","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei, Christian Brothers High School, University of Texas Pan American, Schola Europaea, James Madison University, Heriot-Watt University, Prince of Songkla University, Queen Mary University of London, University of Nevada - Reno, University of Georgia - Athens, Saint Peter's University, California State University,Bogaziçi University, Pennsylvania State University, University of Notre Dame","contributors":[{"id":4029,"contribution":"Author","primary":true,"corporate":false,"title":"Dr.","first_name":"Richard","middle_name":null,"last_name":"Hammack","location":"Virginia Commonwealth University","background_text":"Richard Hammack, PhD is an Associate Professor in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. He received his PhD in mathematics from the University of North Carolina at Chapel Hill."}],"subjects":[{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":311,"url":"http://www.people.vcu.edu/~rhammack/BookOfProof/","year":null,"created_at":"2018-09-07T12:22:38.000-05:00","updated_at":"2019-06-05T15:38:38.000-05:00","name":"Richard Hammack"}],"formats":[{"id":499,"type":"PDF","url":"https://richardhammack.github.io/BookOfProof/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":500,"type":"eBook","url":"https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472124/ref=sr_1_1?keywords=9780989472128\u0026qid=1559766364\u0026s=gateway\u0026sr=8-1","price":{"cents":1230,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":8,"reviews":[{"id":150,"first_name":"Milos","last_name":"Savic","position":"Assistant Professor","institution_name":"University of Oklahoma","comprehensiveness_rating":5,"comprehensiveness_review":"This text is intended for a transition or introduction to proof and proving in undergraduate mathematics. Many of the elements needed for this transition are here, including predicate and propositional logic. The index is provided and extensive.","accuracy_rating":5,"accuracy_review":"I have contacted the author about one typographical error I found during my reading, but it is error-free for the majority of the textbook.","relevance_rating":5,"relevance_review":"I love the content of this textbook. Since this topic is relevant for many aspiring mathematicians, the text will live a long life.","clarity_rating":4,"clarity_review":"I believe that the clarity of the text is wonderful, with the exception of one section. I thought that section 5.3, \"Mathematical Writing,\" could have been worded a bit differently or presented to the reader with more discussion. It seemed like I was scolded during the section. I understand the intention of the section, and I praise the author for putting in a section like this since most mathematics textbooks do not, but it seemed to be \"good or bad\" instead of what the author stated, \"good or bad writing is sometimes a matter of opinion.\" Perhaps the author could include some statements to have the reader read, like run-on sentences in english, and determine these rules for his/herself.","consistency_rating":5,"consistency_review":"The text is consistent in framework and terminology. I found no discrepancies while reading.","modularity_rating":4,"modularity_review":"There are certain unavoidable parts of the text that are self-referential. This is common with mathematics. I do enjoy that many sections of the text are about techniques of proving, which highlight the technique's importance in mathematics. ","organization_rating":5,"organization_review":"I really enjoyed the topics in the text, including Chapters 4-10. The proving techniques are the cornerstones to mathematics. I will be incorporating these sections in my future courses due to the elegant way the author has handled these techniques. This would get a higher rating if I could.","interface_rating":3,"interface_review":"The interface was fine. It was a PDF version of a proof textbook. What I wanted from the text was to somehow incorporate the additional nuances that make eBooks slightly better than paper. For example, in the index, I would have liked hyperlinks back to the page where the term was defined. Perhaps I am being critical, but I think that eBooks or PDF versions should have these small refinements.","grammatical_rating":5,"grammatical_review":"This text contains no grammatical errors from what I've observed.","cultural_rating":4,"cultural_review":"There is one question for which I contacted the author on. On page 47, after the section on statements and truth of statements, there is an exercise to determine if a sentence is a statement, and if it is, determine if that statement is true. The statement is #15: \"In the beginning, God created the heaven and the earth.\" In my opinion, this question may lead to discussions that stray from the original task. Other than this, I found the text to be not culturally insensitive or offensive.","overall_rating":9,"overall_review":"Although there are certain aspects of the text I would modify, these aspects are minute compared to the amount of understanding and depth that the author introduces. The author has clearly taken his time in developing a textbook that can be accessible and transferrable to subsequent courses. I highly recommend any transition-to-proof or introduction-to-proof course be taught with this textbook.","created_at":"2015-01-12T18:00:00.000-06:00","updated_at":"2015-01-12T18:00:00.000-06:00"},{"id":246,"first_name":"Jess","last_name":"Ellis","position":"Assistant Professor","institution_name":"Colorado State University, Fort Collins","comprehensiveness_rating":5,"comprehensiveness_review":"I use this book for a \"Discrete Mathematics for Educators\" course. The students are all prospective middle and high school teachers, and the main goals are to prepare them for upper level mathematics courses involving proofs, and to give them a brief introduction to discrete mathematics. This book covers all of the needed proof techniques and gives interesting examples for them. I do use Chapter 3 (combinatorics) and add on some graph theory later on in the course. Thus, I would say it does a very nice job of both introducing students to proof and to intro number theory and combinatorics. ","accuracy_rating":5,"accuracy_review":"After two semesters of teaching from it I have not found an error. ","relevance_rating":5,"relevance_review":"Because of the content, this book passes the longevity test. We will not need to prepare students with introductions to other proof techniques (except perhaps proof by computer?), though additional introductory discrete topics would be great additions for me, though I am using the text for a specific course that goes beyond the scope of the book's intentions. ","clarity_rating":5,"clarity_review":"Very clear and well organized, and defines all new terminology. As a book used to transition students to upper level mathematics, this book does a very nice job of calling out mathematical language norms and writing norms. ","consistency_rating":5,"consistency_review":"Very consistent. ","modularity_rating":5,"modularity_review":"The author provides a nice suggested organization at the beginning, but I have deviated a bit and this book is fine for that. I skipped the chapter on combinatorics and have not used those examples in the proofs so far. After the first exam, we will do some combinatorics, and then go back and prove things about combinatorics and add in inductive proof techniques. The book's structure definitely allows for these sorts of easy changes. ","organization_rating":5,"organization_review":"Very well organized. I especially like the advanced organizer that provides suggested exam timing w/r/t the chapters. I am deviating a bit this semester from the given order, but the book makes this easily doable, and it is still well organized even with the order mixed up a bit. ","interface_rating":5,"interface_review":"No issues here. I would love for hyperlinks to be added, so that you could click on the table of contents to get to chapters (for example). It is very easy to just do a search for terms to get there quickly, but this would be a great addition. ","grammatical_rating":5,"grammatical_review":"No errors. ","cultural_rating":5,"cultural_review":"Not applicable? So - it is vacuously highly culturally relevant. ","overall_rating":10,"overall_review":"I really enjoy this book and love that it is free for my students. I've asked my students if they find the book useful and many have said they rely heavily on it. Also, since it is free I feel find going \"off script\" for a while - when I use an expensive text, I feel like I should make the most of the text for the students. But bc it is free I don't feel that pressure. That said, I don't find myself often deviating from the text's content because it meets my needs. ","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":259,"first_name":"Roberto ","last_name":"Munoz-Alicea","position":"Instructor/Academic Support Coordinator","institution_name":"Colorado State University","comprehensiveness_rating":5,"comprehensiveness_review":"This textbook covers an excellent choice of topics for an introductory course in mathematical proofs and reasoning. The book starts with the basics of set theory, logic and truth tables, and counting. Then, the book moves on to standard proof techniques: direct proof, proof by contrapositive and contradiction, proving existence and uniqueness, constructive proof, proof by induction, and others.  These techniques will be useful in more advanced mathematics courses, as well as courses in statistics, computers science, and other areas. The book ends with additional topics in relations, functions, and cardinality of sets. There is a preface, an introduction, an index, and solutions to selected exercises. ","accuracy_rating":5,"accuracy_review":"While spending a few hours reading the book, I did not find any inaccuracies.  The definitions, theorems, and examples given, as well as the notation used, are good, standard, and well presented. For instance, I like how the book explains the differences among theorems, lemmas, corollaries, and propositions, since students sometimes are confused by such labels. ","relevance_rating":5,"relevance_review":"The material covered in this textbook is very relevant and fundamental in mathematics, and this book covers all of the main topics. Relevance and longevity are not issue.","clarity_rating":5,"clarity_review":"The book is quite clear in explaining the various topics covered, particularly when it comes to set theory and basic proof techniques. I was impressed by how easy to read and well organized this textbook is. Furthermore, the examples and figures are outstanding. ","consistency_rating":5,"consistency_review":"The book is consistent in its use of definitions, diagrams, and terminology.  Any redundancy, especially in terms of definitions, can be useful to preserve modularity.","modularity_rating":4,"modularity_review":"This book’s modularity is good, for an introduction to proofs course. One could rearrange the order in which sections and topics in each chapter are covered, although it would be more challenging to rearrange chapters II, III, and IV without covering chapter I first. Chapter IV could be covered before chapters II and III. Also, mathematical induction could be covered before other proof techniques. ","organization_rating":4,"organization_review":"Even though certain sections and topics could be rearranged, given the textbook’s modularity, I think that the order in which the topics are covered is very logical.  The fundamentals of set theory, logic, and counting techniques are covered in chapter I. These concepts are needed in order to cover proof techniques in chapters II and III. While mathematical induction could be covered before other proof techniques, it still works well to have it covered at the end of Chapter III. Relations, functions, and cardinality follow in chapter IV.  ","interface_rating":4,"interface_review":"Interface is not an issue for this book.  The diagrams, charts, boxes, tables, headings, and the use of boldface and italic font to indicate definitions and other key concepts, are very helpful to better organize the material. One of my favorite diagrams is the one used to explain how mathematical induction works.  One way to improve diagrams and figures would be to label all of them, to make them easier to refer to.","grammatical_rating":4,"grammatical_review":"There are no obvious grammatical errors, as far as I could see. I would only suggest to avoid the use of apostrophes in expressions such as “it’s” or “we’ve”.  Instead, write “it is” or “we have”, as these expressions are better suited for professional writing. ","cultural_rating":5,"cultural_review":"Cultural relevance is not an issue for this textbook. ","overall_rating":9,"overall_review":"This book is excellent for an introduction to mathematics proofs course. Not only does it cover all of the main topics for such a course, but it also discusses mathematical writing, which is key when it comes to making mathematical concepts clear. Many students might know how to prove theorems or solve equations, but might not use correct mathematical notation. The book is very useful to prepare students for courses such as advanced calculus, which is a proof-intensive course.  The numerous examples and diagrams used are useful, not only to make the material easier to understand, but also to motivate students to learn more. I would recommend this textbook to any instructor who teaches introduction to mathematical proofs, and to any student who is being exposed to this subject for the first time or needs to review this material. ","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":1153,"first_name":"Edwin","last_name":"O'Shea","position":"Associate Professor","institution_name":"James Madison University","comprehensiveness_rating":4,"comprehensiveness_review":"The text is very suitable for an \"introduction to proofs/transitions\" course. I have used this book as the primary text for such a course twice, a course with two main goals: prepare the student for proof-centric classes like abstract algebra and real analysis, and introduce the student to what the major ought to look like and what mathematics hopes to achieve beyond the calculus. \nOn the first role, the book really shines in its treatment of logic -- sentences with quantifiers and their negations -- methods of proof, induction(basic and general), equivalence relations, functions, and cardinality. Numerous examples are intertwined with introduction of concepts and thoughtful exercises echo the themes of each section. A high point is that the text ends with a rigorous treatment of the serious and magical results of Cantor on cardinality in addition to the Schroeder-Bernstein theorem.  Some instructors might see a lack of an introduction to delta-epsilon arguments as a weak point. Others might see the lack of delineation between logic and axiomatics as a weakness. \nOn the second role, the book lacks a sense of what the major might expect out of a mathematics degree and so when I use this book in a course I normally assign a cheap Dover secondary text for this purpose, along the lines of Ian Stewart's \"Concepts of Modern Mathematics,\" the chapters of which naturally complement those of this text.","accuracy_rating":5,"accuracy_review":"Errors are rare, content is accurate.","relevance_rating":5,"relevance_review":"There is no shortage of such texts on the book market yet I don't see myself changing this choice of text for my course anytime soon. The text also allows for a variety of pedagogical styles -- with a nice mixture of good direct writing, examples, and a lot of relevant problems.","clarity_rating":5,"clarity_review":"The writing style of the text is best described as direct. Students, who were expected to read considerable sections of the text before coming to class also reported that the text was very good (and they liked that the price was right!).","consistency_rating":5,"consistency_review":"The book is consistent in terms of terminology.","modularity_rating":5,"modularity_review":"While almost every chapter depends on chapters preceding it there are pockets that I think are optional. I value the Euclidean algorithm and Bezout's Theorem (\"the gcd of two integers can always be written as the integer linear combination of those two integers\" and its corollaries) but I don't like the proof presented here and I think the topics can be held back until a course in number theory or in the opening weeks of abstract algebra. Likewise, the perfect number theorem's proof felt like a jump too high for many students so if time is pressing one could opt to postpone these topics in Chapters 7 and 8 respectively.  A reversing of the order of Chapters 2 and 3 is also something I would recommend.","organization_rating":5,"organization_review":"The topics are presented in a clear fashion with themes in each section clearly stated and how one sections theme builds upon previously developed themes.","interface_rating":4,"interface_review":"The text is available online (for free) or for hardcopy purchase (~$15) and the two versions line up. The online interface is a plain pdf that appears just as you would expect from the hardcopy. In the long run, the text might benefit from a mathjax-designed interface like that of, say, Judson's \"Abstract Algebra.\"","grammatical_rating":5,"grammatical_review":"No grammatical errors.","cultural_rating":4,"cultural_review":"For better or for worse, cultural relevance does not typically play into a mathematics text and this text is no different. I think this is a real shame -- a price we have paid collectively for emphasizing mathematics chiefly as a technocratic and scientific problem solving discipline as opposed to a humanistic and democratic problem framing one --  but this is not a stick I wish to beat this text with, or at least this text alone. As another reviewer pointed out, some of the problems in the logic section -- negate \"you can fool some people all the time, all....\" -- are perhaps a bit unusual but my students and I appreciated the ambiguity present in the real world and these problems presented an opportunity to contrast mathematical definitions with the ambiguity of language more generally.","overall_rating":9,"overall_review":null,"created_at":"2017-04-11T19:00:00.000-05:00","updated_at":"2017-04-11T19:00:00.000-05:00"},{"id":1647,"first_name":"Michael","last_name":"Barrus","position":"Assistant Professor","institution_name":"University of Rhode Island","comprehensiveness_rating":4,"comprehensiveness_review":"This book covers all of the major areas of a standard introductory course on mathematical rigor/proof, such as logic (including truth tables) proof techniques (including contrapositive proof, proof by contradiction, mathematical induction, etc.), and fundamental notions of relations, functions, and set cardinality (ending with the Schroder-Bernstein Theorem).\n\nThere are a few things I would like to see dealt with in more depth--specifically, a few more examples and exercises for  each of uniqueness proofs, \"the following are equivalent\" proofs, the Well-Ordering Principle, and strong induction. However, the choice and emphasis on most topics is highly satisfactory.","accuracy_rating":5,"accuracy_review":"The content is accurate and error-free.","relevance_rating":5,"relevance_review":"The content contains standard proof techniques and results and, given its subject matter, is in no danger of becoming obsolete any time soon. The approach in teaching the various proof outlines is especially relevant to novice proof-writers, particularly in Chapter 4 where illustrations show a proof being constructed, step by step, from the outline.","clarity_rating":5,"clarity_review":"The text is written in a conversational tone that is easy for students to follow. New terms are always carefully defined, and a number of useful diagrams throughout the text add to the clarity of the explanations.","consistency_rating":5,"consistency_review":"The book is very internally consistent, in both approach and pacing.","modularity_rating":5,"modularity_review":"The text proceeds with one major topic per chapter (suitable for discussing most chapters in one to two class periods). Each chapter further has a number of sections (typically 3-5) which make it easy to follow the book's progression and to find relevant topics.\n\nAs it is a mathematics textbook, and particularly one on proof, notation and approaches to proofs adopted early in the text are used in the later chapters, but most readers will rarely if ever need to refer back to a previous chapter because of a reference in a later one.","organization_rating":5,"organization_review":"The organization of the text is one of its strengths. The book's chapters are divided into four parts (Fundamentals; How to Prove Conditional Statements; More on Proof; and Relations, Functions and Cardinality), and each part logically follows from the previous ones in a clear way.","interface_rating":4,"interface_review":"The text is very easy to navigate, and there are no issues with the PDF files. One slight quirk is that the page numbers in the PDF file, due to introductory matter, are exactly 10 pages off from the page numbers appearing in the text, but it is easy to adapt to.","grammatical_rating":5,"grammatical_review":"There are no known grammatical errors.","cultural_rating":5,"cultural_review":"The text is not culturally insensitive or offensive in any way. The examples used are from mathematics and largely devoid of references to any particular culture or background.","overall_rating":10,"overall_review":"I have taught using this textbook in an introduction-to-proofs course over four semesters, and I am in general very satisfied with it. As mentioned previously, there are a few topics I feel the need to supplement when I teach, but on the whole I have felt very comfortable making this book an integral part of my course.","created_at":"2018-02-01T18:00:00.000-06:00","updated_at":"2018-02-01T18:00:00.000-06:00"},{"id":2807,"first_name":"David","last_name":"Miller","position":"Professor","institution_name":"West Virginia University","comprehensiveness_rating":5,"comprehensiveness_review":"This textbook is very comprehensive. Covers a basic review of sets and set operations, logic and logical statements, all the proof techniques, set theory proofs, relation and functions, and additional material that is helpful for upper-level proof course preparation (like a chapter on proofs in calculus). There is plenty of material in the book for a very thorough treatment of proofs and flexibility with other chapters devoted to counting, calculus, and other material.","accuracy_rating":5,"accuracy_review":"I have not found any errors in the textbook other than a place where the author says he is using a proof of the contrapositive but proceeds to prove it by a proof by contradiction.","relevance_rating":5,"relevance_review":"The textbook is very relevant and has served as a good textbook for an introduction to proof course. Adding some more homework problems that present a new mathematical definition and corresponding proofs dealing with this new definition would be very beneficial for introduction to proof students (to prepare students for aspects in upper-level proof courses).","clarity_rating":4,"clarity_review":"The clarity of the book is very good. I just have one minor thing that would help with clarity. \r\n\r\nI stress at the beginning of the class the mathematical norms of the class (what we expect in terms of proofs and proving in the class for the semester) and the book points out that proofs are written in paragraph form with complete sentence. However,  the book contradicts this throughout the book with proofs that do not follow this format. ","consistency_rating":4,"consistency_review":"The textbook is very consistent except on the aspect listed in the previous comment about paragraph proofs.","modularity_rating":5,"modularity_review":"The way the book is organized, things are easily divided into smaller sections. There is a few longer chapters, but these chapters are divided in to manageable sections. Usually I can cover at least one section or two for each class.","organization_rating":5,"organization_review":"The author does a great job on organizing the book. The only chapter that I don't usually cover is Chapter 3 and the Chapter on proofs in Calculus. ","interface_rating":5,"interface_review":"I love the downloaded pdf with quick links to particular Chapter and Sections in the book. I have not had an issues with this book.","grammatical_rating":5,"grammatical_review":"I have not observed any grammatical errors in the text. \r\n","cultural_rating":5,"cultural_review":"I haven't found any text in the book that is culturally insensitive or offensive.\r\n","overall_rating":10,"overall_review":"I would definitely recommend this textbook to other colleagues.","created_at":"2019-04-18T23:59:02.000-05:00","updated_at":"2019-04-18T23:59:02.000-05:00"},{"id":35084,"first_name":"Kenneth","last_name":"Levasseur","position":"Professor","institution_name":"University of Massachusetts Lowell","comprehensiveness_rating":5,"comprehensiveness_review":"This book could serve as a complete text for an introductory course on mathematical proof. It includes all of the important topics that student need to know to study upper-level mathematics courses such as real analysis and abstract algebra.","accuracy_rating":5,"accuracy_review":"I did not encounter any inaccuracies or errors in the book.","relevance_rating":5,"relevance_review":"After completing the calculus sequence, math majors take many classes in which writing and communication of ideas is more central than calculation. They often struggle with this transition and this book, along with the course it is meant for fills an important niche.","clarity_rating":5,"clarity_review":"The goals of the text are clear. The exercises should guide students to an understanding of how to approach the study of mathematics.  Solutions to the odd numbered exercises are generally clear and complete.","consistency_rating":5,"consistency_review":"The text is consistent - I found no discrepancies while reading.","modularity_rating":5,"modularity_review":"Most sections are short enough to digest in one sitting and are clearly written. Some of the material will probably be challenging to some students, but reading mathematics is a process that often requires very slow reading.   Learning this process is important for students.  \n\nPage x of the introduction contains dependency chart that helps an instructor tailor their course to the needs of their curriculum.","organization_rating":5,"organization_review":"Topics are organized in a logical and standard sequence for the subject.","interface_rating":4,"interface_review":"The book is available in two forms, pdf and hard copy. \n\nThe pdf is screen enabled so that you can navigate to topics from the table of contents or index. A link in the table of contents to the index would be useful. Within the text, there are links to referenced items (e. g., if a proof uses an earlier numbered theorem, one can click on the theorem number and be sent to the statement).  However these links are not apparent unless you try clicking on them.  Making the text color of active links a different color would be helpful. \n\nInexpensive paperback and hard cover versions are available.","grammatical_rating":5,"grammatical_review":"No issues found.","cultural_rating":5,"cultural_review":"No significant  insensitive material was detected in this book. One exercise uses a statement of a biblical nature to make a point of how a statement can be a proposition without having knowledge of its truth. It could bother some, but it could really be applied to any cultural word view.  The rest of the book deals abstract ideas that shouldn’t be controversial.","overall_rating":10,"overall_review":"I'm glad to have encountered this book.  I teach a course in mathematical problem solving and plan to use this book as a supplement that will serve as a review of prerequisites to the course and an introduction to a few topics that are included in the course.","created_at":"2024-05-29T06:40:34.000-05:00","updated_at":"2024-05-29T06:40:34.000-05:00"},{"id":35513,"first_name":"Noah","last_name":"Aydin","position":"Professor of Mathematics","institution_name":"Kenyon College","comprehensiveness_rating":5,"comprehensiveness_review":"The book has a good coverage of topics for a course it serves.  There are some topics/chapters that are optional and instructors would not have time to cover in a one semester course. It is okay to have chapters like that.","accuracy_rating":4,"accuracy_review":"The content is accurate. One comment about bias is that the author follows the common Eurocentric naming of mathematical objects (more on this below)","relevance_rating":5,"relevance_review":"As it pertains fundamental notions of higher mathematics, this material will not become obsolete or irrelevant in a short (or long) period of time.","clarity_rating":4,"clarity_review":"The book is written in a clear language.  The necessary technical language to discuss the material is appropriate.","consistency_rating":5,"consistency_review":"The writing is consistent throughout the text.","modularity_rating":5,"modularity_review":"Modularity is good. The material is broken into  many chapters.","organization_rating":4,"organization_review":"In some cases, I would have ordered the topics differently (e.g., Logic before Sets) and I would have done some topics earlier (e.g. Proofs Involving Sets) but overall, the topics are presented in a logical and clear fashion.","interface_rating":5,"interface_review":"I have not seen any such problems.","grammatical_rating":5,"grammatical_review":"No grammatical errors","cultural_rating":3,"cultural_review":"Unfortunately, there is a dominant Eurocentric narrative of history of mathematics and science that everyone learns throughout the education system. One manifestation of this problem is in the naming of mathematics facts/objects. There are many misleadingly named mathematical objects that became standard terminology. While it is hard to change the standard names, it is important to be aware of this problem and make an effort to inform the students about it. One of the striking examples of misleadingly named mathematical objects is \"Pascal's Triangle\". Another one is \"Fibonacci Numbers\". The author does not seem to be aware of this issue and repeats the common narrative which is inaccurate and biased. I would encourage  the author to learn more about this topic and to address the issue in any future edition of of the text.","overall_rating":9,"overall_review":"This is a fine book to use for a book on Introduction to Proofs.  It contains excellent examples and set of exercises.","created_at":"2025-06-08T18:45:06.000-05:00","updated_at":"2025-06-08T18:45:06.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/book-of-proof?locale=es","updated_at":"2026-05-18T12:03:48.000-05:00"},{"id":10,"title":"Calculus","edition_statement":"Third Edition","volume":null,"copyright_year":1991,"ISBN10":"0961408820","ISBN13":"9780961408824","license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.","contributors":[{"id":2184,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Gilbert","middle_name":null,"last_name":"Strang","location":"MIT","background_text":"Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT and an Honorary Fellow of Balliol College. Professor Strang has published eight textbooks. He was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://open.umn.edu/opentextbooks/subjects/calculus?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":52,"url":"https://ocw.mit.edu/","year":2023,"created_at":"2018-09-07T12:22:36.000-05:00","updated_at":"2023-11-29T15:55:22.000-06:00","name":"Wellesley-Cambridge Press"}],"formats":[{"id":59,"type":"PDF","url":"https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/textbook/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":4,"reviews":[{"id":1104,"first_name":"Thu","last_name":"Le","position":"Adjunct Instructor","institution_name":"University of North Texas","comprehensiveness_rating":5,"comprehensiveness_review":"The book was written very well. It covers all of important concepts in Calculus as well as related courses. The author provides real life examples to apply the concepts.","accuracy_rating":5,"accuracy_review":"The content of the book is very accurate.","relevance_rating":5,"relevance_review":"The content of this book is up-to-date and the text is written straightforward and easily to understand.","clarity_rating":5,"clarity_review":"The text is written very clear and lucid.","consistency_rating":5,"consistency_review":"The book is very consistent in terms of terminology and framework. It is easy to follow.","modularity_rating":5,"modularity_review":"The book is easily reorganized and realigned with various sub-units of a course. It can be divisible into smaller reading sections due to purposes of courses.","organization_rating":5,"organization_review":"The topics in the book are presented very well. Concepts are very clear and flow well.","interface_rating":5,"interface_review":"The book is free of significant interface issues. It does not content features that confuse readers.","grammatical_rating":5,"grammatical_review":"The text contains no grammatical errors.","cultural_rating":5,"cultural_review":"The book provides good examples in a variety of races, ethnicity, and backgrounds.","overall_rating":10,"overall_review":"I think this is a good book for teaching Calculus courses.","created_at":"2017-04-11T19:00:00.000-05:00","updated_at":"2017-04-11T19:00:00.000-05:00"},{"id":1638,"first_name":"Yuyuan","last_name":"Ouyang","position":"Assistant Professor","institution_name":"Clemson University","comprehensiveness_rating":5,"comprehensiveness_review":"The book is well written and covers both big pictures and technical details of materials in calculus. However, in the current PDF version the index seems to be missing. From the table of contents it seems that the index pages are supposed to be in the original book.","accuracy_rating":5,"accuracy_review":"The content is accurate and unbiased. There are no errors that I am aware of during the reading.","relevance_rating":5,"relevance_review":"The text is up to date.","clarity_rating":5,"clarity_review":"The text of this book is clear and easy to understand.","consistency_rating":5,"consistency_review":"The book is consistent in terminology and notation.","modularity_rating":5,"modularity_review":"The book is well organized, and it is possible to reorganize the sections to satisfy specific needs of a course.","organization_rating":5,"organization_review":"The structure of the book is clear and the flow is easy to follow.","interface_rating":4,"interface_review":"This comment is not regarding the book itself but rather the PDF version in the open textbook library. Since it is scanned from the book, there are distortion/aliasing of graphs/texts that may be noticed when reading. ","grammatical_rating":5,"grammatical_review":"There is no grammatical error that I noticed","cultural_rating":5,"cultural_review":"The book make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds.","overall_rating":10,"overall_review":null,"created_at":"2018-02-01T18:00:00.000-06:00","updated_at":"2018-02-01T18:00:00.000-06:00"},{"id":2913,"first_name":"Yun","last_name":"Lu","position":"Professor","institution_name":"Kuztown University","comprehensiveness_rating":5,"comprehensiveness_review":"The textbook is well written and clearly organized. The content is comprehensive yet the textbook includes many examples and figures to help students understand the concepts. The index of important calculus tools at the end of the  book provides a good summary as well.","accuracy_rating":5,"accuracy_review":"The textbook content is accurate and the language used is precise.","relevance_rating":5,"relevance_review":"Textbook has up-to-date contents with a lot of real life examples.","clarity_rating":5,"clarity_review":"The textbook is written clearly and it provides adequate context for any newly introduced concepts.","consistency_rating":5,"consistency_review":"The textbook is consistent.","modularity_rating":5,"modularity_review":"The textbook is well organized and can be easily and readily divisible into smaller sections according to various course purposes.","organization_rating":5,"organization_review":"The topics in the textbook are presented in a clear fashion that helps students to better understand the material.","interface_rating":4,"interface_review":"The original textbook is free of significant interface issues. But the scanned copy  on the open textbook library is not very clear and could be updated for a better reading quality.","grammatical_rating":5,"grammatical_review":"The textbook is well written and I am not aware of any grammatical errors.","cultural_rating":5,"cultural_review":"The textbook is not culturally insensitive or offensive in any way. The examples in the textbook generally don't indicate races or ethnicities.","overall_rating":10,"overall_review":"This textbook is well written and clearly organized. It contains a comprehensive list of contents and also includes many good examples and assignments which would help students succeed.","created_at":"2019-05-16T09:30:10.000-05:00","updated_at":"2020-11-09T09:52:47.000-06:00"},{"id":34579,"first_name":"Shahrooz","last_name":"Moosavizadeh","position":"Professor","institution_name":"Norfolk State University","comprehensiveness_rating":5,"comprehensiveness_review":"The textbook is certainly well written.  The author uses simple terms and easy to follow approach/format.  The applications are used to relate the topics to real-world problems.  Presenting topics in calculus via examples and applications is perhaps the best feature of this book.  \nThe study guide for chapter 1 and Index were missing in the PDF version I reviewed.","accuracy_rating":5,"accuracy_review":"The content is accurate and the language is suitable for audiences comfortable with the prerequisites - precalculus.","relevance_rating":4,"relevance_review":"The sections related to calculators and programming will be obsolete in a near future; however, the textbook's high quality applications and examples will keep the book competitive for years to come.","clarity_rating":4,"clarity_review":"Given the required background and knowledge in precalculus, the textbook is easy to follow and clear in its explanation of concepts.","consistency_rating":4,"consistency_review":"The textbook is consistent in terms of terminology.  The traditional variables x and y are heavily used throughout the book.  I highly recommend the use of more variables, other than x and y, and notations in each section of the book.","modularity_rating":5,"modularity_review":"The textbook can easily be divided into modules to support a specific order of coverage or presentation.","organization_rating":5,"organization_review":"The textbook is well organized and flows smoothly.  The last chapter on Mathematics after Calculus, though a nice idea, will most likely not be covered in a typical calculus course.","interface_rating":3,"interface_review":"The PDF version does not offer the best reading quality.  The textbook could certainly use more graphs to better explain concepts such as the limit definition of a derivative at a specific point in the domain. Use of multiple colors on graphs would improve student learning.","grammatical_rating":5,"grammatical_review":"The textbook is well written and free of grammatical errors.","cultural_rating":5,"cultural_review":"The book is not culturally insensitive and it is not written with any specific race, ethnicity, or background in mind.  The applications are carefully selected from different disciplines to convey the concepts in calculus.","overall_rating":9,"overall_review":"Although I thoroughly enjoyed reading the book, it may not be suitable for use in all institutions.  The book does require better than average knowledge of the prerequisites before the applications and examples have the intended impact.","created_at":"2023-05-26T14:58:38.000-05:00","updated_at":"2023-05-26T14:58:38.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/calculus?locale=es","updated_at":"2026-05-18T12:03:48.000-05:00"},{"id":12,"title":"College Algebra","edition_statement":null,"volume":null,"copyright_year":2013,"ISBN10":null,"ISBN13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as \"Functions First,\" believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The authors also offer a Precalculus version of this text, which has two extra chapters covering Trigonometry.","contributors":[{"id":4062,"contribution":"Author","primary":true,"corporate":false,"title":"Dr.","first_name":"Carl","middle_name":null,"last_name":"Stitz","location":"Lakeland Community College","background_text":"Carl Stitz, Ph.D. is a Professor of Mathematics at Lakeland Community College outside of Kirtland, Ohio."},{"id":4063,"contribution":"Author","primary":false,"corporate":false,"title":"Dr.","first_name":"Jeff","middle_name":null,"last_name":"Zeager","location":"Lorain County Community College","background_text":"Jeff Zeager, Ph.D. is an Associate Professor of Mathematics at Lorain County Community College in Elyria, Ohio. Dr. Stitz and Dr. Zeager co-wrote this college algebra textbook with the vision of creating a high-quality, open-source textbook that is within reach and accessible to the average college student. In recognition of their work, both authors received the prestigious Faculty Innovator Award from the University System of Ohio in 2010."}],"subjects":[{"id":83,"name":"Algebra","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":29,"url":"https://open.umn.edu/opentextbooks/subjects/algebra?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":53,"url":"http://stitz-zeager.com/","year":null,"created_at":"2018-09-07T12:22:36.000-05:00","updated_at":"2018-09-07T12:22:36.000-05:00","name":"Stitz Zeager Open Source Mathematics"}],"formats":[{"id":60,"type":"PDF","url":"http://stitz-zeager.com/szca07042013.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":61,"type":"Hardcopy","url":"http://www.lulu.com/shop/carl-stitz-and-jeff-zeager/college-algebra%2C-3rd-edition/paperback/product-16218473.html","price":{"cents":1639,"currency_iso":"USD"},"isbn":null},{"id":2224,"type":"LaTeX","url":"https://stitz-zeager.com/latex-source-code.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4","textbook_reviews_count":11,"reviews":[{"id":51,"first_name":"Milan","last_name":"Frankl, MBA, PhD","position":"Professor of Business","institution_name":"University Canada West","comprehensiveness_rating":2,"comprehensiveness_review":"The textbook does not cover all the material one would need to address in college algebra, notably the trigonometric functions are absent – even though they appear in the content. Moreover, formalism in theorem proving is absent or inappropriate in most situations.","accuracy_rating":2,"accuracy_review":"Most of the theorems lack proper and formal proof – leaving the reader to find those in other sources. This is a major weakness for a math textbook.","relevance_rating":5,"relevance_review":"No problem with longevity here. All the information has been (and will be) relevant for quite some time.","clarity_rating":2,"clarity_review":"The writing style is colloquial and patronizing. The authors refer to some form of \"inside jokes\" about themselves. The students are addressed in a non-professional manner throughout the text. One needs to consider that in an online environment, mature students could form the majority of the reading audience.","consistency_rating":2,"consistency_review":"Some inconsistencies appear in various chapters. The terminology is adequate but lacks formality – an essential element in mathematics.","modularity_rating":2,"modularity_review":"The text consists mostly of exercises (more than 50 in each chapter) with little associated theory supporting the solution process. Some exercises are solved in a detailed and stepped way – easy to follow. Lack of formal rigour is present in most cases.","organization_rating":2,"organization_review":"The theory is presented in short segments without proper substance – mostly referring the reader to outside sources. Again, lack of formality is a major weakness – this book is supposed to cover math material were rigour is essential","interface_rating":3,"interface_review":"The text contains numerous grammar and style errors, including punctuations weaknesses not acceptable in an academic textbook. Most charts, graphs, and figures are OK and help understand the solutions provided.","grammatical_rating":2,"grammatical_review":"The text contains numerous grammar and style errors, including punctuations weaknesses not acceptable in an academic textbook. The writing tone is informal, it contains colloquial language,slang and jargon which should be voided in formal writing.","cultural_rating":1,"cultural_review":"I found the text offensive because of the condescending nature of some comments, irrelevant humour, inside jokes, and treatment of the reader in a non-professional way. One needs to consider that some readers (students) could be mature students, therefore not open to the patronizing nature of this type of the written material.","overall_rating":5,"overall_review":"Summary: I do not recommend this textbook for various reasons detailed above. This textbook is mostly an exercise manual rather than a college textbook. Its content might be suitable for a face-to-face delivery method in a classroom with very young students. The writing style is condescending, colloquial, informal, and inadequate for mature audiences. If need be, I could attached more detailed comments – however they would cover every chapter of the 700+ pages of this eBook.\r\nThis review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.","created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":52,"first_name":"Allyson","last_name":"Rozell","position":"Math Instructor","institution_name":"Kwantlen Polytechnic University","comprehensiveness_rating":4,"comprehensiveness_review":"I did not see specific coverage of scientific notation, and the text seemed weak in applications, particularly for lower level topics, like linear and quadratic functions, which are quite important for a college algebra class. I believe it would benefit from a more extensive index.","accuracy_rating":5,"accuracy_review":"Content seemed accurate.","relevance_rating":5,"relevance_review":"Content was somewhat lacking in applications, but generally would not date quickly.","clarity_rating":2,"clarity_review":"I found the language used to be too technical for our typical college algebra student. I personally enjoyed reading the text, but I think the style will be alienating for the student. I feel the level of exposition is more appropriate for a pre-calculus class than for a college algebra class. Also, the density of the text on the page, and the rather dry layout is also off-putting for the math-wary student.","consistency_rating":5,"consistency_review":"I saw no inconsistencies in the text.","modularity_rating":4,"modularity_review":"The modularity of the text was useful; it would be fairly easy to use only parts of the text.","organization_rating":5,"organization_review":"The organization was clear, and the logical structure of the text was good.","interface_rating":3,"interface_review":"I had no interface issues in dealing with the text, however, while the TeX formatting is familiar and clear for mathematicians, I think it is stark and unfriendly for the college algebra student.","grammatical_rating":4,"grammatical_review":"The informal, conversational tone they use for much of the text tends to introduce a variety of extremely common and minor grammatical errors, which will not be noticed by most people. I saw no egregious grammatical errors. I would like more commas, but I believe they are currently out of grammatical fashion.","cultural_rating":3,"cultural_review":"The names used in exercises seem to be largely of European extraction, so more diversity might be helpful.","overall_rating":8,"overall_review":"The text is out of Washington State, and many of the examples are local to the area. This makes them still pretty local for the lower mainland of BC, and I like that. Examples and exercises primarily use imperial units; I would prefer to have a better balance of imperial and metric questions.\r\nThis review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.","created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":53,"first_name":"Nora","last_name":"Franzova","position":"Assistant Chair for Math and Stats Department","institution_name":"Langara College","comprehensiveness_rating":5,"comprehensiveness_review":"The text definitely covers all topics that are covered in a usual College Algebra class, and actually it covers much more. The extensive coverage of Systems of Equations and Matrices can not be really squeezed into a one semester College Algebra class, but a 1st Linear Algebra class could definitely take that chapter and spend almost a month on it. Similar comment would describe the Sequences and Binomial Theorem chapter. Since according to the Open Textbook project, one can use any parts of the book, according to their needs, then I believe the book provides more than enough to choose from and covers ideas of the subject exactly as needed for our College Algebra class. Index and Glossary are detailed and the links worked well for me.","accuracy_rating":5,"accuracy_review":"Content is accurate to such a point where even the most likely trouble spots for the students are picked out and presented and explained. The authors do not try to avoid the trouble spots, while many other books do. Exercises are abundant, and full solutions follow each group of exercises. That is of course great, but at the time of adoption of this book, we would have to remove the solutions to the even number problems and then collect those in some \"Instructor's Supplement\". Also the fact that full solutions immediately follow the exercises would be something we would have to change. Even though authors claim that they cut down on endless \"drill and kill\" questions, I feel there is really a lovely group of exercises (I'd even called some of them \"cute\".) and students will get good level of practice once they tackle these. All the graphs are clean and clear, for some reason in the later chapters I noticed that there are 2 different \"font types\" under figures. I guess one is from the graphics itself and one from LaTeX. (see Example 6.4.2 or Example 8.1.1 and others) It is not a problem, just my observation. There are only very few colored images and those are not exactly spectacular, but I know that stuff is hard to make.","relevance_rating":4,"relevance_review":"Since College Algebra is not likely to change in the near future, this should not become an issue for the text. One thing that can be mentioned is the endless issue of graphing calculator use in a College Algebra class. The book can be definitely followed without using graphing calculators, but . . . there is enough exercises to make one feel that students will feel shortchanged if graphing calculators are not allowed. (That is the case at our college.) These are usually the more challenging exercises and they often come from Calculus with the promise that in Calculus, students will be able to solve them without a graphing utility. If we adopt the text, we might need to address this.","clarity_rating":4,"clarity_review":"This is an interesting point. The text is clear, well written, technical terminology is used and explained. The text contains an endless line of \"foot notes\" in which the authors tease each other and comment on each others opinions. (For example we learn: \"According to Carl, Jeff thinks symmetry is overrated.\" (btw, I agree).) In any case there is a bit too many of these and when I started the reading of the book, this surprised me. The humorous foot notes, are taking away the possibility of me adding humorous comments in class. Students now might think, I just read them from the book. If the book just has facts, the instructor can make them more personal, or funny, or more digestible. When the book has the facts and the jokes, it will make it harder for me (the instructor) to add something more. I still like the book. I like the jokes/comments too, I just worry about my role. Although \"Hooked on Conics\" as a chapter title was quite brave.","consistency_rating":5,"consistency_review":"I found no problems here.","modularity_rating":4,"modularity_review":"Some times the \"paragraphs get to be too long\" and thus more likely to be skipped by the students. These are all well written and correct, they just trail of to lengthy explanations. To be exact, the length is no more then 10-15 lines, but in a math text, that is usually a lot. I was already reading the text and looking which sections we can skip and which to include and it seemed to be fairly easy to do, since there are many separate sections that one can choose from. Since the book is typed in LaTeX the self-referencing issues will be automatically dealt with during the typesetting.","organization_rating":5,"organization_review":"The flow is exactly as I would follow. Maybe the composition of functions being left only for Chapter5 (just in time for inverse functions) feels a bit late. Although it was not missing in the flow of the previous chapters. Sometimes the authors venture into more detail that is needed in a basic College Algebra class. (for example the discussion about minima and maxima). But that does not harm the clarity of the text.","interface_rating":3,"interface_review":"There were no navigation or distortion issues. The only problem I had that when I downloaded the .pdf file to my Mac it was not complete. Just the first 9 chapters.","grammatical_rating":5,"grammatical_review":"I did not observe any grammatical errors, but I do not consider myself an appropriate judge of this.","cultural_rating":5,"cultural_review":"The text uses in its examples \"imaginary\" characters and places. Chewbacca and Sasquatch (like Sasquatch Tonic or Sasquatch Berry Pies ) are frequently mentioned as well as dOpis media players. This is a dilemma all instructors have to address. Using real names and real places or imaginary ones? We all make our choice. Some feel that students will relate to reality better, I believe that imaginary places and names are well within the spirit of the book. The book does have real time data too – lets say from Federal Bureau of Transportation. All such data is from US of course, since the authors are from there.","overall_rating":9,"overall_review":"The book uses imperial units, while Canada is on a metric system. This would take some effort to change. But textbooks that we normally use also mainly use imperial units.\r\nThis review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.","created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":54,"first_name":"Karen","last_name":"Yeats","position":"Assistant Professor","institution_name":"Simon Fraser University","comprehensiveness_rating":4,"comprehensiveness_review":"The version of the text we were provided had the trigonometry chapters cut out (This was done simply by clipping the pdf rather than recompiling the latex, so the table of contents and index still reflect the full text, which is silly and unprofessional, but only a very minor point.). In order to cover the material we cover in precalculus the trigonometry sections would need to be put back in. Chapters 7,8, and 9 are unnecessary for our precalculus course; they are covered in other introductory math/macm courses. The index is comprehensive, and the pdf is searchable. The background assumed is generally appropriate. There are a few small exceptions, for example students are expected to know polynomial division. Some common student points of confusion are clarified, though others are not. For example in 1.1.2 the distinction between (a,b) as interval notation and (a,b) as a point in the cartesian plane is not clarified. There are some important issues with regard to intended audience, which will be dealt with more substantially in a later question, but in summary this text seems to be targeted to mathies in spirit (not in difficulty) despite the fact that in our system such people will have covered this material before university and so will not be in our precalculus classes.","accuracy_rating":4,"accuracy_review":"Accuracy seems very good. I did not see any errors; however, I did not give a line by line reading so may have missed some errors.","relevance_rating":4,"relevance_review":"There are some cultural references which will not age well, but they are more stylistic issues than content issues. For example the movie \"8.99999...\" is a joke which will not resonate once the original movie (from 2009) has been largely forgotten, and \"hooked on conics\" is a joke for those of us who grew up in the '90s and watched some American TV. I would not view this as a major issue. All computational examples expect a graphing calculator. As far as I have seen these single purpose devices are not used out in the real world, their only benefit seeming to be that some jurisdictions require them in high school so students from these jurisdictions already have them. An open text might be favourable to discussing an open CAS (computer algebra system) which students could use no matter where they go next, but the standard commercial CASs are also good and widely available choices, and as graphing calculator apps for smart phones mature they will become increasingly viable, not to mention web tools like Wolfram Alpha. On the positive side, there are many weblinks, to Wikipedia as well as to other sources, particularly to support asides and problems with data.","clarity_rating":4,"clarity_review":"The authors voices come through loud and clear in a very charming way. It is quite conversational, and commendable in how well it puts the jargon in context and avoids unnecessary jargon. It has many asides and comments, mostly in footnotes, which enrich the text but can also be distracting or confusing. Similarly, the conversational style, while generally increasing readability, will be a challenge for some ESL students, particularly along with the jokes and asides which require American cultural knowledge. I feel that the prose and style of this book is simultaneously its greatest strength and its greatest weakness. I liked reading this book; I would have liked learning out of it when I was first encountering this material. Although very much itself (particularly the way the authors banter with each other), its style has some similarities to Spivak's calculus, which has a great cult following in the mathie crowd. However, the mathie crowd is very much not the audience of our precalculus courses, and I think the typical precalculus student's response to the style would be half confusion and half eye-rolling. I am particularly mystified by this as the authors are both at community colleges. Is their education system sufficiently different from ours that they get the sort of geeky audience who would appreciate this book? Do I misestimate our students' interests and abilities? Do the authors' students largely not get it? Ultimately I can only recommend that an instructor looking at this text look at the style and consider whether it fits with their own style and whether it is likely to be appreciated by their students.","consistency_rating":4,"consistency_review":"The text is generally consistent. It makes explicit reference to itself in useful but not excessive ways. It is well structured. When the consistency is weaker it is in places where standard usage is often inconsistent, for example in colloquial usage","modularity_rating":5,"modularity_review":"The sections are of a reasonable length. The dependencies within the text make sense given the material, and are generally clear.","organization_rating":4,"organization_review":"Notwithstanding the style comments mentioned in a previous question, the presentation is sensible and is appropriately rigorous for the level; the proofs of many results are beyond the scope of such a course but the authors make efforts to motivate and contextualize the results so that the reader can largely see how they can be natural and important even though they cannot prove them. The order is fairly standard and the authors explain their reasoning behind those deviations from standard order which they use. There are some cases where sections do not flow well, for example section 1.1 begins with sets of numbers and moves onto interval notation which together form 1.1.1, and then jumps in 1.1.2 to cartesian coordinates. These initial sections are essentially developing background for use in the upcoming chapters on functions, and so by their nature are somewhat disjointed.","interface_rating":4,"interface_review":"While not glossy like commercial textbooks, the book is clean and professional. The pdf contains useful internal links and external links. The one exception to the professionalism of the text is that certain sections were cut in the pdf we were given, but the latex was not recompiled, so the table of contents and index did not reflect the cuts.","grammatical_rating":5,"grammatical_review":"I saw no grammatical errors.","cultural_rating":4,"cultural_review":"The book is not insensitive or offensive in any way. The core material and most problems are purely mathematical. Only some problems and asides touch cultural issues at all. The problems based on real world data are all based on American data. Broadening the sources of data would improve the book. The occasional problems involving units are imperial, not metric. The book makes American cultural references, but generally ones which would also be familiar to Canadian students, such as popular movies.","overall_rating":8,"overall_review":"Two final comments. First, the authors leave some unanswered questions (such as some well placed \"why?\"s) for the reader to think about. These are great for stronger students but will frustrate those who aren't getting it. Second, I find the matrix chapter weak, but it is not relevant to the precalculus course we offer in any case. Generally, I find the book very charming, but am concerned that the intended audience may not have the same response to it.\r\nThis review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.","created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":179,"first_name":"Don","last_name":"Drummond","position":"Mathematics Faculty","institution_name":"Minnesota State Community and Technical College","comprehensiveness_rating":4,"comprehensiveness_review":"The textbook covers all of the traditional College Algebra content.  If some institutions of higher education would embed the trigonometry within the College Algebra / Pre-Calculus, these authors have another text to cover the trigonometry.  The content is covered accurately and succinctly allowing the mainstream student an opportunity to engage in gaining a better understanding of the content.","accuracy_rating":4,"accuracy_review":"From the mainstream students' perspective, the content is very accurate.  From a faculty perspective, some of the content lacks proof; however, any quality faculty member can supplement the proof.","relevance_rating":4,"relevance_review":"This content will stand the test of time as the text is arranged in a way which concisely and comprehensively covers the content with breadth and depth.","clarity_rating":4,"clarity_review":"The text's clarity is nicely done.  One item which could better be addressed are some of the examples - many times Sasquatch is referenced.  More real-world examples would enhance the quality of the text.","consistency_rating":4,"consistency_review":"The text constantly adheres to similar terminology and delivery of content.","modularity_rating":4,"modularity_review":"This text would quite easily be parceled into units or be adjusted so that the text's content could be covered in a different order or utilized with other resources","organization_rating":4,"organization_review":"The text's flow was thoughtfully-done starting with some basic and traditional content pertaining to all functions and moving through more specific types of functions.","interface_rating":5,"interface_review":"There are no issues with distorted images nor are there any navigation problems with the downloadable .pdf eBook.","grammatical_rating":4,"grammatical_review":"I observed very few grammatical errors.","cultural_rating":3,"cultural_review":"Some of the examples containing Sasquatch or the Star Wars character Chewbacca take away from the real-world relevance of the text; however, there are no culturally insensitive or offensive remarks in the text in any way.","overall_rating":8,"overall_review":"Certainly there are some College Algebra texts which are written with a more formal focus; however, the concise nature by which this text was penned is respectable.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":192,"first_name":"Jacqueline","last_name":"Lindquist","position":"Mathematics Instructor","institution_name":"Central Lakes College, Brainerd, MN","comprehensiveness_rating":5,"comprehensiveness_review":"This text does cover all of the topics that are presented in a typical College Algebra course. The chapter covering Systems of Equations and Matrices is more in-depth than is common. The chapter on Conics is often-times included and is very useful. The number of topics and their depth would prove challenging to complete in one semester. The text could be used with chapters and/or sections omitted, which would give instructors ample material to choose from and use in their classrooms. My copy did not include chapters that I believe were in other pdfs, covering topics such as Trigonometry. Also, although referenced in my copy, Chapters 10 and 11. The index seemed completed and useful. There was no glossary in my version.","accuracy_rating":5,"accuracy_review":"Content seemed accurate. Solutions follow each exercise set. Examples are abundant with thorough explanations. I was surprised at the number of problems in the exercise sets. In the Preface, the authors asserted that endless \"drill and kill\" questions are not productive, while there is a good number of problems in each set. The diagrams and graphs are clear.","relevance_rating":4,"relevance_review":"I enjoyed some of the cultural references in the text. They seem to arise from US popular culture. I do wonder if they would be relevant to students outside of this culture. There also seemed to be local/geographical references which may be puzzling for many students. Although a graphing calculator is mentioned in the Preface as not a necessary tool for the text, there are numerous examples of its use throughout. This particular calculator may not be in use in the near future, while other less-costly options may be utilized. The content itself is relevant and will be for some time. The text uses English units, which would only be useful in the US and a few other countries. ","clarity_rating":4,"clarity_review":"The text is clearly written and terminology is explained and defined. I was pleasantly surprised, initially, at the tone of the text. While clear, it is friendly and conversational. The numerous footnotes, however, are distracting. Some enrich the text with references to linked material and are useful. Others seem to be inside jokes and teasing between the authors. I feel that students would be distracted by these and start to avoid them. Some students may find this condescending.  An instructor would have to consider this prior to adoption. ","consistency_rating":5,"consistency_review":"The text is consistent. I saw no problems with this.","modularity_rating":5,"modularity_review":"I find the modularity useful. This text could be divided into smaller sections or rearranged. I did find that some of the explanations were long. Many students will disregard a lengthy explanation. The writing is accurate and complete, but in some areas lengthy.","organization_rating":5,"organization_review":"I found the flow and organization clear. I was surprised at the introduction of functions in the first chapter, but felt it may be a useful order. The authors explain their reasoning for this in the Preface. The sections are of a reasonable length.","interface_rating":5,"interface_review":"The text is professional in its interface. Since the version I received was missing some chapters that had been referenced, this was a bit problematic in that they were referenced in footnotes. The diagrams and figures were adequate. Although lacking in the color of commercial texts, the graphics were useful.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors in the text, although I did examine it line-by-line. I also do not consider myself an expert in this.","cultural_rating":3,"cultural_review":"The use of English units is only pertinent to a certain audience. Much of the data was from US sources. Many of the footnotes and cultural references are from US culture. More diversity would be useful. The book is not offensive. Again, some students may find some of the footnotes condescending.","overall_rating":9,"overall_review":"I found the textbook friendly and accessible, with a strong organization and modularity. The textbook would be more useful in a classroom situation with a certain audience and instructor.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":193,"first_name":"Mamfe ","last_name":"Osafo","position":"Mathematics Instructor","institution_name":"Centrral Lakes College ","comprehensiveness_rating":4,"comprehensiveness_review":"The text book covered all the topics in college algebra. The only two sub topics which were not in detailed is Linear Functions and Quadratic Functions. Under the Linear functions sub topics, there should have been a sections which would talk more about solving linear equations in one variable,including solving linear equations involving fractions . The other issue is under the quadratic functions there is not a subsection which talks about solving quadratic equations algebraically using the factoring method, the square root method, completing of squares method and quadratic formula method. Also finding the equations of lines with parallel line and perpendicular lines should have been explained a little bit to refresh the students mind. Overall  this is a good book and my students love it. Am using it in two of my classes this semester. ","accuracy_rating":4,"accuracy_review":"The content is accurate and unbiased. There are no errors.","relevance_rating":3,"relevance_review":"The context is up to date but I would recommend having different application questions from different fields added to the content so it can address questions in different student disciplines and career paths. Also the tex files are not included by the publisher to change or edit any content. Its a pdf and very hard to change anything. ","clarity_rating":5,"clarity_review":"The words, phrases, symbols, diagrams and graphs,  and mathematical formulas used in the book were clear and precise and straight to the point. The questions and solutions to the questions were clear and students understood each question. Since using this book from the beginning of the semester I have never had complains from students about the clarity and technical terms used in the book. The clarity is good","consistency_rating":5,"consistency_review":"The textbook has a very good consistency in terms  of terminolgy and Framework. Alot of times the book made reference to some other techniques used in the previous sections. ","modularity_rating":4,"modularity_review":"The book can easily  be divisibles into smaller reading sections that can be assigned at different points in the course. You can easily break up some sections to different modules during the course. For examples, in chapter 3 you break up some of the different subsections and connect or combine with other subsections in chapter 3. Also because the author used Latex its very much easy to create modules from it. ","organization_rating":5,"organization_review":"Overall the organization/structure wasn't bad, but my recommendations would be there authors moving chapter 5.1 and 5.2 to chapter. The composition of functions should have been added the arithmetric operations of function section 1.5. So the author should have combines 5.1 and 1.5 together. Adding inverse functions to chapter 1 would be also a good idea. ","interface_rating":4,"interface_review":"The interface of the book is fine and there are no issues with interface.  Thats the best quality you can get from using Latex.  ","grammatical_rating":5,"grammatical_review":"There were no grammatical errors. ","cultural_rating":5,"cultural_review":"The authors did a great job in writing this book in that the book is not insensitive or offensive in any way. I think there should more application questions from different cultures around the world. ","overall_rating":9,"overall_review":"More application questions would be very helpful to students. Am using this book in two of my classes and my students love the book. I type my own homework questions and exams questions. My recoomendations to the authorsn is  to add a review section to each chapter with different questions as a review for that chapter.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":245,"first_name":"Nicholas","last_name":"Lytal","position":"Graduate Associate","institution_name":"University of Arizona","comprehensiveness_rating":4,"comprehensiveness_review":"The textbook covers a full range of subjects expected in most college algebra classes, including some topics--such as systems of equations and matrices--that delve into Linear Algebra. It is worth noting that while the text includes large numbers of exercises for students to solve, formal proofs are largely ignored, so the text is not suitable for a class with an emphasis on the latter. The text has several calculator-specific problems, complete with display printouts, for those who allow or encourage calculator usage in class.","accuracy_rating":5,"accuracy_review":"There did not appear to be any errors in the chapters I reviewed.","relevance_rating":5,"relevance_review":"Since the material is foundational for many subsequent subjects, there is no danger of the mathematics losing relevance. Updates should be simple to perform.","clarity_rating":3,"clarity_review":"Some of the solutions provided for example problems are rather verbose and potentially confusing for students depending on their experience level. At times the casual tone of the explanations, problems, and footnotes can be distracting as well. The somewhat informal style of several sections and questions may be hit-or-miss among both students and instructors, depending on the classroom.","consistency_rating":4,"consistency_review":"Terminology and tone remain consistent throughout, with no notable exceptions.","modularity_rating":4,"modularity_review":"There are many questions at the end of each section, allowing instructors to narrow down a preferred list or to separate specific problems to be used for review materials. The sections themselves can be easily reordered or modified to suit the class at hand if instructors prefer to focus more or less on individual sections in a chapter.\r\n","organization_rating":3,"organization_review":"We typically switch the order of the first two chapter subjects, introducing the basics of linear and quadratic equations before defining functions and transformations in more detail, but the order can work as given too. The answers for section exercises would be better placed in a separate index rather than directly after the corresponding problems so students do not need to flip or scroll through pages of solutions between sections, though this is more of an issue in the physical text than the digital one.","interface_rating":5,"interface_review":"An excellent feature of the digital version is the hyperlinks to previous definitions in the book or separate webpages for concepts like the Pythagorean Theorem or Newton’s Law of Cooling. It is a very useful way to review or learn about recurring formulas without flipping back through physical pages constantly or bookmarking several sections. Even the Index has direct links to appropriate pages. No issues exist with graphs and images, which are typically clear and relevant.","grammatical_rating":5,"grammatical_review":"I did not notice any glaring grammar mistakes in the text.","cultural_rating":3,"cultural_review":"There is somewhat of a focus on US data, units, and references, which could be expanded to other countries, systems, or cultures without needing to alter the writing style too much.","overall_rating":8,"overall_review":"The text is solid in its given form, but it may need extensive modification to fit a particular course more effectively. Thankfully, the ease in doing so makes it a reasonable base for a college text.","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":1326,"first_name":"Marcella","last_name":"Jones","position":"Mathematics Instructor","institution_name":"Minneapolis Community and Technical College","comprehensiveness_rating":4,"comprehensiveness_review":"This text is somewhat comprehensive in that it covers a number of  main topics, subjects and ideas that are covered by most colleges/universities in a college algebra course. It includes a number of the topics that would be classified as extra or additional topics for a more enriched and challenging college algebra course.  The index is detailed enough to allow a student to successfully find the location of a particular topic via the index.","accuracy_rating":4,"accuracy_review":"The content is accurate and error-free and unbiased.","relevance_rating":5,"relevance_review":"The information and content of the text is relevant and will remain so.","clarity_rating":3,"clarity_review":"The text does not present clear and easy to follow explanations and information for the concepts and ideas presented. Unnecessary comments and humor are found throughout.   If a student is learning the material and not merely reviewing it, the student would need to resort to other sources in order to learn many of the ideas which are new and unfamiliar to the student.  I find explanations lacking in fullness and completeness.","consistency_rating":3,"consistency_review":"The text is consistent in its presentation and approach and use of terminology, which throughout is somewhat outside of the normal way in which these ideas are usually presented.  The presentation is casual and unconventional.","modularity_rating":3,"modularity_review":"The text subdivides the topics into appropriate and helpful smaller reading sections.  The text would be more helpful for students if some of the discussions for ideas and exercises, included more tables, illustrations, flowcharts, etc., to aid in the presentation and discussion of concepts and ideas.  In some instances, large text-filled blocks could be broken into smaller parts with highlighted and boxed main ideas.","organization_rating":3,"organization_review":"I found the presentation of main ideas insufficient and too brief for the student to have the necessary information to understand and apply the material independent of reading and reviewal of the solutions to the exercises and even these were sometimes difficult to follow.  Restructuring the presentation of the main ideas would better help students to follow the logic and introduction of new concepts and ideas.  The lack of variety of color, text boxes and figures to highlight new and challenging ideas would make this text hard for most students to follow.  The style is old-fashioned and very dull and does not emphasize common errors and misunderstandings.","interface_rating":4,"interface_review":"The book was primarily free of any interface issues.  I found it easy to navigate from one part of the book to another and the text was free of distortion of images and charts.  There were no display features that were distracting or confusing.","grammatical_rating":3,"grammatical_review":"Though I did not find grammatical errors to be an issue, the text was lacking in using formal mathematical terminology and descriptions in the presentation of various ideas and concepts.","cultural_rating":3,"cultural_review":"I did not see the usefulness or helpfulness of some of the humor and unnecessary comments made in the presentation of the material.  I did not find anything culturally insensitive or offensive in the text.","overall_rating":7,"overall_review":"I would not elect to use this text for my College Algebra course.  I think that my students would find it difficult to read and remain engaged in the presentation of ideas.  I also felt that students would feel the need to have additional sources and explanations of the concepts presented.  The text was more like a collection of notes and exercises with solutions rather than a complete and rigorous textbook.","created_at":"2017-06-20T19:00:00.000-05:00","updated_at":"2017-06-20T19:00:00.000-05:00"},{"id":5055,"first_name":"Jack","last_name":"keating","position":"Professor of Mathematics","institution_name":"Massasoit Community College","comprehensiveness_rating":5,"comprehensiveness_review":"Massasoit has both College Algebra and Pre-Calculus  For the College Algebra course Chapters 1, Relations and Functions,, Chapter 2  Linear \u0026 Quadratic Functions, Chapter 3 Polynomial Functions and Ch 5 Further Topics in Functions in Functions would be used. Our Pre-Calculus course \r\nwould use Ch 4 Rational Functions, Chapter 6 Exponential and Logarithmic Functions and I believe the authors have a book which includes  lots of Trigonometry-we generally use one book for both courses. (Currently Sullivan \u0026 Sullivan)","accuracy_rating":5,"accuracy_review":"Seems fine to me and very readable.\r\nI like the use of the boxes too highlight important material","relevance_rating":5,"relevance_review":"I think the material is a great in the study  for use in later Calculus courses and the explanations are very useful and helpful","clarity_rating":5,"clarity_review":"The authors have spent a lot of time in their writings and explainations","consistency_rating":5,"consistency_review":"Again the format is neat and very easy to read","modularity_rating":5,"modularity_review":"Again broken into relevant parts and easily to read","organization_rating":5,"organization_review":"Most definitely. Topics are logically presented and one section flows into the next in a logical progression","interface_rating":5,"interface_review":"The graphs are very well done","grammatical_rating":5,"grammatical_review":"I'm a math prof. so \"grammatical errors\" are not my specialty but it looks fine to me","cultural_rating":5,"cultural_review":"We have several college committees dealing with cultural topics today and it looks fine to me.","overall_rating":10,"overall_review":"I think it is very well written, flows well, graphs and their explanations are easy to understand. I will, when I get time look into the similar book (by the same authors) which contains Trigonometry\r\nCollege Algebra is a staple course that testing of many students before allowing them to take math courses occurs in many institutions. This book allows students to keep going because some of the topics in these 4 chapters 1,2,3,\u00265 students may remember.\r\nI think the book is very well done and probably will consider eventually using it.","created_at":"2021-06-08T07:05:45.000-05:00","updated_at":"2021-06-08T07:05:45.000-05:00"},{"id":33732,"first_name":"Prateek","last_name":"Kunwar","position":"Instructor","institution_name":"Honolulu Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The book covers all the topics that would count as intermediate college algebra material. It builds up upon fundamental of functions before going on the various types of function classes. It rounds up with a discussion on conics, system of equations and binomial theorem (along with induction). Personally I would system of equations after the introduction of linear functions, as an application, but that is a pedagogical choice.","accuracy_rating":5,"accuracy_review":"The information presented in the book is accurate and is well-phrased. The language used is concise and direct without being terse.","relevance_rating":5,"relevance_review":"The contents of the textbook are relevant and will remain so.","clarity_rating":4,"clarity_review":"The text is mostly clear and straightforward (for the chapters that I reviewed). A bit more real world application would make it more interesting. It does get a bit too verbose at certain parts, but not too much. Overall I like how the ideas are presented.","consistency_rating":4,"consistency_review":"The test is consistent with its style, pace and terminology.","modularity_rating":4,"modularity_review":"The detailed index page is quite helpful in locating exact content. It also makes it easier to assign reading assignments.","organization_rating":4,"organization_review":"The flow of the book is well thought  - it starts with the basic idea of function and builds upon it with various classes of functions to re-iterate the properties and definitions exposed at the  beginning.","interface_rating":4,"interface_review":"I did not find any issues with the interface of the textbook.","grammatical_rating":4,"grammatical_review":"I observed very few grammatical errors in the chapters that I reviewed.","cultural_rating":4,"cultural_review":"There were some contemporary references but I did not find anything that I thought was culturally insensitive in any way.","overall_rating":9,"overall_review":"Overall, the textbook is well organized and concisely written. I look forward to using it in my class.","created_at":"2022-03-09T19:18:03.000-06:00","updated_at":"2022-03-09T19:18:03.000-06:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/college-algebra?locale=es","updated_at":"2026-05-18T12:03:48.000-05:00"},{"id":13,"title":"Elementary Algebra","edition_statement":null,"volume":null,"copyright_year":2011,"ISBN10":null,"ISBN13":"9781453300923","license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"unknown","description":"It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course. This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below: Equivalent mathematical notation using standard text found on a keyboard A variety of applications and word problems included in most exercise sets Clearly enumerated steps found in context within carefully chosen examples Alternative methods and notation, modularly integrated, where appropriate Video examples available, in context, within the online version of the textbook Robust and diverse exercise sets with discussion board questions Key words and key takeaways summarizing each section This text employs an early-and-often approach to real-world applications, laying the foundation for students to translate problems described in words into mathematical equations. It also clearly lays out the steps required to build the skills needed to solve these equations and interpret the results. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems. In addition to embedded video examples and other online learning resources, the importance of practice with pencil and paper is stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.","contributors":[{"id":2809,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"John","middle_name":null,"last_name":"Redden","location":"College of the Sequoias","background_text":"John Redden earned his degrees at California State University–Northridge and Glendale Community College. He is now a professor of mathematics at the College of the Sequoias, located in Visalia, California. With over a decade of experience working with students to develop their algebra skills, he knows just where they struggle and how to present complex techniques in more understandable ways. His student-friendly and commonsense approach carries over to his writing of Elementary Algebra and various other open-source learning resources."}],"subjects":[{"id":83,"name":"Algebra","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":29,"url":"https://open.umn.edu/opentextbooks/subjects/algebra?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":101,"url":"http://www.saylor.org/site/textbooks/Elementary%20Algebra.pdf","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2018-09-07T12:22:37.000-05:00","name":"Saylor Foundation"}],"formats":[{"id":246,"type":"PDF","url":"http://www.saylor.org/site/textbooks/Elementary%20Algebra.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":247,"type":"Online","url":"https://www.e-booksdirectory.com/details.php?ebook=5732","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2220,"type":"eBook","url":"https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2013/05/ElementaryLinearAlgebra_v2-EDITS-10-10-2012.epub","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4","textbook_reviews_count":12,"reviews":[{"id":167,"first_name":"Mel","last_name":"Taylor","position":"Mathematics Faculty","institution_name":"Ridgewater College, Willmar, Minnesota","comprehensiveness_rating":4,"comprehensiveness_review":"The text covers all areas of Elementary Algebra appropriately and covers some areas of Intermediate Algebra. There is so much material in this text that it could not possibly be covered in one semester. Of course since this text is open source, an instructor could pick and choose what he/she would like to cover and simply not use the rest. For example, exponents, square root and the Pythagorean Theorem all occur in Chapter 1.  Rational expressions and radicals appear in Chapters 7 and 8. Solving quadratic equations, graphing parabolas and completing the square occur in the last chapter. There is no index or glossary that I could see. Therefore I had to page through the whole text to see where everything was located. All areas of Elementary Algebra that are normally covered did occur somewhere in the text but a person would need to search for it. The part of the text that I liked the most was  the excellent problem bank. There is a wide variety of problems, both rote problems and many application problems. I certainly would use this textbook as a resource for problem bank alone if nothing else.","accuracy_rating":5,"accuracy_review":"The book seems accurate in all the material that is presented. The concepts are presented step-by-step in an easy to follow flow. Common mistakes were also shown side by side the correct mathematical steps. There was one case that parenthesis was used where it would have been more appropriate to use the multiplication sign. Other than that, the text seemed pretty error-free and unbiased.","relevance_rating":5,"relevance_review":"The material seemed up- to- date as far as the application problems. The application problems would be easy to update when needed.","clarity_rating":3,"clarity_review":"The text was easy to follow as far as understanding. However, I think that some concepts, like square roots and the use of exponents in the first chapter were out of the correct order that they should be. There were many references to use of technology and instructions of how to use that technology. The main problem that I saw was the order in which some of the concepts were introduced and used.","consistency_rating":5,"consistency_review":"The text was very consistent in it's framework. Each section start.ed out with Learning Objectives, followed by the material. The material contained a variety of examples explained in great detail. At the end of each section came the Key Takeaways, followed by the Topic Exercises. The problem bank for most sections was huge with some excellent application problems. The answers for the problem bank then followed. Each chapter contained a Review along with a Review Problem Bank. Lastly came a Sample Exam along with the solutions to the Sample Exam.","modularity_rating":4,"modularity_review":"The text could easily by divided and reorganized and I would certainly suggest doing so. I also would suggest dropping some concepts that fit better into an Intermediate Algebra text. There is no way that an instructor could cover all this material in one semester. We need to remember that students taking this course have probably not had success in high school and/or have been out of the classroom for so long that some concepts need to be introduced slowly and not rushed through.","organization_rating":4,"organization_review":"This seems to be a bit of a problem as exponents and square roots normally do not come in the first chapter of an Elementary Algebra textbook to the extent that they were used here. Basic exponent usage and simple square roots are more common in the first chapter. However, an instructor certainly could again pick and choose what they want to use. Otherwise, the logic of other topics seemed to follow the order of other Elementary textbooks.","interface_rating":2,"interface_review":"There is a major problem here with type size in the problem bank. Some problems were easy to read and some problems were in so small a type size that they were hard to make out. Also, when writing fractions the \"/\" in the fraction of say 1/4 did not come out, all I could see was 1 4. This certainly needs to be fixed as students would not understand at all what the problem was. Also the radical sign came after the number, so it would be 144, square root symbol. Now, this may not show up on everyone's computer like this, but if it was this way on my computer, it would be on someone else's also.","grammatical_rating":5,"grammatical_review":"The mathematical terminology was correctly used and did not contain any grammatical errors.","cultural_rating":5,"cultural_review":"The application problems seemed to be culturally relative and diverse. A variety of names, occupations and locations made the problems seem relevant to a variety of cultures.","overall_rating":8,"overall_review":"I would say that the best part of this text was the use of Learning Objectives, Key Takeaways and the large problem bank. I think the variety of problems in the problem bank were great. The Application problems in particular were well done.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":176,"first_name":"Laurence","last_name":"Stone","position":"Math Instructor","institution_name":"Dakota County Technical College","comprehensiveness_rating":4,"comprehensiveness_review":"Presently (March 2015) the book has neither table of contents nor index.  I had to build my own table of contents by hand before I could settle down to review this book.  This, of course, makes a score of 5 impossible.  Actually, the book is riddled with so many typesetting errors it is unusable (by students) in its present form.  Hopefully this can be remedied soon, because the book has the potential to serve as an excellent reference text.\r\n\r\nAll of the usual sections are here: real numbers, solving linear equations and inequalities, factoring polynomials, radicals and rational exponents, quadratic equations and graphs.  The treatment is thorough and precise, with plenty of warnings about common mistakes, and large exercise sets with answers to the odds provided.\r\n\r\nMy only concern (aside from the many typesetting errors) is with graphing.  Although straight lines and parabolas are covered thoroughly, I see hardly any examples of other kinds of graphs.  Instructors who like to showcase a broader array of patterns (such as exponential growth) early in a student's graphing experience will need to supplement.","accuracy_rating":5,"accuracy_review":"Mathematical ideas are everywhere most carefully stated, with only one exception that I found.  On page 4 it reads: \"When studying mathematics, we focus on special sets of numbers.  The set of natural (or counting) numbers is combined with zero.\"  What, always?  It goes on to define the whole numbers as the natural numbers combined with zero, which of course is the intent of the paragraph, but due to some typographical error or whatever it doesn't quite begin right.","relevance_rating":5,"relevance_review":"\"At the moment\" this material seems timeless.","clarity_rating":4,"clarity_review":"Ideas are stated precisely, as in any other mainstream math text.  This could make it an excellent, authoritative reference.\r\n\r\nFor most beginning students, however, precision and lucidity are two different things.  Consider, for example, this Key Takeaway for section 6.3: \"If a trinomial of the form ax^2 + bx + c factors into a product of two binomials, then the coefficient of the middle term will be the sum of certain products of factors of the first and last terms.\"  I realize it's not a super-advanced sentence; nonetheless, most of my elementary algebra students would struggle to understand what is being said.\r\n\r\nThen again, most examples and so on are quite clear about \"do this, then do this, but don't do this.\"  At the risk of making math seem like a collection of memorized steps, it does clearly show what needs to be done.  But the overall narrative behind the examples is not the best fit for my students, so I cannot give a perfect rating for \"clarity/lucid and accessible prose.\"","consistency_rating":4,"consistency_review":"Excellent overall, in the presentation of facts.  No complaints there.\r\n\r\nI was, however, hoping for a tighter correspondence between the stated learning objectives and the review questions/questions on the sample exams.  Just to pick section 9.5, graphing parabolas: finding the maximum/minimum earns a subtitle in this section, and related questions appear in the review and on the sample exam, but it is not one of the stated objectives.  Also: one of the stated objectives is to find the vertex by completing the square, but this specific objective is not measured in the review questions or the sample test.  Students are asked to find the vertex, certainly, but are not asked to complete the square.","modularity_rating":4,"modularity_review":"This book is as \"modular\" as any other math text I've seen, in the sense that one could skip certain sections towards the ends of the chapters if one felt crunched for time, or even come back to cover them at a later time.  But if modularity is considered a strength, I see no reason why this book should score more points than any other.\r\n\r\nOne non-modular aspect: students will see examples involving functions at the ends of many sections.  The instructor could choose to ignore them, of course, but would not have a way to hide them from students' view.","organization_rating":3,"organization_review":"I already mentioned it's missing its table of contents.  Other structural problems: section 4.1 is presented twice, on page 539 and again on page 560; section 4.3 is presented twice, on page 594 and again on page 611.  Chapter 10 is not really a chapter but a short appendix with some area and volume formulas.  Chapter 7 is missing its title.  Many sections (if not most) begin at the bottom of a page.\r\n\r\nThe typesetting issues are so numerous that the text is actually unusable in its present form (for students, anyway).  Fraction bars are missing, exponents are not superscripted, sometimes the radical symbol follows instead of preceding its contents, etc.  \r\n\r\nObviously, these errors are \"minor\" in the sense that it shouldn't take too many days for someone to clean them up.  Hopefully this is in progress even as I write this review.\r\n\r\nBut my next question  would be: where are the embedded video examples promised in the preface?  Are these also under construction?  The .pdf file I was able to download contains no such links or otherwise.  It is impossible to assign a high score when I haven't had the chance to see all that is promised.\r\n\r\nLooking at the print version, I do like the ordering of topics well enough.  None of the chapters have any motivating introductions, though; adding some would be a nice touch.","interface_rating":3,"interface_review":"The only viewing option I have in March 2015 is to download the .pdf file.  I tried reading it on screen, but ended up printing it out (4 pages per sheet, double-sided, some trees were spared) to write this review.  As mentioned above, I have not been able to view any embedded videos, as promised in the book's preface.\r\n\r\nIf this were meant to be a print reference, then I might be able to give a high score once the many typesetting issues are resolved; if it is meant to be more than that, then I haven't had a chance to see what it will be.","grammatical_rating":5,"grammatical_review":"It's not the grammar but the typesetting that hurts, as described elsewhere.","cultural_rating":5,"cultural_review":"I see no issues here.","overall_rating":8,"overall_review":"I went back and reread the preface.  It says this book makes no assumption of prior algebra experience, though it certainly assumes a high proficiency in reading.  I also saw, in the section on negative exponents, that it assumes a certain familiarity with the dimensional analysis method of converting units.\r\n\r\nIt also says this is \"by far the best elementary algebra textbook offered under the creative commons license.\"  Well, as described above, the typesetting still needs major cleaning up.  With that done, however, I do expect this text could serve as an excellent reference… but then there is the question of whether it will have any embedded videos, and how good those will be.\r\n\r\nIt claims modularity, but I'm not seeing how this book is any more or less modular than any other math text.\r\n\r\nIt says it stresses the importance of paper/pencil practice, but I'm not sure what this is referring to.  I do remember the author saying that learning to factor polynomials takes a lot of practice and patience, but I don't recall any specific exhortations to write out steps by hand.\r\n\r\nObviously this is a work in progress, and I have not seen the final product.  Perhaps the author is fishing for some early feedback.  Well, I'd say it's a great start, but later reviews will have to trump mine.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":181,"first_name":"D","last_name":"Bobzien","position":"Mathematics Instructor","institution_name":"Central Lakes College","comprehensiveness_rating":5,"comprehensiveness_review":"The textbook covers all of the chosen topics very thoroughly.","accuracy_rating":5,"accuracy_review":"The math is correct and what it should be.","relevance_rating":5,"relevance_review":"This book writes math problems using the traditional notation as well as textual notation, so it can be emailed and communicated electronically without a special keyboard or software. This was the first time I have seen this. This is just one example of how I feel the textbook is current but yet has staying power. I can see it being reused for quite a while. ","clarity_rating":4,"clarity_review":"the book is written so it is easily understood. I felt it was a bit wordy but since it was clear I could deal with that. I also think a few more pictures would enhance the experience.","consistency_rating":5,"consistency_review":"Even with modular chapters I found the book to be fairly consistent.","modularity_rating":5,"modularity_review":"Chapters can be skipped and it does not hurt the future lessons.","organization_rating":5,"organization_review":"This textbook presents topics in the same order as all other books I have used. This is the organization I would use.","interface_rating":5,"interface_review":"I had only one issue with the textbook's navigation.","grammatical_rating":5,"grammatical_review":"I did not catch any grammar issues--but then grammar is not my forte.","cultural_rating":5,"cultural_review":"It is hard to be culturally insensitive in math. I saw no problems with this textbook.","overall_rating":10,"overall_review":"I like the Key Takeaways and Tips charts the author used. I will probably adopt this book for my Fall 2015 class. I will add comments or re-review this textbook after that.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":295,"first_name":"Harmony","last_name":"Richman","position":"Mathematics Instructor","institution_name":"Dakota College at Bottineau ","comprehensiveness_rating":4,"comprehensiveness_review":"The book covers a wide variety of topics, in detail that I cover in my current Algebra Prep 1, Algebra Prep 2 and Algebra Prep 3 course.  Each course is 8 weeks long so could use the text to use over the entire semester and half that is needed.  A very good comprehensive book to help prepare students in all aspects who need to brush up on their skills before attempting College Algebra.  Although there were some areas where topics delved a little more deeply than students may be ready for; however, an instructor could easily pick and choose what they feel their students need. ","accuracy_rating":5,"accuracy_review":"The book appears accurate throughout the chapters.  The book uses color to determine step by step guidance which is extremely important to help my students follow along more easily while working on their own. ","relevance_rating":5,"relevance_review":"The charts/graphs were up to date and could easily be updated as needed.  They also appeared relevant in today's society with topics students may have an interest in.","clarity_rating":4,"clarity_review":"All terminology was used appropriately and accurately among the book.  The one area that seemed a little stand-offish is the step by step guides, I feel it's important for students in an Algebra Prep course to understand why we are doing what we are doing, not just a simple memorization of steps.  If a student can understand the why they are more apt to retaining vs. remembering a bunch of steps to get there.  ","consistency_rating":5,"consistency_review":"Each section started off with the section title, then the \"Learning Objectives.\"  The Learning Objectives at some points seem to be a little vocab advanced for the topics covered; however, with instructor guidance can be followed nicely.  The Learning Objectives are followed by step by step instructions with examples and \"Try this!\" problems.  At the end of every section there is a Key Takeaway portion which leads into multiple topic exercises and solutions.  ","modularity_rating":5,"modularity_review":"Each unit and subsection of each unit is broken down in such a way that as a teacher teaching 3 different 8 week courses, I could pick and choose what I need to cover for each course to meet the objectives easily.","organization_rating":4,"organization_review":"There were some instances where I personally would rearrange some topics simply based on what I know about my students and their needs, but overall the structure is fairly logical. ","interface_rating":3,"interface_review":"Maybe it's just the online PDF version, but I'm struggling with the fraction section as many of the problems in the homework sets and within the lesson portion the fractions don't have fraction bars.  For example the problem asked to reduce 105300, but there was no fraction bar to indicate what was what fraction.  As you continued down the page you see through the work through portion that it should have been 105/300.  The only indication that you are working with fractions is the numbers appear in smaller text than the other numbers not represented in fractional form.  When we hit the radical section, it appears the radical symbol comes after the number so it is unclear to a student what they may have to do or it's stated as \"square root 36\" this is also would be confusing to my students especially.  ","grammatical_rating":5,"grammatical_review":"I did not notice any grammatical errors throughout the text.","cultural_rating":4,"cultural_review":"Although the book did use a variety of occupations, social standing, and students.  There was a lot of \"a man,\" \"a woman,\" \"a student.\" I felt that the book slightly lacked a variety of races and ethnicities.  ","overall_rating":9,"overall_review":"I particularly liked the length of practice questions at the end of each section and the variety of difficulty level, specifically the discussion board topic questions to encourage writing/researching/reading within mathematics.","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":583,"first_name":"Wendy","last_name":"Rawlinson","position":"Mathematics Instructor","institution_name":"Lane Community College","comprehensiveness_rating":5,"comprehensiveness_review":"This book provides very clear and comprehensive coverage of the usual Elementary Algebra topics, as well as some Intermediate Algebra material. The book provides plenty of examples and very robust, well-constructed exercise sets. The author has gone the extra mile to include special notes, cautions, and even some alternate solutions to examples. \n\nThere is no index or glossary, which is a significant problem. While navigating the book to simply review it, I spent a lot of time searching (scrolling) for specific topics. One example of this is, when the AC method is discussed in section 6.3, the text says “…using the AC method described previously.” Finding where it had been “…described previously” wasn’t trivial (especially since I think the logical place to introduce it was IN section 6.3, as opposed to earlier). I expect that the lack of an index could deter students from using the book as a resource, and may inhibit learning the material.\n\nThe embedded videos are a very useful feature. Students benefit greatly from easy access to videos that demonstrate and reinforce the material, and care has been taken to choose appropriate videos. However, there were no videos linked for certain topics that I think would specifically call for them (one example: students often struggle mightily with the AC method, but I couldn’t find a linked video demonstrating the technique). If I were using this text for my class, I would likely supplement with additional videos for my students.\n\nOverall, this is a good, comprehensive book for Elementary Algebra.","accuracy_rating":4,"accuracy_review":"In reviewing the book, I saw very few content errors. Care has been taken to use proper vocabulary, to show appropriate mathematical processes, and to address common student errors.\n\nThe main “accuracy” issues are with notation use and variation depending on the application/browser used.","relevance_rating":5,"relevance_review":"With algebra content, longevity isn’t as big an issue as with some other disciplines. This book’s content will still be “current” many years from now. If, by chance, groundbreaking algebraic methods or strategies come into fashion, this book could be easily edited to incorporate them.\n\nExamples and exercises are fairly factual and generic. By avoiding \"real world\" contexts and references, they are somewhat insulated from becoming outdated. The downside to this approach is that problem introductions are a bit dry and potentially hard for students to relate to.\n\nIn section 1.5, there are some pie charts based on 2009 data. If those graphics (or others) make the book feel outdated at some point, it could be easily updated with newer data from the cited source.","clarity_rating":1,"clarity_review":"The clarity of this book seems in line with most other mainstream elementary algebra books. The very nice use of color and graphics is effective and helps with readability. \n\nSome of the notation and examples may be a bit advanced and confusing for this level of student (for example: the description of factoring by trial and error uses p, q, m, and n, in addition to the expression’s variable, x). \n\nAdditionally, while searching for particular videos, I found it difficult to scroll through quickly and find the video links. I would like to see video links offset by a color or special graphic for clarity and ease of use.","consistency_rating":3,"consistency_review":"There is a very nice, consistent structure throughout the book. Sections begin with numbered “Learning Objectives”, and end with “Key Takeaways”. Also consistent throughout the text are the “Incorrect vs. Correct” examples, the “Notes”, and the “Try This!” features.\n\nConsistent use of colored boxes for various features makes scanning for important, “key” features easy. For example, blue boxes make finding exercise sets fast and easy.\n\nDepending on how the book is being accessed, there can be significant variation in how notation is used, even from one exercise to the next. I experienced inconsistencies between browsers, and between the pdf versus online version. \n\nOne example is exponents. Sometimes they are superscripted, sometimes the “^” is used, and sometimes the exponent simply follows the base – making “3 squared” appear as 32. \n\nAnother example is the placement of the radical symbol. Sometimes it was written correctly, and other times the radical symbol was typed after the radicand. \n\nThe inconsistency (and inaccuracy) are very problematic, and would certainly need to be addressed before I would feel comfortable using this book. \n\nThe consistent structure used within each section would earn a rating of \"5\" from me. But the other major inconsistencies mentioned lower my ranking.","modularity_rating":3,"modularity_review":"Chapters and sections are numbered, but then those numbers aren't referenced in the online version's table of contents. And, even though each section begins with a chapter and section number, the pdf version does not provide a table of contents, at all.\n\nThe advantages of having each chapter and section numbered would include the ability to explicitly list the content, by number, in a table of contents. I am confused as to why this wasn't done, but suppose it wouldn't be a big job to edit that information in, if desired. The disadvantages of having each section numbered is that it complicates re-ordering content.\n\nThe book is somewhat self-referential (example, “… as described earlier …”), but lacks an index. This would make re-ordering or omitting sections a bit more complicated, and would likely necessitate significant editing.\n\nOne nice feature is the sub-sections (objectives) of each section. The topics are bite-sized, and are compatible with spreading a section over multiple class meetings and/or re-ordering material to suit a particular course.","organization_rating":5,"organization_review":"The book’s organization is fairly traditional, and it could work really well for a conventional series of algebra courses. There is some material introduced earlier than usual (square roots, for example), but that approach improves the modularity of the material. \n\nOverall, the organization of material makes sense.","interface_rating":2,"interface_review":"This is the area in which the book stumbles, somewhat. Depending on which browser or format I used, the notation and fonts were pretty wildly inconsistent and sometimes totally meaningless.\n\nI was using a Mac, and viewed the book using both Chrome and Safari. I also downloaded the pdf to view on my laptop.\n\nIn Chrome, the exercise sets at the end of each section were virtually empty of content. In Safari, I was able to view the problem sets. \n\nIn Chrome, many of the mathematical expressions and equations were simply missing from the body of the text. In Safari, they showed up okay.\n\nNeither browser allowed me to view videos by simply clicking on “click to see video”. On Chrome, I had to right-click and view in a separate tab. In Safari, I never was able to figure out how to view the videos. \n\nThe font size varied dramatically, even within single problem sets. Further, fraction bars were often missing, making the content unreadable.\n\nIf students encounter any or all of these issues, it could certainly be a significant barrier to their learning. There did not seem to be one application through which I could access the full, correct version of the book.\n\nIn general, I like this book. But I would need to figure out how to provide students with a reliably correct version of it before using it for a course.","grammatical_rating":5,"grammatical_review":"The book's English grammar is good and mostly at an appropriate reading level. The statement of the examples and exercises tends to be a bit dry, but the grammar appears to be correct.","cultural_rating":3,"cultural_review":"Most of the examples and word problems in this text are very factual and seem to intentionally avoid the common, “real world” set-up, hence avoiding most cultural context and references.\n\nHowever, in the “Applications of Linear Systems” section, the “Topic Exercises” use the following set of Anglo-sounding names:  Mary, Sally, Joe, Millicent, Jerry, James, John, Dennis, Billy. I would prefer to see more cultural variety represented in this simple way.\n\nAnother example: In the “Order of Operations” section, the word problems reference Mary, Joe, Margaret, Bill, Audry, Mark, and Janet. (And, Mark and Janet are traveling home for Thanksgiving.)\n\nWhile I didn't encounter anything that I consider \"offensive\", I think some opportunities were missed, and this book could have been made to feel more inclusive.","overall_rating":7,"overall_review":"Overall, I like this book. \n\nI would absolutely consider using it in my courses, with some edits and notational corrections.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":589,"first_name":"Kristin","last_name":"Lassonde","position":"Mathematics Faculty","institution_name":"Klamath Community College","comprehensiveness_rating":4,"comprehensiveness_review":"The book covers almost every topic one might use in the course and many topics which are frequently covered in the next course. Small lacking in comprehensiveness might be a treatments of simple absolute value equations or inequalities. Another small lacking is the absence of a 'review' chapter or appendix which is typical for this level of a course.","accuracy_rating":3,"accuracy_review":"Although almost all of the content is accurate, I scored this category lower (3 of 5) due to numerous 'errors' in the text, which are frequently typesetting errors. However, a typesetting error becomes a math error when it makes the math incorrect. For instance, in section 1.1 the answer to number 16. in the \"TOPIC EXERCISES\" is the square root of 7. While accurate in Firefox, this answer doesn't display at all using Google Chrome (an issue to be dealt with later in interface) and the typesetting is reversed in the PDF version showing the square root after the 7. This type of error provides in a sense inaccurate information to students and several errors of this type are common throughout the text. If these were resolved, I would raise my rating here to 4 or 5, depending on if any other errors were left at that point.","relevance_rating":1,"relevance_review":"While the math content will never be obsolete as long as we require this style of algebraic learning in school, the text itself is currently obsolete merely based on the fact that it does not meet accessibility guidelines of the Federal government. As such, the way the laws are currently written, it is my understanding that using the text in a course, even as a resource, is not allowable by the Federal government (unless equitable accessible materials are also provided).","clarity_rating":3,"clarity_review":"Similarly for accuracy (above), while much all of the content is clear, I scored this category lower (3 of 5) due to numerous typesetting errors which will cause students to not find the content clear. These same type of issues, as described above in the accuracy section, provide unclear information to students and several issues of this type are common throughout the text. Additionally unclear are the lack of accessible content due to the missing alt tags on numerous images throughout the text, which frequently contain all the steps for solving a particular problem type. As such, students using a screen reader will be unable to view any of these steps. If these types of issues were resolved, I would raise my rating here to 4 or 5, depending on other clarity issues that may still exist.","consistency_rating":4,"consistency_review":"The book is mostly consistent throughout, however, there are some minor inconsistencies such as the use of variables. For instance, in many sections the book will use x, y, a, b all throughout, and then in the homework Greek letters like alpha and beta appear. This is literally a new alphabet and should probably be discussed somewhere in the book (at least the preface or an appendix since this is not a prerequisite for the book).","modularity_rating":4,"modularity_review":"The text is pretty easy to divide into smaller reading sections, and reorganization should be fairly easy for most teachers, but certain sections will be challenging to reorder due to some implicit self-references.","organization_rating":4,"organization_review":"The topics in the text are mostly presented in a logical and clear fashion. The discussion on absolute value seems disjointed between the first chapter and then 8 and 9, and it seems to overly assume that the student has studied and comprehended everything in 8 prior to studying 9 (which is frequently not the case in basic algebra courses), specifically in reference to taking the square root of both sides of an equation and the result of an absolute value. Additionally, while the subsections are numbered in the text, they are not listed in the table of contents and it is also difficult to determine which section you are in while in the midst of the text.","interface_rating":1,"interface_review":"The text has significant interface issues, including the following. First, the PDF version of the book does not display content correctly. The PDF version of the book needs to be significantly revised or it should be removed from the site so that users can focus on the web-based version, which is more accurate. However, in the web-based version, many problems still exist. For instance, some of the mathematical expressions are coded using MathML, which is not supported on numerous common web browsers including Google Chrome, Internet Explorer, and Microsoft Edge. With this in mind, at minimum the book should specify at least in the preface, which browser is recommended for best compatibility. Further, many items throughout the book are images without an alt tag provided, making them completely unreadable to screen-readers and difficult to navigate for students using mobile devices. Additionally, there are \"Video Solution\" links provided which include embedded YouTube videos using a Flash-player embedding. Using Flash Player is outdated, and results in videos not playing in mobile browsers or browsers where Flash Player is not installed or blocked, which includes an increasing number of browsers. Modern embedded features should be used, which would include the use of HTML5 videos. Finally, the videos provided are not properly subtitled, again as required by Federal accessibility standards.","grammatical_rating":5,"grammatical_review":"Although I have not read every sentence in the book, all of the grammar I saw seems to be correct.","cultural_rating":3,"cultural_review":"The text is not particularly insensitive to specific races or ethnicities that I am aware of, however, with a lack of emphasis placed on Federal accessibility standards, the text is not sensitive to students from different backgrounds who require implementation of the accessibility guidelines.","overall_rating":6,"overall_review":"This book has a lot of potential and I hope to see improvements in the future! As mentioned by another reviewer, at minimum, this book can be used right now as a reference/problem bank for the instructor.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":592,"first_name":"John","last_name":"Salisbury","position":"Mathematics Instructor","institution_name":"Rogue Community College","comprehensiveness_rating":4,"comprehensiveness_review":"The book covers all usual topics in an elementary algebra text book, commencing with integers and continuing through linear expressions, linear equations and inequalities, systems of linear equations, and other topics.  The book concludes with a nice treatment of the solution of quadratic equations with the quadratic formula and introduces complex numbers.  The treatment of factoring using guess and check and the ac-method, factoring by grouping, and special products is thorough and well presented.   Any student who was taught from this book and covered all chapters would have a good grounding in the subject matter.\n\n\tThere is no glossary, index or table of contents, which does detract from an otherwise comprehensive book.","accuracy_rating":5,"accuracy_review":"I found no biases in the book.  I found one misspelling but the book is well written and edited and substantially error-free.  I found the presentation of the material to be objective and clear.","relevance_rating":5,"relevance_review":"The subject of algebra is timeless, so there should be no short-term problem with relevance or longevity.  There a numerous graphs which present current statistics and trends, but it would not be difficult to update these as the years go by.  For example, the number of Americans over 65 or a period of recent years is presented.  This could be made more current easily.  Regular later editions of this book could be published to update the material in the years to come.","clarity_rating":4,"clarity_review":"The language is simple straightforward and presented clearly.  The terms are well defined.  The presentation is not highly rigorous.  There are almost no proofs or demonstrations of the truth of what is being presented, but this is not a higher level book so that does not really detract from the overall presentation.  .","consistency_rating":5,"consistency_review":"Terms are presented consistently and clearly.  A glossary would be helpful to absolutely be able to check how the author defines and views the terms that he uses.","modularity_rating":4,"modularity_review":"Sections and subsections of the book are presented in bite-sized chunks that would not overwhelm a student who has math anxiety or little previous experience with math.  One way in which the book is thorough and distinctive is in the sheer number of problems.  A teacher using this book would have numerous options in choosing easy or difficult problems to do.  The lack of a table of contents or an index would definitely make looking up specific topics in the book problematic.","organization_rating":4,"organization_review":"There are no problems here.  The book builds nicely on beginning concepts and progresses logically.","interface_rating":3,"interface_review":"The lack of the usual apparatus of a textbook (table of contents, glossary, index, etc.) make navigation in the book very difficult.  Also, there are equations where the spacing is bad, at least in the pdf format that I read.  These could be cleaned up in any final edition.","grammatical_rating":5,"grammatical_review":"I found the text to be clear and almost entirely free from grammatical mistakes.","cultural_rating":4,"cultural_review":"The book is not culturally insensitive or offensive.  (Very few algebra books would be, I would think).  I did notice that the names used in word problems are a little old fashioned, e.g., Mary, and maybe in a later edition more contemporary names could be introduced.","overall_rating":9,"overall_review":"There were excellent suggestions for historical research that would be a great stimulant to further learning and study by an interested student. It would be helpful if there were more provocative and interesting problems and questions for gifted students to mull over","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":596,"first_name":"Berri","last_name":"Hsiao","position":"Faculty","institution_name":"Lane Community College","comprehensiveness_rating":4,"comprehensiveness_review":"This book is the most comprehensive Algebra textbook that I have seen as an OER material.  The book covers sections and topics that are appropriate for the math 60-65 sequence at the community college level that I teach.  The sequence in which the topics appear is very appropriate for the level of audience.  The book almost could be used in math 95 (Intermediate Algebra) as well, except a few more advanced topics such as introduction of basic function notations and logarithms.  The exercise sets are large enough for instructors to choose from and for students to gain practice from.  I am impressed by the learning objectives as well as the sample review exercises and sample exams at the end of each chapter.   It is a thoughtful book that includes many key features that I find useful: key take-aways, discussion board topics, note section, video solutions, and incorrect v.s. correct way of solving a problem side by side.  \nThe book itself is very comparable to a traditional textbook that I have seen in its layout and organizations.  The only things I do not see are some kind of online homework system for instant feedback that can be used in an online course format and an index (or glossary) at the end of the book. The answers to the even-number problems of the sample tests are also not listed but maybe it’s stored somewhere else for instructors to find that I’m not aware of.","accuracy_rating":4,"accuracy_review":"Notations and explanations seem fairly accurate in this book, although I did not do a detailed line-by-line reading to check if there errors to the solutions.   The book also includes notations not commonly mentioned in a traditional textbook, for computer programming purposes or on a calculator.","relevance_rating":5,"relevance_review":"The book seems comparable to other textbooks that I have seen in its relevance and I could see it being useful for a long while.  The concepts covered in the book are not going to change so it’s not an issue for a long-term usage.  The real-life applications provided in the book are general enough that changes would not be necessary.  I believe the nature of the licensing allows easily adaptability for an instructor to include other examples as one sees fit.","clarity_rating":4,"clarity_review":"The book has good clarity overall and is very readable to students at this level, except in a few places.  For example, in section 1.2 (adding and subtracting integers) good explanations are provided for how to add two integers.  However, how to subtract two integers are is not presented,  yet it is referenced in an addition problem of two integers that involves the second number being negative.  This section would be so much clearer to the students and robust if subtracting integers is introduced in the same way as adding, with the visuals of the number line and clear examples provided.","consistency_rating":5,"consistency_review":"The book has really good consistency throughout sections and chapters.  The flow is consistent and clear in each section in terms of how concepts are introduced.  The author uses consistent terminology as in most other textbooks.  The only problem in consistency that I see is in the exercise sets and answers.  For examples, fractions and radical notations are not always displayed using the same format and font sizes appear to be inconsistent as well.  But this is more of an 'interface' problem.","modularity_rating":4,"modularity_review":"he book is fairly useful in its modularity except in a few places where references to materials covered in the previous section(s) are mentioned.  For example, in factoring trinomials with leading coefficient being not 1, the AC method is referred as ‘described before’ but it is not listed as to where ‘before’ is.   It does not hurt (actually would be more helpful) to have this method listed again in this section as this is where the method is really needed.","organization_rating":5,"organization_review":"This is a strong aspect of the book in my opinion.  Every section starts with learning objectives, followed by definitions and appropriate vocabulary, and easy to follow examples and steps are provided before students reach the practice exercises at the end of the section.  I particular enjoy the visual layouts, colors, and useful information such as common mistakes listed in a way that is visually clear and pleasing fashion.","interface_rating":2,"interface_review":"This area is the weakest aspect of the book.  I read the book in different formats to find that the online format in Chrome is not compatible in many places – various mathematical symbols are simply missing as well as entire exercise sets not showing up.  It can create confusion to the students.  Using Safari on a Mac works fairly well, but I was not able to view the videos in Chrome or Safari.  The only way to view the video for me is to right click in Chrome and choose “open link using a different tab or window”. Viewing the book using the PDF version is not helpful, especially when it comes to mathematical symbols being not readable or lost.  The font sizes are not consistent either. This is surprising to me as I was expecting the PDF version to be the best in preserving the formatting for the students. I think providing the URL address to let students know that videos do exist could be helpful in the PDF version.","grammatical_rating":5,"grammatical_review":"I did not notice any grammatical error.  The language used in the book is clear and appropriate to the level of students.","cultural_rating":4,"cultural_review":"The book does not have as many culturally inclusive examples as other traditional textbooks.  However, I could understand that the level of mathematical concepts are mostly algebraic and perhaps requires a little more work to write examples that include cultural relevance.  It certainly would be beneficial to incorporate more culturally diverse examples for our diverse student population.","overall_rating":8,"overall_review":"Overall, it is a well written book and I really like the formats and the flow of the book.  I'm hoping to adopt this book for my algebra courses so viewing it from this perspective, I would have to figure out how to make the interface of the book much more friendly and usable to the students.  \nI am happy to see that the quality of this book is quite good and I hope to find useful online tutorial and homework systems that can be incorporated to make this book a more complete one to use in an online format.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":2308,"first_name":"Bill","last_name":"Diss","position":"Instructor","institution_name":"Portland Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The book is very comprehensive.  There is a table of contents but no glossary.","accuracy_rating":5,"accuracy_review":"I did not see any errors.","relevance_rating":5,"relevance_review":"The book's relevance/Longevity is one of the strongest features.  The book does not have that much text, which is very good for fast learning and reading.  Additionally the efficient use of text results in short worded problems.  The worded problems do not have a great deal of special names of people or places or events, thus they appear to be applicable to many groups and should be pertinent for many years.","clarity_rating":5,"clarity_review":"The book is very clear.  Diagrams are simple.  There is a lot of space.  The explanations are very clear and the wording is very efficient.","consistency_rating":5,"consistency_review":"The book is very consistent.  The outline of each chapter and topics are very consistent between chapters.","modularity_rating":5,"modularity_review":"The book is very modular and each chapter is broken up into short manageable sections that are easily accessed by clicking in the table of contents.","organization_rating":5,"organization_review":"The organization, structure and flow are well designed.  Objectives are first shown, some introductory text and then some great examples are finally presented.  At the end of each section, there are many problems.  The odd answers are also at the end of the sections and this allows students to quickly verify answers and not look in other books or all over the book for answers.","interface_rating":5,"interface_review":"Navigation is very easy and the charts and images are simple but powerful.","grammatical_rating":5,"grammatical_review":"Grammar is fine.","cultural_rating":5,"cultural_review":"The simple explanations and efficient wording of worded problems appear to have the effect that there should not be any offensive problems for certain races, etc.","overall_rating":10,"overall_review":"I thought the book was one of the better introductory algebra books.  The examples and methods are very clear and simple.  I think the book is especially useful for ESL users.","created_at":"2018-08-02T19:00:00.000-05:00","updated_at":"2018-08-02T19:00:00.000-05:00"},{"id":3766,"first_name":"Said","last_name":"Raki","position":"Mathematics Instructor","institution_name":"NTCC","comprehensiveness_rating":5,"comprehensiveness_review":"The book gives students a good insight about pre-Algebra concepts. I gave is a five because of the breaking down of the problems and the use of the colors to reach the visual learners. There is no glossary, but a table is given.","accuracy_rating":4,"accuracy_review":"Looking at the examples, and exercises given to students for practice, the book is accurate. I did not find any errors. I cannot say that the book is culturally sensitive. The book is not as diverse as our today classrooms.","relevance_rating":4,"relevance_review":"The longevity of the bool is good. The topics will be still good many years to come. It won't be a lot of changes. The use of certain symbols like the radical could more clear at times so student will not make mistakes reading them.","clarity_rating":5,"clarity_review":"The vocabulary use is clear and easy to understand for student of that age group.","consistency_rating":4,"consistency_review":"The book is consistent all the way. I gave a high rating for that.","modularity_rating":5,"modularity_review":"The book is split in good and easy to read parts. It makes is easy for teachers and students as well.","organization_rating":4,"organization_review":"The book is well organized. There is a linearity in the topics studied and I can see a logical follow up. The only minor point, is a small review before starting the new chapter so the students can rely on the previous chapters for better understanding.","interface_rating":3,"interface_review":"There is inconsistencies on the PDF version of the book. The book is using different platform to display content (like math symbols) which are not clear on the PDF version of the book, It is always better to tell the audience which platform to use for better reading.","grammatical_rating":5,"grammatical_review":"I did not see or encounter any grammatical errors even though I did not read every sentence in the book.","cultural_rating":3,"cultural_review":"I did not see any relevance of cultural insensitivity, but looking at the diversity of our classrooms, the book should add some cultural items to help the minority students understand the topics using their cultural background.","overall_rating":8,"overall_review":"The book has a lot of potential to it. There is a need for cultural sensitivity on the mathematical topics, and also raising the bar to help some advance students get a head, and get more challenged.","created_at":"2020-04-27T12:57:53.000-05:00","updated_at":"2020-04-27T12:57:53.000-05:00"},{"id":4698,"first_name":"Jesna","last_name":"Nissam","position":"Instructor","institution_name":"Hawaii Community College","comprehensiveness_rating":4,"comprehensiveness_review":"Online Version: \r\nA great book for the beginners in Algebra. Provides a very clear picture of the common elementary algebra contents. Also covers few intermediate algebra contents needed for the students of that stage. The exercise set is well defined and legible. There is no glossary but the table of content is available in orderly manner. I like the way how the examples are presented in a very simple and clear manner.\r\n\r\nWith regard to PDF version the table of content is not given, there are plenty symbolic errors seen in the text book specially in the radical section.","accuracy_rating":4,"accuracy_review":"Good accuracy is seen in the online version of the book. But I found few error specifically in the radical section when I downloaded the book in PDF format and figured out the roots in the question is not clearly located. Specially for the students who like a hard copy of textbook for their reference, it will be difficult for them to understand the questions.","relevance_rating":5,"relevance_review":"The relevancy of book is good. The contents for elementary algebra and the method of solving will remain the same for years to come. The word problems are also presented in a simple layman's language so that its easier for students to understand which should be good for years to come.","clarity_rating":3,"clarity_review":"For online users the clarity is good. The presentation is simple, legible and easy to understand. For PDF users the clarity of mathematical symbols should be taken care of.","consistency_rating":5,"consistency_review":"I like the consistency of this book. Each chapter starts with learning objectives, there are boxes for cautions, video solutions are available , tips are given based on the topics required and the chapter ends with key takeaways.","modularity_rating":3,"modularity_review":"For online access of the book: Modularity is a strong point of this book. The chapters are broken into easily accessible sections.\r\nFor PDF version there is no content of table given.","organization_rating":5,"organization_review":"For online access: The book is organized in very clear order. A teacher has an option to choose good range of questions based on the difficulty level.","interface_rating":3,"interface_review":"There are lots of inconsistencies seen on the PDF version of the book. A teacher using this book should give clear guidance on using the online version and should make the students aware of the errors seen in the PDF version.","grammatical_rating":5,"grammatical_review":"No grammatical error seen.","cultural_rating":3,"cultural_review":"For a diverse classroom some of cultural related questions can help students get a better understanding.","overall_rating":8,"overall_review":"Overall this is a good book. The book is organized in a very neat manner with a lot examples and exercise questions. I would not hesitate using this book as my textbook for the class if relevant changes are made in the PDF version such as including the table of content and fixing the symbolic errors.","created_at":"2021-03-18T14:14:22.000-05:00","updated_at":"2021-03-18T14:14:22.000-05:00"},{"id":4925,"first_name":"Loretta","last_name":"Waldroupe","position":"Math Specialist","institution_name":"Cowley Community College","comprehensiveness_rating":4,"comprehensiveness_review":"Our college uses the same textbook for Elementary and Intermediate Algebra. This book is missing some of the Intermediate Algebra content that we cover. However, as just an Elementary Algebra book I feel the book covers all the necessary material. There is no glossary/index which I feel would be very helpful.","accuracy_rating":3,"accuracy_review":"The accuracy depends on the version you use. In the PDF version the fractions are not displayed correctly. They do appear correctly in the online version. However, for those students who prefer the physical version of the text this could create some issues.","relevance_rating":5,"relevance_review":"The thing with math is the concept does not change. Even in updated versions of book the content stays the same. The only thing they change is updating some word problems to more current data. So, I feel the relevance of the book is excellent and is not something that will change quickly like some subjects do.","clarity_rating":4,"clarity_review":"The book is clear and easy to understand. I love the key take-aways idea. The graphs are nice and clear. I feel for clarity purposes some of the inconsistencies between the online and PDF versions should be take care of. The explanation are clear and easy to understand. This is important for this level of math student.","consistency_rating":4,"consistency_review":"For the most part the consistency of the book is good. There are some places that need fixed where the equation is sometimes quite a bit smaller than the text in the PDF version. This occurs even if it is right next to the text and could be a hindrance to some students. Other than that I like the consistency.","modularity_rating":4,"modularity_review":"I love how the book is broken down into short sections. The graphs are big enough to actually see without feeling like you need a magnifying glass to read the points on the graph.","organization_rating":5,"organization_review":"The organization of the book is great. I feel it covers the topics in a good order making sure they build on a solid foundation. I really like the odd answers being at the end of the section so that you do not have to keep flipping to the back of the book to check your answers. There are a good variety of questions to choose from and the teacher can choose some with the answers given so the student knows if they are right and some without so that the teacher knows the student is actually working out the problems and not just giving answers.","interface_rating":4,"interface_review":"I did not have any problems with navigating through the textbook. The table of contents made it easy to navigate to whatever section I wanted to go to.  I like the idea of getting there quickly and efficiently. I wish there was a glossary/index to help the student find the page of certain terms more quickly.","grammatical_rating":3,"grammatical_review":"I found several errors in the PDF version of the text. Fractions were displayed correctly and would look like a whole number instead of a fraction. This can cause confusion for the students.","cultural_rating":4,"cultural_review":"I did not see any issues with the cultural relevance of the book.","overall_rating":8,"overall_review":"I feel if the PDF version did not have the grammatical errors it would be a good text for any Elementary Algebra student.","created_at":"2021-05-14T13:56:07.000-05:00","updated_at":"2021-05-14T13:56:07.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/elementary-algebra?locale=es","updated_at":"2026-05-18T02:10:20.000-05:00"},{"id":24,"title":"Linear Algebra","edition_statement":null,"volume":null,"copyright_year":2016,"ISBN10":null,"ISBN13":"9781944325039","license":"Attribution-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.","contributors":[{"id":4100,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Jim","middle_name":null,"last_name":"Hefferon","location":"Saint Michael's College","background_text":"Jim Hefferon, Professor of Mathematics at St. Michael's College in Colchester, Vermont. B.S., M.S., Ph.D. University of Connecticut."}],"subjects":[{"id":83,"name":"Algebra","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":29,"url":"https://open.umn.edu/opentextbooks/subjects/algebra?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":57,"url":"http://hefferon.net/linearalgebra/index.html","year":2020,"created_at":"2018-09-07T12:22:36.000-05:00","updated_at":"2021-01-03T17:37:06.000-06:00","name":"Jim Hefferon"}],"formats":[{"id":539,"type":"PDF","url":"http://hefferon.net/linearalgebra/index.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":540,"type":"Hardcopy","url":"https://www.amazon.com/dp/1944325115/ref=as_sl_pc_tf_til?tag=linearalgeb04-20\u0026linkCode=w00\u0026linkId=3bdf2f21c72097c43fe2d21143d912cc\u0026creativeASIN=1944325115","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":1980,"type":"LaTeX","url":"https://gitlab.com/jim.hefferon/linear-algebra","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":4,"reviews":[{"id":190,"first_name":"Aaron","last_name":"Wangberg","position":"Associate Professor","institution_name":"Winona State University","comprehensiveness_rating":4,"comprehensiveness_review":"This text provides a fairly thorough treatment of topics for an introductory linear algebra course.  It builds up the theory of linear algebra in order to answer important questions about they solutions and the types of solutions associated with systems of linear equations, and transitions to utilizing those techniques to further answer questions pertinent to vector spaces and maps between vector spaces.  In this build-up, the focus is placed upon interpretation of results, concepts and theory.  The text can be used before an intro-to-proofs course, and it provides many applications in the form of end-of-chapter Topics.  The text is lighter in topics like matrix algebra, systems of equations over fields other than the real numbers, computational linear algebra, the geometric interpretation of vectors and linear transformations, and the analysis of data sets using linear algebra.\r\n\r\nThe first chapter focuses on solving systems of equations and understanding the types of solutions associated with various types of systems.  The second chapter focuses on properties of vector spaces and uses the techniques of the first chapter to build the concepts of linear independence, dependence, and basis.  In the the third chapter, which focuses on maps between vector spaces, the techniques from Chapter 1 are again utilized to understand properties of the maps through studying the vector subspaces impacted by the maps.  Matrix multiplication and matrix inverses are finally presented as composition of maps and inverse maps.  Chapter 5 and 5 then focus on techniques appropriate for square matrices.  Chapter 4 focuses on determinants and includes a section on the geometry of determinants, while Chapter 5 covers eigenvalues and eigenvectors.  Many of the techniques used to answer questions in Chapter 1 are thus refined and re-used in later chapters.","accuracy_rating":5,"accuracy_review":"I've used the text for four semesters, and have found the text to be accurate and error-free.  Homework solutions are available, and most solutions utilize algebra or theory.  Occasionally solutions could be simplified had they utilized geometric meaning.  The text provides a non-standard definition of linear transformation and uses it consistently throughout the text.","relevance_rating":5,"relevance_review":"The content and end-of-chapter topics are up-to-date.  Most of the topics will withstand the test of time, a possible exception being the inclusion of the Page Rank topic pertinent to internet search.","clarity_rating":4,"clarity_review":"The writing is clear and supported by illustrations.  The illustrations and explanations nicely explain and summarize content;  I've sometimes needed to provide additional introduction or explanation of the illustrations for students.  Chapter 3 is long (110 pages)  contains a lot of material, many of it introduced just when it is needed.  For this reason, it may be helpful to split out some of the Chapter 3 topics early as a short interlude before beginning the chapter, or to frequently remind students of the end goal as they progress through the chapter.","consistency_rating":4,"consistency_review":"The text utilizes a consistent style for definitions, theorems, and examples.  End-of-section problems can be linked to their solutions, which can be a nice feature or flaw.  The author consistently provides end-of-section problems which utilize a set of systems of equations but changes the underlying question tuned to the particular section;  This is also done with some examples throughout the text.  This is a particularly nice feature of the text.","modularity_rating":3,"modularity_review":"Each chapter is divided into sections and subsections which are manageable.  Some sections and subsections can be skipped, and the author nicely suggests when this may be done without impacting the course.  The text could be re-arranged with care, but  this may heavily interfere with the careful buildup of Chapters 1, 2, and 3.","organization_rating":4,"organization_review":"The organization is very standard.  One nice feature available with the .pdf files is that the homework problems in the text can be hyper linked to the solutions in the associated .pdf solution file.\r\n","interface_rating":4,"interface_review":"I've used the text as both a printed and a .pdf file;  The interface works well in both situations, and does not prefer one format to the detriment of the other.  The .pdf file contains enough navigation and hyperlinking to be helpful.","grammatical_rating":4,"grammatical_review":"I found no grammatical errors.","cultural_rating":3,"cultural_review":"I did not find the text to be culturally insensitive or offensive. It avoids examples using race and ethnicity.","overall_rating":8,"overall_review":null,"created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":288,"first_name":"Iuliana","last_name":"Oprea","position":"Associate Professor","institution_name":"Colorado State University","comprehensiveness_rating":5,"comprehensiveness_review":"The book covers the standard material for an introductory course in linear algebra. The material is standard in that the topics covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors.  The approach is developmental, the topics are covered in a comprehensive fashion, and the mathematical language of the book is very rigorous and proof-based.  Nearly everything is proven either in the main text or in the exercises,  which is helpful for readers who are trying to bring more rigor to their mathematical thinking and mathematical maturity.  \r\nThe book is well balanced, substantial yet concise and has extensive exercise sets, with levels of difficulty varying from routine verifications to challenging problems, with worked answers and detailed solutions to all exercises. Each chapter   closes with a selection of related special topics, usually applications to real world examples from physics, biology, economics, probability and abstract algebra that could be assigned as individual or group projects or could be presented in class. These special topics, such as crystals, stable populations, electrical networks, dimensional analysis, voting paradoxes and so on, together with the many interesting applications throughout the text, make this book more valuable than the average undergraduate linear algebra textbook. \r\nOn the web page of the author beamer slides for classroom use are available, that draw from the text source with respect to the notations, the numbering of theorems etc, but contain different examples than in the book.  The web page also hosts a lab manual for computer work (using Sage) and links to a repository with the latex source files.\r\n","accuracy_rating":5,"accuracy_review":"I used the book as a textbook for two semesters and found the text to be accurate and error free.  The book is available for download since 1995.  The book has been tested over many years at a number of different schools and by a number of different instructors, and the author continuously improved the book based on their feedback, so it is ready to use today. ","relevance_rating":5,"relevance_review":"The book content and presentation of topics  have been updated and improved over the years; the content of the present edition is up-to-date.\r\n\r\n","clarity_rating":5,"clarity_review":"The text presentation is very clear and well motivated; the proofs are rigorous, unambiguous  but include plenty of details that make them accessible and easy to follow. ","consistency_rating":5,"consistency_review":"The text is consistent in terms of terminology and framework.","modularity_rating":5,"modularity_review":"The text is easily and readily divisible into smaller reading sections that give enough flexibility to an instructor in the organization of the lectures.  There are subsections, in the table of contents, marked as optional if some instructors will pass over them in favor of spending more time elsewhere. The book comes with a very useful semester’s time table, too.","organization_rating":5,"organization_review":"The topics are presented in a logical, clear fashion; a wealth of examples throughout the book is provided, and the author gives a lot of motivations for the study of most of the topics. A positive aspect is that – unlike many other textbooks - it starts with linear transformations rather than starting with matrices and then develops the intuition behind matrices. ","interface_rating":5,"interface_review":"I had no problems using the interface and no navigation problems.  The pdf file is easy to use. A nice feature is that if the pdf files for both the book and the solutions are saved in the same folder then clicking on an exercise sends you to its answer and clicking on an answer sends you back to the exercise.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors.","cultural_rating":5,"cultural_review":"The book is neither culturally insensitive nor offensive.  ","overall_rating":10,"overall_review":"This is a great free resource to be used as a textbook for an introductory course in linear algebra, or as a complementary material or for individual study.   ","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":370,"first_name":"Abraham","last_name":"Smith","position":"Assistant Professor","institution_name":"University of Wisconsin-Stout","comprehensiveness_rating":5,"comprehensiveness_review":"This is a complete textbook for Linear Algebra I.  It proceeds through the expected material on vector and matrix arithmetic on examples, then it makes a nice transition to abstract vector spaces and linear operators.  The major theorems in linear algebra are all covered, with nice proofs and clear examples and good exercises.","accuracy_rating":5,"accuracy_review":"After using the textbook for three courses, I have found no significant errors in the book.  Perhaps a minor typo or two over hundreds of pages.","relevance_rating":5,"relevance_review":"This is a good contemporary book on linear algebra.  It would be appropriate for any sophomore-level linear algebra course for pure math, applied math, CS, or related fields.  It includes some nice sections on computing that could lead naturally into a course on numerical methods.","clarity_rating":5,"clarity_review":"The text is very clear.  It follows modern notation, deviating only when it makes sense for clarity for the students.   The proofs are nicely written, and the author does a good job of mixing exercises into the body of the proofs.","consistency_rating":5,"consistency_review":"The book is of consistently high quality throughout.  ","modularity_rating":4,"modularity_review":"Being a thorough mathematics textbook, overall modularity is limited by the logical nature of the subject matter, but the later chapters are definitley re-organizable.  For example, I am someone who prefers to teach eigenvectors and Jordan form before I teach determinants, and this is easy to do with this book.  ","organization_rating":5,"organization_review":"The material is logical and clear, to contemporary mathematical standards.   A good student could read chapter-to-chapter and learn the subject.  ","interface_rating":5,"interface_review":"The text is a straightforward PDF e-book.  It is well-typeset and easy to read.  The LaTeX for the book is available, and the author has made some nice commands to typeset certain types of objects (like augmented matrices) that can be useful when writing supplementary material.","grammatical_rating":5,"grammatical_review":"Overall excellent and clear to both native and non-native speakers.","cultural_rating":5,"cultural_review":"The text is pure mathematics with few examples.  There is nothing insensitive or offensive in it.","overall_rating":10,"overall_review":"I used this textbook for two years at Fordham University for Linear Algebra I and also as a supplement for the advanced Linear Algebra II course.    It was an excellent resource for myself and for the students.  The problems are very good, and the logical flow of the book is easy to follow.  It is now my first choice for a Linear Algebra I book.  (For Linear Algebra II, I prefer the more abstract approach of Axler's \"Linear Algebra Done Right\", but I still use this as a supplement in case students aren't comfortable with earlier material.)","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":2444,"first_name":"Daniel","last_name":"Drucker","position":"Professor and Associate Chair","institution_name":"Wayne State University","comprehensiveness_rating":4,"comprehensiveness_review":"This text does a good job of covering the theory in detail, especially in Chapters Two and Five. Uniqueness of reduced echelon form is proved in detail. (It’s in a section unhelpfully entitled “The Linear Combination Lemma”). Optional sections in Chapter Five give a more comprehensive treatment of Jordan canonical form than is found in most introductory texts, many of which omit this topic entirely. The author does not focus on the four fundamental subspaces, a point of view popularized by Gilbert Strang in his books Linear Algebra and Its Applications and Introduction to Linear Algebra. He emphasizes concepts and theory much more than calculation, and linear transformations much more than matrices. Matrix factorizations (LU, QR, etc.) are not covered. Orthogonality is viewed as an optional, not a central, topic. Least squares is an add-on end-of-chapter Topic, and only lines of best fit are discussed. The spectral theorem for symmetric matrices is not mentioned. Positive definite and positive semidefinite matrices are not covered. Neither are pseudoinverses or the singular value decomposition, which means that diagonalization of non-square matrices is never mentioned. Numerical linear algebra is mentioned only in the context of Gaussian elimination and the method of powers, which appear as Topics at the ends of Chapters One and Five. Operation counts and iterative methods (other than the method of powers for sparse matrices) are not discussed. Although complex vector spaces are used in the sections on diagonalization and Jordan form, there is no discussion of hermitian, skew-hermitian, unitary, or normal matrices. Many of these topics are not included in most introductory courses, but current introductory texts often include them in optional chapters to provide instructors with topics for projects and to provide students with additional material to read on their own.\r\nThe applications are interesting and varied, but limited in length and depth. They include: use of bases to describe the structure of several crystals, the use of linear systems of equations to analyze voting paradoxes, dimensional analysis (using linear systems), lines of best fit, the geometry of linear maps (nomographs for functions from R to R, and projections, rotations, reflections, and shears), magic squares (calculation of the dimension of the space of n x n magic squares), Markov chains (nontrivial examples analyzed with the help of Sage), orthonormal matrices (standardly called orthogonal matrices, though the term orthogonormal matrices is actually better), Cramer’s rule (which, like orthonormal matrices, is a topic that I think should be part of the regular exposition, not an end-of-chapter Topic), speed of calculating determinants (timing with Sage shows we shouldn’t use the permutation expansion formula), Chiò’s recursive method of calculating determinants using 2 x 2 minors, projective geometry (an excellent section identifying three types of central projection and including a proof of Desargue’s theorem), the method of powers for finding the largest eigenvalue of a sparse matrix, eigenvalues that yield static and dynamically stable population distributions, a greatly simplified version of Google’s Page Rank algorithm, linear recurrences (sometimes called linear difference equations—they can be viewed as discrete versions of differential equations), and coupled oscillators (partial solution of a particular pair of differential equations). Note that a number of these “applications” are considered mainstream topics in other texts. Omissions include linear programming, general systems of linear differential equations, classification of the behavior of 2 x 2 systems of linear differential equations, the fast Fourier transform, graphs and networks in general, image compression, quadratic forms and classification of second degree curves, computer graphics (except for a brief mention on pp. 315–316), and various geometrical topics (such as affine geometry; barycentric coordinates; convexity; problems about points, lines, and planes).\r\nThe author’s choice of topics is consistent with his goal of wanting to develop mathematical maturity in students early in their college programs. I suspect that many of the sophomores at my university, most of whom commute and work considerable hours at a job while in school, and who struggle with elementary linear algebra’s abstractions, would have even more trouble with a theory-oriented exposition like this one. Its suitability at a given school surely depends on the aptitude, level of preparedness, and time constraints of the students.\r\nThe author provides a preface, an index of notations, a comprehensive bibliography, and an index, but they are not listed in the table of contents. There is no glossary.","accuracy_rating":5,"accuracy_review":"I found a small number of errors in punctuation, spelling, and grammar, but they do not interfere with reading the text. The problem solutions that accompany the text appear to be correct, though I’ve only sampled them randomly as I’ve never taught from this text.","relevance_rating":5,"relevance_review":"I don’t think the content of this text will become obsolete any time soon. After all, the theory of linear algebra is not going to change. The choice and number of applications may need to change as tastes in topical coverage evolve.","clarity_rating":4,"clarity_review":"I found the author’s writing to be clear, though some discussions seem unnecessarily long-winded. His illustrations are helpful, with the one problem that he tends not to label his axes. As for jargon/technical terminology, the author does use some nonstandard notations (e.g., RepB,B’) and terminology (e.g., inter-reducible). These are not obstacles in reading the book, but they may make it harder for students to read the same topics in other books on linear algebra. \r\nI found the geometrical motivation for Cramer’s rule to be forced and unhelpful.","consistency_rating":5,"consistency_review":"The style and terminology are consistent throughout the text. ","modularity_rating":4,"modularity_review":"Changing the order of coverage of the main sections would likely disrupt the careful development of theory in the first three chapters. End-of-chapter Topics can be covered in any order, or omitted. In the Preface, the author suggests going through the text (exclusive of Topics) in order and suggests the rate at which that can be done. He also marks some sections as optional, so that they can be skipped to devote time to other parts of the text.","organization_rating":4,"organization_review":"The material is logically ordered and divided into five chapters, but Chapter Three is much longer than any other chapter. It could be split into two chapters, the second one on orthogonality and its applications.","interface_rating":5,"interface_review":"Links in the .pdf file’s table of contents allow the reader to jump easily to any section of the text. There are also links to references in the bibliography. I found no display features that could distract or confuse the reader, except for figures in which the coordinate axes are not labeled. It is worth mentioning that the text is presented in an attractive and readable font.\r\nHyperlinks connect the exercises in the text with their solutions, provided the names of the files are not changed. I tried changing the file name of the text to something more descriptive than book.pdf and found that clicking on the number of an exercise did not get me back to the exercise in the text. Changing the name of the text’s file also changed my Mac’s numbering of pages in the pdf file.","grammatical_rating":4,"grammatical_review":"There are a few grammatical errors and a few places where the author seems to omit a word or string two sentences together, but these do not seriously interfere with reading the text.","cultural_rating":5,"cultural_review":"Examples in this text do not mention race, ethnicity, or people’s backgrounds. Thus they are not culturally insensitive or offensive in any way.","overall_rating":9,"overall_review":"The author not only provides .pdf files of the book and solutions manual with helpful links, but also includes a lab manual that introduces the interested reader to Python and Sage. Besides those, he includes extra problems with solutions, an introduction to proofs, and an article on matrix arithmetic. Professor Hefferon tries hard to motivate every topic he covers and almost always succeeds. He is to be commended and appreciated for doing everything he could to help students and instructors to benefit from and make maximal use of his text. Even when it is not used as the text for a course, it can serve as a useful reference.","created_at":"2018-12-05T13:14:06.000-06:00","updated_at":"2018-12-05T13:14:06.000-06:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/linear-algebra?locale=es","updated_at":"2026-05-18T12:03:49.000-05:00"},{"id":52,"title":"Whitman Calculus","edition_statement":null,"volume":null,"copyright_year":2010,"ISBN10":null,"ISBN13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available. This textbook has been used in classes at: Boise State University, Claremont McKenna College, University of Minnesota, University of Puget Sound, Western Connecticut State University, Whitman College.","contributors":[{"id":3586,"contribution":"Author","primary":true,"corporate":false,"title":"Dr.","first_name":"David","middle_name":null,"last_name":"Guichard","location":"Whitman College","background_text":"David Guichard is a Professor of Mathematics at Whitman College in Walla Walla, Washington. He received his Ph.D. from the University of Wisconsin, and his research interests include Graph Theory."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://open.umn.edu/opentextbooks/subjects/calculus?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":56,"url":"http://www.whitman.edu/mathematics/calculus","year":null,"created_at":"2018-09-07T12:22:36.000-05:00","updated_at":"2019-12-29T15:35:27.000-06:00","name":"David Guichard"}],"formats":[{"id":70,"type":"PDF","url":"http://www.whitman.edu/mathematics/calculus/calculus.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":71,"type":"Hardcopy","url":"http://www.lulu.com/shop/david-guichard-et-al/single-variable-calculus-20130629/paperback/product-21148221.html","price":{"cents":980,"currency_iso":"USD"},"isbn":null},{"id":1927,"type":"Online","url":"https://www.whitman.edu/mathematics/calculus_online/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":6,"reviews":[{"id":44,"first_name":"Michael","last_name":"Nyenhuis","position":"Instructor","institution_name":"Kwantlen Polytechnic University","comprehensiveness_rating":4,"comprehensiveness_review":"The text covers the standard topics in first-year calculus, but I think a regular student would have trouble using it. It covers the contents at a more mathematically sophisticated level than students are usually used to. For example, limits are introduced using the epsilon-delta definition. That may be appropriate in an honours section of calculus, but not for a regular section. Graphs or diagrams that would help in understanding the material are missing. For example, the text states that “rightward” is the positive x direction and upward is the positive y direction, but includes no diagram. Exercises are often skimpy, and emphasize only one view of calculus.  For example, the section on the quotient rule has only 4 algebraic exercises, none of which combine other rules. I would have liked to have seen graphical questions, such as asking students to sketch the derivative of f(x) given the graph of f(x). \n\nI think students would find the text more difficult to read than Stewart, say, and \ninstructors will need to supplement the exercises.\n\nThe index is good.","accuracy_rating":4,"accuracy_review":"Content is mathematically correct, but students might prefer a less mathematically rigourous approach.","relevance_rating":5,"relevance_review":"Calculus does not change much, but how it is taught has changed over the years. The text seems to focus on the algebraic approach. Instructors who want to emphasize the graphical approach may not be happy with it. \n\nBecause the source TeX files are publicly available, it is, in principle, easy to edit the text. Some experience in TeX would be needed, however.","clarity_rating":4,"clarity_review":"The text is written in fairly standard math. Definitions are provided. ","consistency_rating":5,"consistency_review":"It is internally consistent.","modularity_rating":3,"modularity_review":"Sections are usually fairly brief and most cover a single topic, so they could be assigned as reading. I think, however, that most students will find the text hard to understand, making assigned reading kind-of moot. \n\nMany sections begin with a reference to previous sections, but these could be edited out. \n\nMath texts usually assume material is covered in the same order as it is presented in the text, \nand this text is no exception. However, instructors who like to cover topics “out of order” are \nalready familiar with this problem. ","organization_rating":4,"organization_review":"For a mathematician, the topics are presented in a clear, logical fashion. Students may wonder what the author is getting at, but math instructors should have no difficulty in doing so.","interface_rating":4,"interface_review":"The text is a pdf document, so navigation is kind-of primitive. My one beef is that exercises are followed by an arrow leading to the answers, but no arrow follows answers leading back to the questions! Images and charts are clear.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors.","cultural_rating":4,"cultural_review":"I did not find the text culturally insensitive or offensive. The author works in Washington State, so some exercises and examples refer to locations in Washington.","overall_rating":8,"overall_review":"The text strikes me as OK from a Canadian mensuration perspective. Most questions involving miles do not require a conversion to feet. Some acceleration questions are in feet. The work section has several examples in feet and pounds, which will obviously cause problems. How many Canadian students are aware that the unit of mass in the Imperial System is the slug?\n\nAdditional observations:\n\nI checked the internet for other open-source calculus texts. Most are either lecture notes, or multimedia (video-based), or non-traditional (emphasizing infinitessimals, for example). The only other complete, standard text was a scan (sometimes of low image quality) of Strang’s 1991 Calculus text. It is dated (there's a reference to \"A Thousand Points of Light\") and cannot be edited. I think Guichard’s book may be a good choice for an honours calculus class, but I would hesitate recommending it for any other. However, it is also the only candidate. If an open-source text must be chosen, I think Guichard’s text is the only choice.","created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":45,"first_name":"Sam","last_name":"Pimentel","position":"Assistant Professor of Mathematical Sciences","institution_name":"Trinity Western University","comprehensiveness_rating":4,"comprehensiveness_review":"The textbook covers all the topics necessary for a Calculus 1 course.  The entire textbook, chapters 1-11, cover material for a Calculus 2 course, with the exception that the current copy received for review doesn’t include a section/chapter on first-order separable differential equations.  (A chapter on differential equations is made mention of in the small print on the inside front cover, but does not appear in the contents).","accuracy_rating":5,"accuracy_review":"No major inaccuracies were discovered.","relevance_rating":5,"relevance_review":"Updated versions of the textbook are made available on the website.  The TeX files used to generate the textbook are freely available as well, thus allowing users to update and edit the text themselves, if required.  Some familiarity with LaTeX is required, in this regard, simply downloading the TeX files and using LaTeX to generate a pdf textbook won’t work without some tinkering with the various options on offer.","clarity_rating":5,"clarity_review":"A conversational writing style makes the text very readable and the presentation of material has a natural flow.","consistency_rating":5,"consistency_review":"No major issues found.","modularity_rating":5,"modularity_review":"Section and subsection labeling are used well.  Definitions, Theorems, Examples, and Exercises are helpfully numbered.","organization_rating":5,"organization_review":"The textbook has a sensible ordering of chapters and sections that, for the most part, follows the usual structure of other introductory calculus textbooks.  Organization of the material that is perhaps slightly unusual includes introducing the derivative before introducing continuity, leaving limits at infinity until later (Section 4.10), introducing integration by parts and integration of rational functions using partial fractions before any applications of integration.  The partition between a Calculus 1 and a Calculus 2 course is often such that some integral applications are required as part of the Calculus 1 syllabus, but that integration by parts and integration using partial fractions is not encountered until Calculus 2.  Again, having the tex files allows for rearranging and omitting certain material as required for particular course offerings.","interface_rating":4,"interface_review":"Some figures contain so-called “AP” links to interactive applets, these were broken in the copy under review.  This is only relevant for the pdf of the textbook.","grammatical_rating":5,"grammatical_review":"U.S. spelling is used throughout e.g. center rather than centre.  This could be quickly and easily changed, if desired, by running a Canadian English spell check through the textbooks .tex files.","cultural_rating":3,"cultural_review":"By the natural of the textbook in question issues of cultural relevance are limited.  However, Math examples involving cultural references are U.S. focused e.g. U.S. geographical locations, baseball, U.S. income tax data, etc.  Imperial (rather than metric) measurement units are frequently used e.g. feet, miles, pounds etc.","overall_rating":9,"overall_review":"The text is straightforward in appearance, e.g. no sidebars, boxed material, or special highlighting.  No special attention is made, therefore, on highlighting key material and core ideas.  On the other hand, students can have free reign of the highlighter pen and annotate the text to their hearts content without any fear of reducing the resale prize on the second-hand textbook market!  The text is also free of the little historical vignettes or anecdotes that are often found in the major Calculus textbooks.  The material is too the point and keeps the book to a reasonable length.  There are less figures and diagrams than is standard in the major textbooks.  More graphs (and in some cases coloured lines on existing graphs) may improve explanations for students.  Calculus students may find themselves wanting more worked examples, although presumably these would be provided in class lectures.  On a similar note, the question sets are small, instructors may find themselves needing to set problems outside of those provided.  This would also be important to avoid too much repetition with multiple offerings of the course year in, year out.  Students themselves may like to try further exercises than the textbook currently supplies.  A supplementary worked examples and problem set may need to be provided in addition to the textbook. ","created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":46,"first_name":"Bruce","last_name":"Aubertin","position":"Instructor","institution_name":"Langara College","comprehensiveness_rating":5,"comprehensiveness_review":"The text reviewed here is a version (May 2013) of the single variable portion (chapters 1 -11; 318 pages) of the full text, Calculus – Early Transcendentals  by Guichard et al, which includes both single and multivariable calculus and can be found at: http://www.whitman.edu/mathematics/multivariable/\n\nThe single variable edition is a complete course presented in a traditional sequence, except that differential equations do not appear at all until chapter 17 of the multivariable text. Separable DEs, mandatory in the BC curriculum, are treated in 17.1, so adopters/adapters of the text may wish to have this section appended or inserted as an additional section in Chapter 9, Applications of Integration.\n\nThe index could certainly be improved, particularly for those using a print copy and unable to do a search as a pdf file would allow. For example, section 8.8 on numerical integration covers the trapezoidal rule and Simpson’s rule with formulas for the errors (incidentally, the midpoint rule, standard in most texts, is not discussed here), however, there is no mention in the index or in the table of contents of “trapezoidal rule.” The term “related rates” appears in both the index and table of contents, while “Newton’s method” appears in the table of contents and not in the index. The term “cycloid” does appear in the index (one of my tests of an index in any calculus text!), in addition to “hypercycloid” and “hypocycloid”, pointing to nice exercises in the text expanding the discussion of parametric equations in 10.4.  While the economies taken in the body of the text in producing such a wonderfully readable and complete text in about half the number of pages of a typical commercial text are much appreciated,  the index is a different story, and 300+ pages demands a good index!\n\nDiagrams in the text are relatively few and far between, though are used effectively when present. The book does favour algebraic/analytical reasoning working from definitions over  graphical arguments, and limits (including one-sided limits) receive the full epsilon-delta treatment. But there are instances/acknowledgement of graphical reasoning in the text! To illustrate, the Squeeze Theorem presented in 4.3 is followed by the comment, “This theorem can be proved using the official definition of limit. We won’t prove it here, but point out that it is easy to understand and believe graphically.” There follows immediately the classic example of (x^2)sin(pi/x) as x approaches 0, complete with a diagram that illustrates the theorem perfectly.  \nAnother example appears in 4.7, where the derivative of ln(x) is derived graphically using the fact that the derivative of exp(x) is itself. I liked to see this very much! This reviewer never waits for implicit differentiation, as most texts do, before demonstrating that if dy/dx exists at (a, b) and is not zero, then dx/dy also exists at this point, and equals 1/(dy/dx). (If I am running twice as fast as you at a certain instant, then at this instant you are running half as fast as me!) The graphical derivation in the text is then followed by:\n\n “We have discussed this from the point of view of the graphs, which is easy to understand but is not normally considered a rigorous proof—it is too easy to be led astray by pictures that seem reasonable but that miss some hard point. It is possible to do this derivation without resorting to pictures, and indeed we will see an alternate approach soon.”\n\nLeft and right continuity are not mentioned in the text (unusual), and nor are one-sided derivatives (usual). But these are not seen as omissions; instructors with any text will want occasionally to amplify or draw diagrams, and expand/extend concepts. For example, a question such as (one of my favourites) “What is the slope of the graph of cos(sqrt(x)) at x=0?” would not be at all out of place in this book. Conversely, of course, an instructor using this text may wish not to follow the rigorous epsilon-delta approach to limits. For this reviewer, in first year, I take the limit laws to be all intuitively obvious, and no use at all on all of the “interesting” limits (what I call the indeterminate forms!)\n\nThe exercises at the end of each section are well chosen and numerous enough in applications such as optimization and related rates where they need to be. They range from routine practice to more challenging questions, and most have short answers in the back of the book. These could be supplemented using the open-source online homework system WeBWorK  http://webwork.maa.org/  (This reviewer has currently only had experience with the commercial systems WebAssign and MathXL).\n\nOverall, I like this book a lot. It is very well written and friendly to read, without the usual clutter of sidebars, footnotes and appendices! It moves quickly through all the important definitions and theorems of calculus with many examples and also a certain amount of just-in-time precalculus (for example, with the exponential and logarithm functions). There is appropriate rigour throughout, though the book is not at all in the style of Rudin’s classic graduate text, “Principles of Mathematical Analysis!” It is much more conversational, and suited even for self-study. Maybe slightly too much so, as sometimes definitions or important formulas appear in the flow of the discourse and are not highlighted for easy visual reference for the student. Most are numbered, but the conversion formulas for switching from polar to rectangular coordinates in 10.1 would be a case in point. ","accuracy_rating":5,"accuracy_review":"The text appears to be remarkably free of errors of any kind, and any question of bias in the sense intended here not applicable. I did notice somewhere a period missing at the end of a sentence. Also, in the remark in parentheses at the end of Example 1.4 in section 1.3, which reads: “(You might think about whether we could allow 0 or (minimum of a and b) to be in the domain. They make a certain physical sense, …),” the term “(minimum of a and b)” should be replaced with “min(a, b)/2.” I did also notice, in the discussion immediately following Theorem 11.17 in section 11.2, that the constant c was not taken to be nonzero explicitly as it should have been.\n\nOf course there are natural biases expected in terms of style, rigour, choice of definitions etc., and these are mostly very agreeable to this reviewer. For example, it is refreshing to see the function 1/x declared continuous, following the definition of continuity given in section 2.5 - Adjectives for Functions. Though I may continue to say that there is an infinite discontinuity at x=0. It does go slightly against the grain however, to allow as the book does, the endpoints of an interval [a, b] to be local extrema.\n\nI like the book’s treatment in 6.5 of the Mean Value Theorem (MVT), or Motor Vehicle Theorem as I call it, and let me contrast it with that given in Stewart’s Calculus - Concepts and Contexts, another admirable text with which this reviewer is familiar and has taught from for some time. Both texts state the theorem and illustrate its usefulness and interpretation with respect to motion. The text under review fully proves it from Rolle’s Theorem, which in turn is proved from the (unproved) Extreme Value Theorem. There is no diagram in this section, and the function g(x) = f(x)-m(x-a)-f(a) used to derive the MVT from Rolle’s Theorem appears pulled out of a hat and is not explained. By contrast, Stewart does not mention Rolle’s Theorem or prove the MVT, but does provide diagrams making it seem plausible. Annoyingly, however, the hypothesis in Stewart’s MVT is that f(x) is differentiable on the closed interval [a, b], making it not applicable, for example, to the square root function on the interval [0, A]. ","relevance_rating":5,"relevance_review":"The content in a mainstream calculus text such as this is relatively timeless. The book is regularly being updated by the author, taking into account feedback from users of the text. I will leave it to other reviewers more familiar with manipulating source code to comment on the ease of editing the text.","clarity_rating":5,"clarity_review":"The writing of this text is exemplary.","consistency_rating":5,"consistency_review":"The text uses standard mathematical terminology throughout.","modularity_rating":5,"modularity_review":"The text is structured in a standard and traditional sequence for a calculus text.","organization_rating":5,"organization_review":"The organization and flow of this text is exemplary.","interface_rating":5,"interface_review":"There are no significant interface issues with this text. The internal hyperlinks in the pdf version of the text are a very nice feature, taking you instantly to a referenced diagram, definition, or solution of an exercise.  However, it would be nice if there was a way to return to the exact previous position in the text with a single click, after viewing the reference, rather than having to navigate back using the bookmarked pages or sections of the text. I did find that clicking on the external links labeled (AP) that are attached to many of the diagrams resulted only in “page not found.” I don’t know why, but it can’t be serious.","grammatical_rating":5,"grammatical_review":"I did not notice any grammatical errors in the text.","cultural_rating":5,"cultural_review":"The text is culturally neutral.","overall_rating":10,"overall_review":"It has been a real pleasure reading this book.","created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":47,"first_name":"James L.","last_name":"Bailey","position":"Chair, British Columbia Committee on the Undergraduate Program in Mathematics and Statistics","institution_name":"College of the Rockies","comprehensiveness_rating":4,"comprehensiveness_review":"The BCcupms Core Calculus Report (revised 2013):      In 2002 the British Columbia Committee on the      Undergraduate Program in Mathematics and Statistics (BCcupms)      accepted the Core      Calculus Report. It was reviewed in 2007 and revised in      2013.      This document has a list of core topics which all first year      (two semester) Science Calculus courses must include and a      list of additional topics, at least four of which must be      chosen. Any text which is adopted for a first year Science      Calculus course must be consistent with this report.      Core topics:              Limits, continuity, intermediate value theorem.                                    Limits are introduced in Section 2.3 where              Definition 2.3 is the $\\epsilon, \\delta$-definition              of a limit. The definition is used to show that              \\[\\lim_{x\\rightarrow2}x^2=4\\] (Example 2.5, page 40).              Properties of limits are stated in Theorem 2.7 (page              42).              One sided limits are defined, together with an              example, in Section 2.3.                                      Continuity is covered in Section 2.5. There is a              problem with Figure 2.3(a) (the left half of the              figure below is my attempt at reproducing it). The              author states that ``a function $f$ is continuous if              it is continuous at every point in its domain'' (page              53). It is claimed that Figure 2.3(a) is the graph of              a discontinuous function, but it is not clear that              the function is defined at the discontinuities, viz.              $x=-1,0,\\text{ and }2$. In fact, the function would              be continuous if it were not defined at              these values. Something like the right half of the              figure would have made it clearer what function              values were intended at the discontinuities ($x=-1$              and $x=1$).                image not available             Figure 2.3.a in the Text, Discontinuities.                            There is no discussion of removable or jump              discontinuities.                                      The Intermediate Value Theorem is found in Section              2.5 together with an application, using a binary              search to approximate a zero of a function.                                                Differentiation                                    First and second derivatives with geometric and              physical interpretations. The following are              covered:                              The derivative of a function is introduced at                the bottom of page 32, as a summary of the                procedure used to find the slope of the tangent to                $\\sqrt{625-x^2}$ at any point. Section 2.4                introduces the main notations, $y'=f'(x)$ and                $\\frac{dy}{dx}$, and has a discussion of places                where a function does not have a derivative                (corners and cusps). The dot notation, $\\dot x$, is                introduced on page 128.                                  Interpretations of the derivative: slope of                  tangent line; velocity, acceleration (velocity                  and acceleration are also discussed in Section                  9.2 when discussing integration); rate of change                  in general.                                                  The second derivative does not have its own                  section. It is first introduced with the second                  derivative test for extrema (Section 5.3) and                  concavity (Section 5.4).                                                  Interpretations of the second derivative:                  concavity and acceleration.                                                                    Mean Value Theorem              The Mean Value Theorem is treated in Section 6.5.              The authors first prove Rolle's Theorem and then use              that to prove the Mean Value Theorem.                                      Derivatives of the exponential and logarithm              functions, exponential growth and decay.              The derivatives of the exponential and logarithm              functions are covered. On page 85 where the authors              find the derivative of $\\log_ax$ they show that              $\\log_ae=\\frac{1}{\\ln a}$. For no more work they              could have derived the change of base formula,              $\\log_ax=\\frac{\\ln x}{\\ln a}$ and then found the              derivative of $\\log_ax$ more economically.              Exponential growth and decay is not covered,              presumably because there are no differential              equations.                        Derivatives of trigonometric functions and their            inverses.              The derivatives of $\\sin x$, $\\cos x$, $\\tan x$,              and $\\sec x$ are covered; $\\cot x$ and $\\csc x$ are              left as exercises.              On pages 75--76, in giving the usual geometric              argument that \\[\\lim_{x\\rightarrow0}\\frac{\\sin              x}{x}=1,\\] the authors argue that, with a little              algebra, \\[\\frac{\\cos x \\sin x}{2} \\leq              \\frac{x}{2}\\Rightarrow \\frac{\\sin x}{x}\\leq              \\frac{1}{\\cos x}.\\] They do not point out that we              need $0\\lt x\\lt\\frac{\\pi}{2}$ in order to keep the              various quantities positive and avoid problems with              the inequalities. Because the argument is essentially              geometric, and this is the restriction which is              implied by the diagram, they may feel that it is              unnecessary to point this out.              The derivatives of the inverse trigonometric              functions: the derivative of $\\arcsin x$ is done, but              the derivatives of $\\arccos x$, $\\arctan x$, and              $\\text{arccot}\\, x$ are left as exercises. The              derivative of $\\text{arcsec}\\, x$ is not              discussed.                                      Differentiation rules (including chain rule,              implicit differentiation)              The authors start by deriving the power rule              $\\frac{d}{dx}x^n=nx^{n-1}$ for integer $n$ using an              ad hoc argument which gives the first two terms of              the Binomial Theorem (page 56); rational exponents              are handled after they have covered implicit              differentiation. The other rules (constant multiple,              sum, product, quotient, and chain) are presented in              order. Finding derivatives by implicit              differentiation is covered, but finding the second              derivative of an function defined implicitly is              discussed only in the section on polar coordinates.              Logarithmic differentiation is not covered.              On page 67, where they show how to differentiate              \\[f(x)=\\frac{x^2-1}{x\\sqrt{x^2+1}}\\] they say: \"The              last operation here is division, so to get              started we need to use the quotient rule first,\" but              there is no indication why this is important. It may              be better to state the implied rule, that the              differentiation rules are applied in the reverse              order to that which is used when doing a              calculation.                                      Linear approximations and Newton's Method              Newton's Method is well covered but the section on              Linear Approximations is a little thin. In              particular, I would have liked to see problems such              as \"Use a linear approximation to estimate              $\\sqrt{10}$,\" and some problems which do not have a              unique answer because the student has to make              choices.                                      Optimization --- local and absolute extrema with              applications              Optimization is well covered with a large number              of exercises.                                                Taylor polynomials and special Taylor series          $\\left(\\sin x,\\,\\cos x,\\,e^x,\\, \\frac{1}{1-x}\\right)$,          plus enough sequences and series to understand the radius          of convergence; in particular, the concept of series and          convergence, the ratio test, and how to find the radius          of convergence.          These are all covered. In addition, differentiation          and integration of power series are covered and there is          a proof of the Lagrange form of the remainder.                          Curve Sketching.          Chapter 5 covers curve sketching. Intercepts are not          discussed. Horizontal and vertical asymptotes are          discussed but the authors say that slant asymptotes \"are          somewhat more difficult to identify and we will ignore          them.\" Even and odd symmetry is mentioned.                Integration                                    Definition of the definite integral and              approximate integration.              Both are covered. There is an example of using the              limit of a Riemann sum to calculate an area, although              the term ``Riemann sum'' is not used.                                      Areas of plane regions              Covered.                                      Average value of a function.              Covered by example although the general formula,              \\[f_{\\text{avg}}=\\frac{1}{b-a}\\int_a^bf(x)\\,dx\\] is              not given.                                      Fundamental Theorem of Calculus              Both forms of the Fundamental Theorem are              covered.                                      Integration techniques: substitution (including              trig substitution), parts, partial fractions.              The following integration techniques are              covered:                                                $u$-substitutions. I have a problem with the                  authors' approach: the authors allow both $x$ and                  $u$ in the same integral. In the example on page                  163 they have \\begin{eqnarray*} \\int                  x^3\\sqrt{1-x^2}dx\u0026amp;=\u0026amp;\\int x^3\\sqrt                  u\\frac{-2x}{-2x}dx\\qquad u=1-x^2,\\,du=-2x\\,dx \\\\                  \u0026amp;=\u0026amp;\\int \\frac{x^2}{-2}\\sqrt                  u\\frac{du}{dx}dx\\\\ \u0026amp;=\u0026amp;\\int                  \\frac{x^2}{-2}\\sqrt u\\, du\\qquad x^2=1-u\\\\                  \u0026amp;=\u0026amp;\\int -\\frac{1}{2}(1-u)\\sqrt u\\, du\\\\                  \\end{eqnarray*} The authors advise that it is                  necessary to \"translate the given function so                  that it is written entirely in terms of u, with                  no x remaining in the expression\" but I have                  found that students often miss this nicety.                                                                     powers of $\\sin x$ and $\\cos x$ are covered in                  Section 8.3, using examples only; it is not                  explicitly stated that for                  $\\int\\sin^nx\\cos^mx\\,dx$ use a $u$-substitution                  if one of $n$, $m$ is odd and the double angle                  formula if both are even. Powers of $\\tan x$ and                  $\\sec x$ are not covered. The use of reduction                  formulae is not discussed.                                                  trigonometric substitutions are covered, but                  not systematically.                                                  there is a section on integration by parts and                  tabular integration. There are no rules of thumb                  to help students decide when to use integration                  by parts. Reduction formulae are not                  discussed.                                                  rational functions are covered, but only the                  easy cases: when the denominator is of the form                  $(ax+b)^n$, $(x-r)(x-s)$, or an irreducible                  quadratic $x^2+bx+c$.                                                                    Applications of integration.              Applications of integration are in Chapter 9.                                                Areas between curves.                                                  Distance, velocity, acceleration.                                                  Volumes by slicing, circular laminae,                  cylindrical shells.                                                  Average value of a function.                                                  Work.                                                  Centre of mass. The formula for $x$-centroid                  \\[\\overline{x}=\\frac{\\int_a^bxy\\,dx}{\\int_a^by\\,dx}\\]                  is given, but they rely on finding the inverse                  function to get $\\overline y$ where in practice                  it is easier to have a second formula:                  \\[\\overline                  y=\\frac{\\frac{1}{2}\\int_a^by^2\\,dx}{\\int_a^by\\,dx}\\]                                                  Kinetic energy.                                                  Probabliity.                                                  Arc length.                                                  Surface area.                                                                              Improper integrals: evaluation and convergence          estimates          Improper integrals including the Cauchy Principal          Value are covered tangentially in Section 9.7. There are          no convergence estimates.                          Separable differential equations          There are no differential equations in the text.                    Additional Topics                        Sequences and series. For example, the following          tests: integral, comparison, alternating series, root,          and limit ratio.          Sequences and series are covered in Chapter 11. The          following tests are covered:                                    divergence test              ($\\lim_{x\\rightarrow\\infty}a_n\\neq0\\Rightarrow              \\sum_{i=1}^\\infty a_i$ diverges).                                      the integral test, $p$-series, truncation              error.                                      the alternating series test, truncation error.                                      the direct comparison test. The limit comparison              test is missing.                                      absolute, conditional convergence.                                      the ratio and root tests.                                                Additional applications of integration.          See the core topics for the list of applications of          integration.                          Additional differential equations topics          There are no differential equations.                          Complex numbers          There are no complex numbers.                          Continuous probability density functions          Continuous probability density functions are covered          in Section 9.8.                          Polar coordinates and parametric equations (with          calculus applications)          Polar coordinates and parametric equations are covered          in Chaper 10. The calculus applications discussed are                                    polar coordinates: slopes and areas.                                      parametric curves: area and arc length.                                                Additional numerical methods (eg. Simpson's Rule) and          error bounds          The Trapezoid Rule and Simpson's Rule together with          their error bounds are covered in Section 8.6.                          Related rates          Related rates are covered in Section 6.2.                          L'Hôpital's Rule          L'Hôpital's Rule is covered in Section 4.2, but          only for the indeterminate the forms          $\\left[\\frac{0}{0}\\right]$,          $\\left[\\frac{\\infty}{\\infty}\\right]$, and          $\\left[0\\cdot\\infty\\right]$. The more difficult ones, viz          $\\left[\\infty-\\infty\\right]$, $\\left[0^0\\right]$,          $\\left[\\infty^0\\right]$, and $\\left[1^\\infty\\right]$, are          not discussed.                    Exercises:      There is an adequate selection of exercises at the end of      each section. Most are routine, although the exercise sets      usually end with a few which are more challenging.      The Index:      The index is quite good, although the following terms are      not in it: arc length, area, average value, curve sketching,      decreasing, increasing, indefinite integral, Newton's Method      (the Newton, a unit of mass, is there), second derivative,      substitutions, surface area, volume.      Conclusion:                        The following topics are not in the text: complex          numbers, differential equations, limit comparison test,          the derivative of $\\text{arcsec }x$ and the integration          techniques which depend on it, and logarithmic          differentiation.                          The following are inadequately covered: partial          fraction decomposition, integrals of powers of          trigonometric functions, trigonometric substitutions, and          improper integrals.               ","accuracy_rating":5,"accuracy_review":" The diagrams are very good. I managed to spot six      errors:                        page 53, figure 2.3.a: It is not clear that the          function is defined at the discontinuities (This has been          discussed under Comprehensiveness).                          Page 83: ``the limit $\\displaystyle\\left[\\lim_{\\Delta          x\\rightarrow0}\\frac{a^{\\Delta x}}{\\Delta x}\\right]$          varies directly with the value of a''. I think that          ``varies directly'' usually means ``is directly          proportional to.'' This is a quibbling point, and I don't          know how it could have been worded better, certainly not          \"is a monotone increasing function of $a$.\"                          page 83: ``figure p. 4.3.'' (``p.'' should not be          there.)                          page 111: ``vertical asymptote where the          derivative is zero'' (should be ``where the          denominator is zero'').                          Page 163: $\\int x^3\\sqrt{1-x^2}$ should be $\\int          x^3\\sqrt{1-x^2}\\,dx$ (the ``$dx$'' is missing).                          Page 200, Exercise 9.3.1: ``$dy$'' missing at the end          of the second integral which should read          $\\int_1^4\\left(1+\\sqrt          y\\right)^2-\\left(y-1\\right)^2dy$.              ","relevance_rating":5,"relevance_review":"There are no problems.","clarity_rating":5,"clarity_review":"The style of writing is clear, informal, almost chatty.      The authors keep jargon to a minimum, perhaps to a fault. For      example, the term ``Riemann sum'' is not used even though      there is an example of calculating $\\int_0^x3t\\,dt$ using $n$      rectangles of equal width using the left endpoint      approximation and letting $n\\rightarrow\\infty$.      The style of the book is to work from the concrete to the      abstract, from the particular to the general. For example, to      introduce the idea of the derivative and to motivate the idea      of a limit they have a long discussion about the slope of the      tangent to the semicircle $y=\\sqrt{625-x^2}$ at the point      $(7,24)$. First working numerically, they calculate the slope      of the secant lines between $x=7$ and $x=7.1$. Next they find      the general formula \\[\\frac{\\sqrt{625-(7+\\Delta      x)^2}-24}{\\Delta x}\\] and substitute $\\Delta x=0.01$ to get a      better approximation for the slope of the tangent. There is a      link in Figure 2.1 to a      \\href{http://www.whitman.edu/mathematics/calculus/live/jsxgraph/secant_lines.html}{Sage      worksheet} of the function $y=2x(1-x)$ in which one end of a      secant line is fixed at $x=0.15$ but the other can be moved,      so it is possible to watch the secant line approach the      tangent line. Next they rationalize the previous expression      to get \\[\\frac{-14-\\Delta x}{\\sqrt{625-(7-\\Delta x)^2}+24}\\]      and argue that as $\\Delta x\\rightarrow0$ the slope of the      secant line approaches the slope of the tangent line,      $-\\frac{7}{24}$. They point out that we are able check this      answer because the line from the centre of a circle is      perpendicular to the tangent, so their slopes must be      negative reciprocals.      They continue by doing the same calculation but with 7      replaced by $x$ to get the slope at an arbitrary point on the      circle and then set $x=7$ to see that the new formula gives      the earlier answer. They then replace $\\sqrt{625-x^2}$ by      $f(x)$ get the derivative of an arbitrary function as the      limit of the difference quotient.      The three approaches used in this example (numerical,      graphical, and algebraic) together with the rather leisurely      pace help the student understand this difficult concept.      Unfortunately the authors are not consistent in the use of      this three-pronged attack. For example, their approaches to      the product rule and the chain rule are purely algebraic;      their argument is rigorous but doesn't give the student any      insight into what is happening. It would have been helpful to      have some visual representation of these rules, perhaps      something like the following figure:              image not available      Visualizations for the Product and Chain Rules.            For the most part the authors do not state general      results, but rather expect the student either to imitate the      process in the examples or to invent their own formulae. This      has the advantage of discouraging students from memorizing a      formula and ``plug and chug'' in exercises.           ","consistency_rating":5,"consistency_review":"Sometimes the authors use terminology before it is discussed.","modularity_rating":5,"modularity_review":"There are no problems","organization_rating":4,"organization_review":"I have a few minor concerns:                        Page 54, Exercise 2.5.4: assumes that the natural          logarithm $\\ln x$ is known (the logarithm function, $\\log          x$, is defined on page 80 and the natural logartithm          function, $\\ln x$ on page 83).                          Page 62: the authors assume that the meaning of $\\sum$          is known when they introduce the notation for a product,          $\\Pi_{k=1}^{n}f_k$. They do not define sigma notation          until page 150.                          Page 87: Exercise 4.7.22 asks the reader to use          implicit differentiation to find the derivative of          $y=\\log_ax$ but implicit differentiation is the topic of          the next section. In fact, using implicit differentiation          to find the derivative of $y=\\ln x$ starts of the next          section!                          Page 91: $\\mathbb R$ is used without any          explanation.                          Page 99: needs to be preceded by a discussion of even          and odd functions. which are not defined until page          112.                          Page 102: injective is used without          definition.                          Page 112, Exercise 5.5: students are asked to find          intercepts even though they are not discussed in the          text.                ","interface_rating":5,"interface_review":"The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader. I have only a minor concern: some of the figures are marked with \"(AP)\" which points to Sage worksheet or an interactive applet. I found that not all the Sage worksheets opened correctly with Internet Explorer (for example Figure 2.1) although they work fine in Firefox and Google Chrome.  ","grammatical_rating":5,"grammatical_review":"I didn't notice any.","cultural_rating":5,"cultural_review":"The examples are similar to those found in any Calculus text.","overall_rating":10,"overall_review":null,"created_at":"2013-10-09T19:00:00.000-05:00","updated_at":"2013-10-09T19:00:00.000-05:00"},{"id":94,"first_name":"Huimei","last_name":"Delgado","position":"Continuing Lecturer","institution_name":"Purdue University","comprehensiveness_rating":4,"comprehensiveness_review":"The book covers standard first semester calculus topics. Topics in the second semester calculus tend to vary a little more from program to program. For the second semester course some instructors might find this text missing some topics, such as first order differential equations. Overall, the text is structured, organized, clear, and free of major errors. It is definitely worth considering for those who are considering adopting an open textbook. Instructors will, however, likely need to provide more in-text examples and post-section exercises as the book does not provide as many as some instructors may like to have. Compared to a standard calculus text, this book has limited figures. For example, Section 4.8: Implicit Differentiation has no graphs presented. Students often find it difficult to understand and visualize what implicit differentiation is and a few graphs in this section would greatly benefit their understanding of the material. With that said, I also would like to point out that some of the currently present figures (marked with AP) allow user interactions, which promotes further understanding of the material with more ease.","accuracy_rating":5,"accuracy_review":"No issues discovered.","relevance_rating":5,"relevance_review":"Given the characteristics of the subject matter, I do not see the need to change any of the topics in the near or distant future. Overtime, in a very slow rate, some applications could be modified or added. The relevancy and longevity of the book is not an issue.","clarity_rating":5,"clarity_review":"Clarity is not an issue.","consistency_rating":5,"consistency_review":"The text is internally consistent in terms of the structure, style, terminology, and framework. In some places, the format is not entirely consistent. For example, on Page 69, Exercise 12 has a fraction written as $\\frac{169}{x}$ and the fraction in Exercise 22 is written as $1/x$. On Page 45, Exercise 6 has a period at the end of the question whereas all the other similar questions do not. These are very minor issues and they do not affect the effectiveness of the textbook.","modularity_rating":5,"modularity_review":"The division of chapters and sections of this text is very reasonable and is similar to many other calculus texts.","organization_rating":4,"organization_review":"Overall, the material is organized in a logical and standard order. The transition from section to section and from chapter to chapter is natural and smooth. Theorems, definitions, and examples, etc., are properly labeled and organized. For some examples and exercises, it would be better to arrange them differently as typically we put similar examples and exercises together and order them by increasing level of difficulty. In some cases, some examples and exercises appear to belong more appropriately in another section. For example, in Section 3.5: Chain Rule on Page 69, Exercises 3, 9, 17, 18, 19, 20, 21, and 23 are of the same type and Exercises 1, 2, and 22 are of the same type. Further, Exercises 1, 2, and 22 are not in the right section since it does not require the Chain Rule to solve these problems. Instead, they belong in Section 3.2. For Example 3.5.6. on Page 69, I believe most students' first instinct would be to use the Quotient Rule directly instead of rewriting the expression and using the Product Rule and the Chain Rule. Since directly applying the Quotient Rule is a more natural and straightforward method, I think a different example would work better here. Also, in terms of the difficulty level, this example is easier than the proceeding examples (Examples 3.5.4 and 3.5.5). Thus, it would be better to put 3.5.6. before 3.5.4.","interface_rating":5,"interface_review":"The book contains many hyperlinks which users can click on and conveniently go to the suggested definitions, theorems, figures, etc. In some cases, the link does not perfectly bring the users to the referred object. For example, on Page 43, if you click on the blue print of Theorem 2.3.6, it will bring you to the content that is right below the suggested theorem. On Page 91, if you click on the blue print of Example 4.8.3. in Exercise 10, it will bring you to the page that starts with the very end of Example 4.8.3. This also happens to many hyperlinks of figures that I have clicked on. However, these imperfect links do not cause much trouble in practice. For each of the exercise questions, there is a blue arrow following the question if the answer to the question is available. By clicking on the blue arrow, users can directly go to the corresponding answer. This is a wonderful feature that brings users lots of convenience. If there were links that can bring the users back from the answers to the questions it would be even more convenient.","grammatical_rating":5,"grammatical_review":"I did not discover any grammatical errors. On Page 21, in the first paragraph under the graphs, \"((see figure 1.3.1)\" has an extra left parenthesis. On Page 69, in Exercise 10, the parentheses in the numerator and the denominator should both be removed.","cultural_rating":5,"cultural_review":"No cultural insensitivity discovered.","overall_rating":10,"overall_review":"Overall it is a good text to consider if one is looking to move to an open textbook. Although some additional editing may be necessary, it provides a solid, main body for a first semester calculus text. I appreciate the author making this text open!","created_at":"2014-07-15T19:00:00.000-05:00","updated_at":"2014-07-15T19:00:00.000-05:00"},{"id":180,"first_name":"Xiaosheng","last_name":"Li","position":"Mathematics Instructor","institution_name":"Normandale Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The current open textbook under review is Whitman Calculus (single variable) in pdf format. The text covers appropriately all areas and ideas of standard calculus 1 and calculus 2 courses taught at US universities and colleges, although the ordering of the contents might be a little bit different from other popular calculus texts such as Stewart Calculus or Thomas’ Calculus. There are eleven chapters in the text including: chapter 1 analytic geometry, chapter 2 instantaneous rate of change: the derivative, chapter 3 rules of finding derivatives, chapter 4 transcendental functions, chapter 5 curve sketching, chapter 6 applications of the derivative, chapter 7 integration, chapter 8 techniques of integration, chapter 9 applications of integration, chapter 10 polar coordinates, parametric equations and chapter 11 sequences and series. The Whitman Calculus provides an effective index and glossary with linked page numbers for easy and quick referencing purposes.","accuracy_rating":5,"accuracy_review":"The contents of Whitman Calculus are accurate, error-free and unbiased at the same level as other popular calculus texts normally used by US institutions. Unavoidably there might be a few typos or minor changes, but the author maintains an active change log at http://www.whitman.edu/mathematics/multivariable/changelog.txt.","relevance_rating":5,"relevance_review":"As in other popular calculus textbooks, the contents in Whitman Calculus are up-to-date and will not make the text obsolete within a short period of time. The text is written in a logical manner and the content is arranged in chapters and sections, easy for future updates. In addition the author maintains an active change log in case there might be a few typos found or there might be minor changes needed in future.","clarity_rating":5,"clarity_review":"Whitman Calculus is written in a clear and straightforward manner. The technical terms are explained with enough context elaborating the terms for a better understanding, and are sometimes described in a conversational style which is friendly to readers.","consistency_rating":5,"consistency_review":"The text is consistent in terms of the terminology used in standard calculus. The text is written in traditional math textbook format logically with chapters, sections and exercises after each section, selected answers, useful formulas and the index.","modularity_rating":5,"modularity_review":"Whitman Calculus is easily and readily divisible into short sections that can be assigned section-wise within the course. The author even provides two additional versions of the text: 2-up version (two book pages per printed page) and 4-up version (four book pages per printed page). I think this is really a great feature for college professors and students using the text in classroom. The text can easily be reorganized and realigned without much disruption to the reader.","organization_rating":5,"organization_review":"The topics in Whitman Calculus are presented in a logical and clear manner. The text is organized in chapters and sections with a logical flow of the materials of calculus, covering chapter 1 analytic geometry, chapter 2 instantaneous rate of change: the derivative, chapter 3 rules of finding derivatives, chapter 4 transcendental functions, chapter 5 curve sketching, chapter 6 applications of the derivative, chapter 7 integration, chapter 8 techniques of integration, chapter 9 applications of integration, chapter 10 polar coordinates, parametric equations and chapter 11 sequences and series.","interface_rating":4,"interface_review":"The navigation of the text is simple and easy. The images/charts used in the text are nice and clean to reflect the related contents without any confusion to the reader. The text would be even better if the author could add more images/graphics to the text.","grammatical_rating":5,"grammatical_review":"The text generally contains no grammatical errors.","cultural_rating":5,"cultural_review":"The text is not culturally intensive or offensive in any way. The examples/exercises used in the text are appropriate in terms of races, ethnicities and backgrounds.","overall_rating":10,"overall_review":"I think that Whitman Calculus is a wonderful open source calculus textbook overall, and would like to recommend Whitman Calculus to math professors and college students for classroom use. One area in which the text could be improved is the volume of the exercises. The text could be enhanced if the author would add more exercises to the text. ","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/whitman-calculus?locale=es","updated_at":"2026-05-18T12:03:49.000-05:00"},{"id":57,"title":"College Trigonometry","edition_statement":null,"volume":null,"copyright_year":2011,"ISBN10":null,"ISBN13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"Covers chapters 10-11 of Precalculus.","contributors":[{"id":2217,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Carl","middle_name":null,"last_name":"Stitz","location":"Lakeland Community College","background_text":"Carl Stitz, Ph.D. is a Professor of Mathematics at Lakeland Community College outside of Kirtland, Ohio."},{"id":2218,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Jeff","middle_name":null,"last_name":"Zeager","location":"Lorain County Community College","background_text":"Jeff Zeager, Ph.D. is an Associate Professor of Mathematics at Lorain County Community College in Elyria, Ohio. Dr. Stitz and Dr. Zeager co-wrote this college algebra textbook with the vision of creating a high-quality, open-source textbook that is within reach and accessible to the average college student. In recognition of their work, both authors received the prestigious Faculty Innovator Award from the University System of Ohio in 2010."}],"subjects":[{"id":85,"name":"Geometry and Trigonometry","parent_subject_id":7,"call_number":"QA440-699","visible_textbooks_count":10,"url":"https://open.umn.edu/opentextbooks/subjects/geometry-and-trigonometry?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":54,"url":"http://www.stitz-zeager.com/Precalculus/Stitz_Zeager_Open_Source_Precalculus.html","year":null,"created_at":"2018-09-07T12:22:36.000-05:00","updated_at":"2018-09-07T12:22:36.000-05:00","name":"Stitz Zeager Open Source Mathematics"}],"formats":[{"id":62,"type":"PDF","url":"http://www.stitz-zeager.com/szct07042013.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":63,"type":"Hardcopy","url":"http://www.lulu.com/shop/carl-stitz-and-jeff-zeager/trigonometry%2C-3rd-edition/paperback/product-16218448.html","price":{"cents":1063,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":3,"reviews":[{"id":99,"first_name":"Tim","last_name":"Delworth","position":"Continuing Lecturer","institution_name":"Purdue University","comprehensiveness_rating":5,"comprehensiveness_review":"A quick glance at the table of contents shows that all the major topics of a college trigonometry course are included. We cover Conics and Rational Functions in our Trigonometry course. While not found in this textbook, they are covered in the companion College Algebra textbook. We will have to combine the two text books is some form to continue the same coverage as we have enjoyed in the past.","accuracy_rating":3,"accuracy_review":"Accuracy is something best judged when using the textbook during the semester and not during a quick review. It seems to be as accurate as any textbook I have used. I like the simple layout. The graphs and diagrams are clean and straight to the point. I am concerned that the few aviation problems use bearings, instead of a compass. Aviation uses due North as 0 degrees and the angles open clockwise to 360 degrees. As we have a very large Aviation Technology program at Purdue, we will have to edit the text for these problems.","relevance_rating":3,"relevance_review":"Trigonometry concepts have not changed for centuries and I expect they will not during my lifetime. The graphing calculator diagrams are fine as long as students are using that type of graphing calculator or if they are allowed to use one. However, that is the great thing about this format. As technology changes, we simple upload an updated version of the textbook. I do not see relevance as an issue.","clarity_rating":5,"clarity_review":"I like the ease of language and pace of the author's voice. It seems more of a conversion rather than a lecture. At some point, it is impossible to avoid mathematical talk, and students will have to read, and reread, sections to fully understand a concept. Brief history lessons as to why the word tangent is used is a nice touch. The grey boxes are easy to understand and highlight important information. The text is clean and to the point.","consistency_rating":5,"consistency_review":"The text is consistent and to the point. It looks to use the same tempo and language throughout the chapters. The pace is easy going. I did not see any large changes in language or evidence that different people wrote each chapter. It all fits nicely.","modularity_rating":5,"modularity_review":"This is tough to determine until we give is a serious look and see how it fits with our current course offering. It seems to be very easy to divide into lessons and rearrange if necessary. We have to get 40 lessons out of this textbook and it looks like that will be easy to accomplish. We will have to drag in some chapter and sections from the companion College Algebra text to complete our course. Again, that is the beauty of this format.","organization_rating":5,"organization_review":"Only 2 chapters, so hard to get disorganized, however, I like that it introduces the unit circle early. It has the normal flow through the topics. Again, we would have to use some of the earlier chapters from the companion College Algebra textbook to fill in the missing topics that are covered in our Trigonometry course.","interface_rating":5,"interface_review":"I do not see any problems with the graphs, diagrams, or examples. The textbook has very clean and clear graphs that add to the students understanding of the material. Now, to get the students to read and study the text...","grammatical_rating":5,"grammatical_review":"Wow, you are asking a math major to critique the textbook's grammar! It looks fine.","cultural_rating":5,"cultural_review":"No problems.","overall_rating":9,"overall_review":"As mentioned before, the aviation problems will have to be edited for accuracy. I am sure we will have other edits if we adopt this textbook, however, it provides a great platform for us to create exactly what we need.","created_at":"2014-07-15T19:00:00.000-05:00","updated_at":"2014-07-15T19:00:00.000-05:00"},{"id":3946,"first_name":"John","last_name":"Niss","position":"Professor of Mathematics","institution_name":"Valencia College","comprehensiveness_rating":4,"comprehensiveness_review":"The content is exactly what I would like for a trigonometry text with the bonus of dot products, projections and parametric equations. Those are in the last few chapters, so they are easily omitted. There are occasions when definitions for term (unit circle, for example) are not included; In that case the index indicates the term is defined on page 501 where the text I have starts on page 693. There must be a previous volume that I am not spotting. I'm sure if I did my research I could find it, though.","accuracy_rating":5,"accuracy_review":"I see no problems with the accuracy of the content. It's not always presented exactly as I would, but that's always the case with any text.","relevance_rating":5,"relevance_review":"The exercises in context in this text are not likely to become dated particularly quickly. It's a trigonometry text so a large portion of those problems from are physics or other sciences and will remain relevant.","clarity_rating":4,"clarity_review":"I understand why the authors might limit the white space in the exposition for the sake of a printed textbook. However, for the e-text version, the text sometimes felt a bit dense.","consistency_rating":5,"consistency_review":"This is a well written trigonometry text and the use of terminology and explanatory style is consistent throughout.","modularity_rating":5,"modularity_review":"Modularity is not really an issue with a Trigonometry text. The material is laid out in a very traditional way and in appropriate length sections. Reorganizing or realigning would be a rotten idea as the material develops in a logically consistent and constructivist approach which reorganizing would destroy.","organization_rating":5,"organization_review":"See the comment for Modularity. This text is very well organized and helps a student move through the development of the logic and skills necessary to master trigonometry.","interface_rating":5,"interface_review":"There are no problems with the interface.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors.","cultural_rating":4,"cultural_review":"There is no cultural insensitivity - unless you are a sasquatch. There are a whole bunch of examples involving them.  Examples seem to be conscious about not including any cultural context, which while not insensitive might be seen as a bit of a cop out.","overall_rating":9,"overall_review":"As instructional materials for a trigonometry course, this is a very reasonable option - particularly as it would be an over $100 savings for students over a traditional text, even used.","created_at":"2020-06-11T13:00:25.000-05:00","updated_at":"2020-06-11T13:00:25.000-05:00"},{"id":35857,"first_name":"Matthew","last_name":"Beyranevand","position":"Assistant Teaching Professor","institution_name":"University of Massachusetts Lowell","comprehensiveness_rating":4,"comprehensiveness_review":"The book is comprehensive in its coverage of trigonometry itself, with strong depth and logical organization. Its only notable gap is that it assumes integration with a companion algebra text for full precalculus coverage. Some topics could be enhanced further because of their importance (graphing sin and cos)","accuracy_rating":5,"accuracy_review":"The content is accurate and trustworthy for instructional use. A few minor typos appear, but there are no significant mathematical errors or biases that would limit its effectiveness in a college trigonometry course.","relevance_rating":5,"relevance_review":"The text is pedagogically and mathematically up-to-date, with strong long-term relevance. Its open license and modular design make it particularly well-suited for ongoing revision, ensuring it can remain current with minimal effort from instructors or institutions. The math does not change :)","clarity_rating":4,"clarity_review":"The text is clear and pedagogically strong, particularly in its explanations and examples. Minor issues with density and presentation prevent it from being exceptional, but it remains highly usable for most students and instructors. Could use some color.","consistency_rating":5,"consistency_review":"The text demonstrates a high level of internal consistency, making it reliable and easy to follow over the course of a semester.","modularity_rating":4,"modularity_review":"The text is flexible and adaptable for most course structures, with clear organization and reasonable independence between sections. Minor dependencies and occasional length/density prevent it from being fully modular, but it remains easy to reorganize with minimal effort.","organization_rating":5,"organization_review":"The text’s organization is a major strength. Its logical sequencing and consistent structure make it easy to follow and effective for teaching and learning. The text is very well organized, with topics presented in a logical and pedagogically sound sequence.","interface_rating":3,"interface_review":"The interface is reliable and usable but clearly dated. It works without major technical problems, but navigation and visual design are less refined than contemporary digital textbooks.","grammatical_rating":5,"grammatical_review":"No issues found.","cultural_rating":4,"cultural_review":"The text is respectful and unbiased, but largely neutral rather than actively inclusive. It avoids problems, though it could do more to incorporate diverse contexts and perspectives. SOmething that could be added is related to the historical development of Trig.  In particular the Indians.","overall_rating":9,"overall_review":"This is a high-quality, academically rigorous, and flexible open textbook. While it lacks modern design features, its clarity, depth, and adaptability make it a very strong choice for college trigonometry, particularly in instructor-led environments.","created_at":"2026-04-09T18:04:58.000-05:00","updated_at":"2026-04-09T18:04:58.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/college-trigonometry?locale=es","updated_at":"2026-05-18T12:03:49.000-05:00"},{"id":58,"title":"Precalculus","edition_statement":null,"volume":null,"copyright_year":2013,"ISBN10":null,"ISBN13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class. The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.","contributors":[{"id":3634,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Carl","middle_name":null,"last_name":"Stitz","location":"Lakeland Community College","background_text":"Carl Stitz, Professor of Mathematics at Lakeland Community College. Kent State University, PhD, Mathematics (Low Dimensional Topology)."},{"id":3635,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Jeff","middle_name":null,"last_name":"Zeager","location":"Lorain County Community College","background_text":"Jeff Zeager, Professor at Lorain County Community College, Science and Mathematics Division. Kent State University, BS, MS, PhD, Pure Mathematics."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://open.umn.edu/opentextbooks/subjects/calculus?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":135,"url":"http://www.stitz-zeager.com/Precalculus/Stitz_Zeager_Open_Source_Precalculus.html","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2018-09-07T12:22:37.000-05:00","name":"Stitz Zeager Open Source Mathematics"}],"formats":[{"id":194,"type":"PDF","url":"http://www.stitz-zeager.com/szprecalculus07042013.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2225,"type":"LaTeX","url":"https://stitz-zeager.com/latex-source-code.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"3.5","textbook_reviews_count":3,"reviews":[{"id":90,"first_name":"Mike","last_name":"Weimerskirch","position":"Lower Division Coordinator","institution_name":"University of Minnesota","comprehensiveness_rating":4,"comprehensiveness_review":"The book is thorough in its treatment of topics. It assumes some algebra skills, the first five chapters will go too quickly for a student that needs a comprehensive college algebra course, but the pace is appropriate for a two semester course designed to get students ready for calculus. Had this been a hard copy text, students would complain about its length (over 1000 pages). That's the beauty of open-source .pdf file texts, and the authors made use of it, including deep topics like rotated conics. It contains a discussion of matrices in the chapter on solving equations and dot products (but not cross products).","accuracy_rating":3,"accuracy_review":"I haven't used the text yet myself, and therefore can't verify that the solution to the problems are correct, but it is in its 3rd edition, so it is likely that lots of these kinks have been worked out. The presentation of the mathematics seems fairly standard.","relevance_rating":2,"relevance_review":"The text has almost no color and is lacking in graphics by today's standards. For example, it is noted that the integers, rationals, reals ... are 'nested' like Matryoshka dolls, but there is no picture, nor even a Venn diagram to illustrate the nesting. Other will contend I am wrong on this, but the degree-minute-second method of measuring angles is a thing of the past. This is one example of where the authors could have examined the standard ways we have taught things for decades and brought them up-to-date. Many of the graphics use a TI-8x series calculator. I am finding that a majority of my students use an online graphing utility (wolframalpha or desmos).","clarity_rating":3,"clarity_review":"The authors attempt to let their personality show in their writing with their humor, but it often comes off as an inside joke. If you have either of the authors as your professor, it probably seems like natural conversation, but I could see it as a bit distracting for most students. The mathematical content is very formal, (ordered pairs as defined as 'abscissa and ordinate') but presented in a very standard way. The graphs support the mathematics clearly.","consistency_rating":5,"consistency_review":"The format is similar to most formal mathematical texts. The authors have done a good job providing links to references. For example, when a theorem from a previous chapter is referenced, you can click on the link to go back and see the theorem. Unfortunately, you may not be able to get back. Problems are linked in a similar way. It is handy be alerted to a future problem that uses the current material, but if you take the link to look at the problem, you may not be able get back.","modularity_rating":3,"modularity_review":"Since the chapters and problem sections are numbered, it's not clear how the links could be reorganized. Otherwise, the material is subdivided in a fairly standard chapter/section/subsection hierarchy. Those that prefer to do trigonometry early could easily move chapter 10 ahead four chapters.","organization_rating":5,"organization_review":"Very standard for a math text, with one exception: The solutions to the exercises are given at the end of the section, not at the end of the book. Again, a great feature of open-source material is that if you prefer to have the answers at the end of the book, or in a separate volume all-together, it could be easily done.","interface_rating":3,"interface_review":"There are many links within the text, taking the reader to statements of previous theorems, previous examples, particular exercises which is a handy feature. Unfortunately, when you follow the link, you may not be able to get back. It seems to work back-and-forth in Firefox, but not in GoogleChrome. There are also links to more detailed work if necessary. The main text works out problems at a standard and appropriately small number of steps. For those whose algebra skills are weaker, there are links to more detailed work, which is handy.","grammatical_rating":3,"grammatical_review":"At times, sentences run on, with the sentence looking more like a paragraph and having multiple commas. Otherwise, the writing looks clean, although at quite a high level.","cultural_rating":4,"cultural_review":"The authors use standard wording to problems and don't try to personalize the material. For example, they say that 'a car is travelling at ...' rather than trying to name the person driving the car in a shallow attempt to include diversity. The book is neutral in this sense.","overall_rating":7,"overall_review":"Overall, the book is very formal in its definitions, which may be good for advanced high school students who will pursue degrees in math and science, but is likely beyond the level of college students taking precalculus. Composition of functions and one-to-one function are dealt with in a very formal algebraic way, and supported with brief graphical representations. The derivation of formulas is quite formal, leading to the formula being highlighted in a box, leaving the reader to believe that the result is an important formula to be memorized, and thus works well if you believe in memorization. If you want your students to pay attention to the process of creating the formula and the underlying concept, the layout of the book will be a hindrance.","created_at":"2014-07-15T19:00:00.000-05:00","updated_at":"2014-07-15T19:00:00.000-05:00"},{"id":33410,"first_name":"John","last_name":"Hammond","position":"Senior Educator","institution_name":"Wichita State University","comprehensiveness_rating":5,"comprehensiveness_review":"This book covers everything one would want to cover in a precalculus course  though with more emphasis on the algebra topics rather than trigonometry.","accuracy_rating":4,"accuracy_review":"I didn't notice any glaring errors in the content.","relevance_rating":4,"relevance_review":"The content is standard pre-calculus topics from algebra and trig. The material has fun \"weird dad\" style of jokes with exercises involving Sasquatch, for example. The footnotes add a fun element to the text but in a way that shouldn't wear out over time.","clarity_rating":4,"clarity_review":"The text is very clear for someone who is well-prepared for the material. That said, I taught with this book for three semesters and advocated its use for our department for a number of years. Many students reported that it was too much much for them - the book is exhaustive - and they found the presentation in the sections too verbose(!) (I personally disagree, but I'm not the student...). \r\n\r\nNew teachers of precalc also had trouble extracting a 16 week course from the 1000+ pages and needed specific guidance for what sections to cover, what to omit.  This isn't a bad thing, just worth noting for those considering adopting the text.","consistency_rating":4,"consistency_review":"I have no comment - the book is internally consistent mathematically and comically - the footnotes almost tell a brief story of Carl which is a fun touch in a math book.","modularity_rating":4,"modularity_review":"The text is very modular with the latex files allowing one to present either the entire book, just algebra, and just trigonometry. \r\nEach section itself is its own latex file, so one could extract any individual section easily for repurposing.","organization_rating":4,"organization_review":"The material is presented in a logical fashion, though I personally rearranged and expanded the trigonometry section to match my personal pedagogical preference.","interface_rating":5,"interface_review":"PDF is easy to read and scales well at different resolutions.","grammatical_rating":3,"grammatical_review":"The grammar seemed fine to me.","cultural_rating":4,"cultural_review":"I didn't see anything that was culturally insensitive and examples tend not use humans at all but instead Sasquatch, Fritzy the Fox, Chewbacca the Bunny, and other silly characters.","overall_rating":8,"overall_review":"As I noted above, I used the text for three semesters. I enjoyed the book and my students responded to it positively (it replaced a text that had cost at the time $306 for a one semester course).\r\n\r\nIt took some extra work on the part of my department to get everyone on board, but we're still using the text in our sections of precalculus after five years, which makes me rate this book quite highly.","created_at":"2021-10-14T10:14:39.000-05:00","updated_at":"2021-10-14T10:14:39.000-05:00"},{"id":35745,"first_name":"Nick","last_name":"Wintz","position":"Assistant Professor","institution_name":"Radford University","comprehensiveness_rating":4,"comprehensiveness_review":"The text is comprehensive from the perspective of preparing community college students for precalculus over two semesters. It does lack depth in modeling in both algebraic and trigonometric functions. Piecewise functions are barely covered, leading potential issues with one-sided limits later. Both sequences and conics are nice additions, while terse. These have been included for completeness or preparation of pre-engineering students.","accuracy_rating":4,"accuracy_review":"The absence of a codomain in the definition of a function leaves much to be desired. The concept of an onto function is also missing when introducing an inverse function, although this is fairly typical in the level of text.","relevance_rating":4,"relevance_review":"The contents of this text are standard for a precalculus course, with enough topics to allow an instructor to tailor their course to their individual needs. The big issue is that the market contains several similar texts more robust in applications and introduction to limits. It is serviceable as a free book for an introduction of these topics. However, for students interested in STEM or business, the lack of models means they would always be better served by other options.","clarity_rating":3,"clarity_review":"The text is written so that a high performing high school junior can understand the topic at hand. The language throughout the text is fairly student friendly and free of mathematical jargon. However, the authors sometimes \"tell\" rather than \"show\" an important concept. For instance, the authors express the relationship between degrees and radians in prose without any accompanying visual. This is a concept average students struggle with when presented with a given graphic, For students who struggle mathematically or learning the material for the first time, As a lot of students only look at the pictures/examples, this absence presents an additional obstacle for them to succeed in their course.","consistency_rating":4,"consistency_review":"The notion is consistent throughout and standard for this level of material.","modularity_rating":4,"modularity_review":"Mathematics is a discipline that in which concepts are built on previously covered material. This text follows suit. While most sections can be considered self-contained in their own right, students must be comfortable with earlier ideas. Students aren't going to understand transformation of functions in 1.7 if they skipped over learning functions in 1.2.","organization_rating":3,"organization_review":"The content is presented in a way conscientious student will be able to understand reading one section and then the next. Some topics would be better served in a slightly different order. For instance, the authors start building the notion of trigonometric identities and equations before students would have an idea what these functions looked like. This can present future problems when introducing inverse trig functions. The sections on vectors and parametric equations are also misplaced, largely to justify the inclusion of direction angles. However, as previously pointed out, these sections are written in such a way that an instructor can rearrange the material as they see fit.","interface_rating":5,"interface_review":"This is the strength of the text. The authors have an excellent LaTeX setup that makes concepts easily searchable. All figures are also generated in TeX that maintain the same consistency throughout. The authors are also kind enough to share their files so that instructors can use them for slides/assignments.","grammatical_rating":4,"grammatical_review":"The grammar in the text appears to be devoid of any obvious errors. This review is for the third edition, which explains their absence. There is also a fourth edition, not reviewed, but most likely to be very similar to the third.","cultural_rating":4,"cultural_review":"The text does not appear to favor any group over another or give any appearance that any group is being disparaged. The language is clear enough for students from multiple cultures to understand. Some students may be caught off guard by the use of the royal we, which is standard among mathematicians but far more noticeable in this text than comparable books.","overall_rating":8,"overall_review":"Not at this time.","created_at":"2026-01-18T19:13:20.000-06:00","updated_at":"2026-01-18T19:13:20.000-06:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/precalculus?locale=es","updated_at":"2026-05-18T12:03:49.000-05:00"},{"id":91,"title":"Vector Calculus","edition_statement":null,"volume":null,"copyright_year":2013,"ISBN10":null,"ISBN13":null,"license":"Free Documentation License (GNU)","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals. The book also includes discussion of numerical methods: Newton's method for optimization, and the Monte Carlo method for evaluating multiple integrals. There is a section dealing with applications to probability. Appendices include a proof of the right-hand rule for the cross product, and a short tutorial on using Gnuplot for graphing functions of 2 variables There are 420 exercises in the book. Answers to selected exercises are included.","contributors":[{"id":2056,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Michael","middle_name":null,"last_name":"Corral","location":"Schoolcraft College","background_text":"Michael Corral is an Adjunct Faculty member of the Department of Mathematics at Schoolcraft College. He received a B.A. in Mathematics from the University of California at Berkeley, and received an M.A. in Mathematics and an M.S. in Industrial \u0026 Operations Engineering from the University of Michigan."}],"subjects":[{"id":84,"name":"Calculus","parent_subject_id":7,"call_number":"QA150-272.5","visible_textbooks_count":31,"url":"https://open.umn.edu/opentextbooks/subjects/calculus?locale=es"},{"id":36,"name":"Pure","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":83,"url":"https://open.umn.edu/opentextbooks/subjects/pure?locale=es"},{"id":7,"name":"Mathematics","parent_subject_id":null,"call_number":"QA1","visible_textbooks_count":177,"url":"https://open.umn.edu/opentextbooks/subjects/mathematics?locale=es"}],"publishers":[{"id":44,"url":"http://www.mecmath.net/","year":2021,"created_at":"2018-09-07T12:22:36.000-05:00","updated_at":"2021-01-07T11:40:09.000-06:00","name":"Michael Corral"}],"formats":[{"id":54,"type":"PDF","url":"http://www.mecmath.net/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":55,"type":"Hardcopy","url":"https://www.lulu.com/shop/michael-corral/vector-calculus/paperback/product-7wd428.html?page=1\u0026pageSize=4","price":{"cents":1000,"currency_iso":"USD"},"isbn":null},{"id":2036,"type":"LaTeX","url":"http://www.mecmath.net/#Download:~:text=LaTeX%20source%20code%3A%20calc3book%2D1.0%2Dsrc.tar.gz","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":1,"reviews":[{"id":34367,"first_name":"Yaping","last_name":"Liu","position":"Professor","institution_name":"Pittsburg State University","comprehensiveness_rating":4,"comprehensiveness_review":"This book contains about enough material for a one semester multivariable calculus or a beginning vector calculus course. It is relatively easy to read and follow. At the end of each section a fair number of exercises are provided, which are divided into 3 categories, A, B, C, roughly based on the level of difficulty. A number of routine examples are provided to demonstrate mathematical concepts and basic techniques in calculation. Color-coded boxes are used in the text to highlight the definitions, theorems, and other important results. Answers and hints to selected exercises are provided in Appendix A toward the end of the book. A useful index is also included.","accuracy_rating":5,"accuracy_review":"This is a neatly organized little book on vector calculus. It is well written with mathematical accuracy. The proofs for some theorems are provided, while some others are left as exercises.","relevance_rating":4,"relevance_review":"This book is concise. The content is carefully filtered. Many relevant topics are omitted, only briefly treated, or left as exercises. The book is for those who share a similar preference over the topics as the author. An instructor will have limited choices. Or one can use the book by selecting the topics one likes and supplements it with content found elsewhere. I personally prefer that it contains some more advanced topics, such as the implicit function theorem and the Taylor series expansion of multivariable functions, and more involved real world examples in physical sciences so that it can also be used as a vector calculus textbook following the calculus sequence. There is such a need among senior or beginning graduate level STEM students. Expansion, if desired, can be done in future updates.","clarity_rating":5,"clarity_review":"This book is nicely structured. Mathematical concepts are sufficiently explained. Fully worked out examples are given as appropriate. Good quality figures are generated and included to illustrate the ideas. Very few long examples with tedious calculations are included. A good student should be able to understand most of the content through self-study.","consistency_rating":5,"consistency_review":"The book is carefully written. The notations and terms used are consistent throughout the book. The examples, definitions, theorems, and figures are numbered separately and sequentially in each chapter. Math styles and different fonts are used appropriately and consistently.","modularity_rating":4,"modularity_review":"The main content is divided into four chapters. Each chapter is then divided into a number of sections. An instructor can easily organize the content into units to suit the flow in their class. Reorganization would be relatively hard due partly to the logical dependence of the topics, which is typical for math textbooks, and partly to the fact that this book is already lean.","organization_rating":5,"organization_review":"The organization is clear. It follows a logical sequence of the topics from vectors in Euclidean space to vector-valued functions, then functions of several variables, and finally line and surface integrals. The content is arranged basically the same way as in other standard books on this subject.","interface_rating":4,"interface_review":"A bibliography is compiled. Further explanation of certain ideas can be found in a number of books referenced in the foot notes. Otherwise the book is self-contained. There are no hyperlinks. Images and charts are properly formatted with little distortion. The flow of the content is smooth and clear.","grammatical_rating":5,"grammatical_review":"It is well written with clear and straightforward English. I didn’t find any conspicuous grammatical errors.","cultural_rating":5,"cultural_review":"This book contains no offensive material. There is little evidence the author tried to come up with real world examples that are inclusive of races, ethnicities, and background. But by being culturally neutral, as most mathematics books are, the book is inclusive by default.","overall_rating":9,"overall_review":"The book's main strength is also its main weakness. By being focused on the selected topics it covers with little extra details or digression on other topics, it limits the way the book can be used. It can serve it's intended purpose very well, i.e., a textbook for calculus 3 or introductory vector calculus. To go beyond this level, it is necessary to supplement it with more advanced materials.","created_at":"2023-01-12T20:32:20.000-06:00","updated_at":"2023-01-12T20:32:20.000-06:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/vector-calculus?locale=es","updated_at":"2026-05-18T12:03:49.000-05:00"}],"links":{"self":"https://open.umn.edu/opentextbooks/subjects/pure.json?locale=es?page=1","total_pages":11,"total_count":102,"next":"https://open.umn.edu/opentextbooks/subjects/pure.json?locale=es?page=2"}}