{"data":[{"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":188,"title":"Linear Algebra","edition_statement":null,"volume":null,"copyright_year":2016,"ISBN10":null,"ISBN13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end, we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independence and dimension given to ready students for a thorough treatment of eigenvectors and diagonalization. The dimension formula therefore appears quite late, since we prefer not to elevate rote computations of column and row spaces to a pedestal. The book ends with applications–least squares and singular values. These are a fun way to end any lecture course. It would also be quite easy to spend any extra time on systems of differential equations and simple Fourier transform problems.","contributors":[{"id":3658,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"David","middle_name":null,"last_name":"Cherney","location":"UC Davis","background_text":"David Cherney, Lecturer, Mathematics, UC Davis. Ph.D., 2010, University of California, Davis."},{"id":3659,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Tom","middle_name":null,"last_name":"Denton","location":"The Fields Institute and York University","background_text":"Tom Denton. York University and the Fields Institute, Toronto, Canada. Postdoctoral research with Nantel Bergeron and Mike Zabrocki on k-Schur functions and other topics in algebraic combinatorics. Fulbright Scholar, Maseno University, Kenya. Project concerned using e-learning platforms and emerging technologies to improve the teaching of mathematics in the developing world. Led math camps for secondary students, and co-founded a new technology hub in Kisumu, Kenya. PhD, University of California, Davis."},{"id":3660,"contribution":"Author","primary":false,"corporate":false,"title":null,"first_name":"Andrew","middle_name":"K.","last_name":"Waldon","location":"UC Davis","background_text":"Andrew Waldron. Professor, Mathematics, UC Davis. Waldron's research is devoted to a broad range of problems in theoretical and mathematical physics. In particular he has made an important contribution to the conjectured Banks-Fishler-Shenker-Susskind (BFSS) matrix model of string theory and M-theory. String theory is a proposed perturbative theory that would unify all of the fundamental forces of physics; in other words it is a \"theory of everything\". Its non-perturbative counterpart is a hypothetical theory called M-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":134,"url":"https://www.math.ucdavis.edu/~linear/","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2019-12-29T15:55:46.000-06:00","name":"University of California, Davis"}],"formats":[{"id":420,"type":"PDF","url":"https://www.math.ucdavis.edu/~linear/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2232,"type":"LaTeX","url":"https://www.math.ucdavis.edu/~linear/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"3.5","textbook_reviews_count":2,"reviews":[{"id":274,"first_name":"James","last_name":"Wilson","position":"Assistant Professor","institution_name":"Colorado State University","comprehensiveness_rating":4,"comprehensiveness_review":"This text covers the material expected in a first term course on undergraduate Linear Algebra, especially in the considerations of a course with many engineering majors.  Major focus is on solving systems of linear equations, Gaussian elimination, matrix decompositions, e.g. LU, LUP, bases, determinants, and eigen theory.  Several less standard topics are included in the closing chapters including kernels, the simplex algorithm, and idempotent projection operators.  Most proofs are held to a minimum or postponed until final chapters thus making it less appropriate for theory based courses.  \r\n\r\nThis text shines in the light of applications involving problems of optimization and tools for numerical methods.  The authors do not wait to introduce helpful early notions of length and and angles which aids in discussion of geometric significance. The orthogonalization process is routine but convincing, and the simplex algorithm has been elegantly simplified in the second chapter without losing accuracy. \r\n\r\nA surprising weakness in this text is the lack of sparse matrices, minimum polynomials, Krylov methods,, and practical general methods to compute characteristic polynomials. Instead all applications concentrate on archaic topics of LU and QR style problems.  This makes the text a less applicable to students of computer and data sciences.\r\n\r\nFor teaching purposes the book also includes a range of sample midterms and a corpus of WebWork enabled online assignments also available for download.  \r\n\r\nWhile the text demonstrates a careful editorial hand, the online assignments are largely ``as is''.  For use within \r\na course it is likely necessary to create new assignments using the exercises contained there in.  That process is not completely transparent since exercises are given unhelpful title such as \"lecture-10\" and these seem to have no correlation with the organization within the text.  There are also occasional exercises that are corrupted and not useable within the current versions of WebWork.  A final point of concern with the online assignments is that many exercises appear to ask for answers in peculiar formats, perhaps to assist in making them easy to check automatically, however this is certainly not always the case.  For example in one instance users are asked to compute eigenvalues and eigenvectors, but the assignment will only accept eigenvectors of unit length.  \r\n\r\nOn the other hand, these reflect a good initial source of problems and substantial investment which will improve overtime with additional exercises.\r\n","accuracy_rating":4,"accuracy_review":"In most standard ways this text is consistent with traditional philosophies for teaching Linear Algebra.  \r\nIt is especially sharp about providing simple discussions of matrix decompositions without losing nuances.\r\n\r\nHowever, some unfortunate logic issues arise.  For example, the authors define all eigenvectors to be non-zero, but then remark that the set of eigenvectors of a fixed eigenvalue form a subspace ignoring the clear omission they have made of the zero vector.  This can be remedied in lectures but it would seem that a text on the subject should settle such confusion preemptively.\r\n\r\nAn unfortunate illusion occurs in the development of characteristic polynomials.  The authors make a wonderful presentation of the determinant  and eigenvalues including discussion in geometric terms.  They then derive a formula for the determinant polynomial and show how to evaluate it efficiently using elementary matrix operations.  However, they do not disclose the impossibility to use such methods to compute the characteristic polynomial (whose entries are variables).  Given emphasis on applications it seems surprising not see mention of actual efficient methods to compute characteristic and minimum polynomials.  (A single exercise considers this point but the message is lost.)","relevance_rating":3,"relevance_review":"This book is in the upper range of texts.  Compared to alternative text the graphics could be characterized as dated and at times comical.  However the content is easily gleaned from the graphics so it does not provide an obstacle to learning.  This text will remain in use provided the supplemental material, i.e. online assignments, and the graphics continue to improve.","clarity_rating":5,"clarity_review":"This is very well written.  It reflects multiple perspective: geometric, algebraic, and heuristic.  It shows a deep understanding of the topics and a comfort level with teaching.  It can be understood by students and taught from easily by first time teachers such as graduate students and post-docs.  The only imperative is that each instructor spend adequate time considering the flow of the chapters and sections since some topics are briefly introduced almost as tangents and their complete treatment awaits later development.  Skimming the chapter and lure the unprepared instructor into spending too much time on a side topic.","consistency_rating":5,"consistency_review":"The notation is standard and fitting with the diversity one sees in most of algebra.  For example lower case letters are reserved for vectors and numbers, uppercase for matrices and spaces.  These conventions are maintained throughout.","modularity_rating":4,"modularity_review":"Each chapter is self-contained enough that one can easily assemble a course in a different order than the table of contents.  In fact the authors include a plausible schedule in their introduction which demonstrates such as permutation of content.   On the other hand, there are certain dependences that must be maintained such as presenting determinants before eigentheory. While that dependence is not required by linear algebra, the approach to eigentheory taken in this text relies solely on the characteristic polynomial defined as det(xI-M) and so an other treatment would need to come from supplemental material on Krylov methods.","organization_rating":4,"organization_review":"The text is organized in a familiar manner ideal for those searching first to find applications of linear algebra.  It is logic and can be reordered to some degree.  It is less flexible for courses electing to focus on theory.","interface_rating":4,"interface_review":"This text is easy to find, download, copy, and print.  The PDF offers links that seem not to work but there are instructions on how to modify this to individual courses using the WebWork system.  ","grammatical_rating":5,"grammatical_review":"I have not found any errors, but then if I did it would be the pot calling the kettle black!","cultural_rating":1,"cultural_review":"This is not culturally relevant, but that seems a criteria I would doubt matters for text in mathematics.","overall_rating":8,"overall_review":null,"created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":1585,"first_name":"Bruce","last_name":"Lundberg","position":"Chair, and Professor of Mathematics","institution_name":"Colorado State University - Pueblo","comprehensiveness_rating":4,"comprehensiveness_review":"Treats the standard topics in Linear Algebra, plus Linear Optimization (Simplex Method and applications), and the SVD. An exploratory introductory first chapter is non-standard but interesting for engaging students right away in seeing and asking about the meaning of Linear Algebra. The Index is adequate and has links to pages cited. There was no collected glossary.  Cross product is assumed, but then stated a few pages later, and not covered (not untypical for LA books). ","accuracy_rating":4,"accuracy_review":"Apart from a number of typo's, the mathematical accuracy looks high.","relevance_rating":3,"relevance_review":"The material covers the standard topics, but the exercise sets and some terms, notations can be nonstandard.  The treatment of hyperplanes, and exercises about them were hard for students (and the other faculty they sought help from).  The matrix and vector entry superscript-subscript notation is neat for preparing engineers for tensor analysis notations, but is non-standard and somewhat confusing for students at the introductory level.  \nLongevity depends on the direction the LA curriculum for engineers evolves. ","clarity_rating":3,"clarity_review":"The treatment of hyperplanes, and exercises about them were hard for students (and the other faculty they sought help from).  The matrix and vector entry superscript-subscript notation is neat for preparing engineers for tensor analysis notations, but is non-standard and somewhat confusing for students at the introductory level.  \nLongevity depends on the direction the LA curriculum for engineers evolves. \n\nThe lack of clarity to other faculty and to students could be an artifact of the non-standard exposition, problems and notations. Faculty just jump in to help, looking for notations they know. When they have to read through the text, and the students see faculty \"do not know how to do the problems\", this gives the limping ones an excuse or scandal. \n\nThat said, this very quality can cause the more capable and motivated students to learn more, and make cheating or mimicry harder for students to carry off.","consistency_rating":3,"consistency_review":"This is hard to tell for sure, without a very careful and thoughtful read and use. But, my impression is that the four author effort shows somewhat in a lack of pedagogical consistency.","modularity_rating":3,"modularity_review":"This is difficult. I would have to skip some sections and chapters in my course, but the non-standard exposition and problems assume the perspectives and exposition of former chapters.","organization_rating":3,"organization_review":"It seems a bit odd or non-standard that Matrices come after vector spaces and after linear transformations. But I think this works in the spirit of the text, which seems to be to introduce the topics after motivation and applied context has been developed.","interface_rating":5,"interface_review":"Text interface is of high quality.","grammatical_rating":4,"grammatical_review":"The writing, apart from some typos, is good.","cultural_rating":5,"cultural_review":"The text is culturally relevant and respectful.","overall_rating":7,"overall_review":"Webworks and Movie ancilarries are supplied!","created_at":"2018-02-01T18:00:00.000-06:00","updated_at":"2018-02-01T18:00:00.000-06:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/linear-algebra-2016?locale=es","updated_at":"2026-05-18T12:03:49.000-05:00"},{"id":533,"title":"Linear Algebra with Applications","edition_statement":"2023-A-D","volume":null,"copyright_year":2023,"ISBN10":null,"ISBN13":null,"license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"unknown","description":"The aim of this textbook is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The content has enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners, whereas Chapters 5–9 contain a second semester course. The textbook is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).","contributors":[{"id":4444,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"W. Keith","middle_name":null,"last_name":"Nicholson","location":"University of Calgary","background_text":"Dr. W. Keith Nicholson earned his undergraduate Degree in Applied Mathematics at the University of Alberta, and received his Ph.D. in Pure Mathematics from the University of California at Santa Barbara in 1970. He then moved to the University of Calgary, and has been a professor in the Department of Mathematics and Statistics since 1979, where he has been carrying out research in a branch of algebra called \"Ring Theory\". His continuing interest in teaching undergraduate students has led to another book in Linear Algebra (now in its third edition), a text in Abstract Algebra (second edition), and the creation (with Professor Claude Laflamme), of an internet tutorial for Linear Algebra called ILAW (Interactive Linear Algebra on the Web). Keith is married and has two grown sons."}],"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":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://open.umn.edu/opentextbooks/subjects/applied?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":508,"url":"https://collection.bccampus.ca/textbooks/linear-algebra-with-applications-2023-a-d-vretta-lyryx-inc-446/","year":2021,"created_at":"2018-09-07T12:22:40.000-05:00","updated_at":"2025-03-12T08:22:51.000-05:00","name":"Lyryx"}],"formats":[{"id":994,"type":"PDF","url":"https://collection.bccampus.ca/textbooks/linear-algebra-with-applications-2023-a-d-vretta-lyryx-inc-446/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":1408,"type":"Hardcopy","url":"https://opentextbook.docsol.sfu.ca/store/product/linear-algebra-with-applications-2023-a-d-lyryx/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":3,"reviews":[{"id":2517,"first_name":"Sandra","last_name":"Sze","position":"Assistant Professor","institution_name":"LAGCC","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers topics in our syllabus.","accuracy_rating":5,"accuracy_review":"I did not find any error reading it.","relevance_rating":5,"relevance_review":"The application sections are good.","clarity_rating":5,"clarity_review":"The text was easy to read.","consistency_rating":5,"consistency_review":"The text is consistent in terminology.","modularity_rating":5,"modularity_review":"The text is easily divided into small sections.","organization_rating":5,"organization_review":"The order of the topics made sense to me.","interface_rating":5,"interface_review":"I did not experience any issues with the interface.","grammatical_rating":5,"grammatical_review":"I did not find grammatical errors.","cultural_rating":5,"cultural_review":"It is not culturally insensitive.","overall_rating":10,"overall_review":"I plan on using this for my course next semester.","created_at":"2019-01-13T11:45:12.000-06:00","updated_at":"2019-01-13T11:45:12.000-06:00"},{"id":2688,"first_name":"Sergio","last_name":"Maria-Fagundez","position":"Mathematics Instructor","institution_name":"Thomas Nelson Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The book covers all main areas and ideas in any regular Linear Algebra course such as: Determinants, Vector Spaces, Eigenvalues, etc. It does a great job in showing real life applications of the concepts presented throughout the book.","accuracy_rating":5,"accuracy_review":"After reading several chapters in the book, I have not found any errors, typos, etc. They did a great job proof reading the material before publishing it.","relevance_rating":5,"relevance_review":"The text content is actual. The book makes reference to companies like Google, Computer design, etc. when presenting their ideas and applications. The wrote them in such a way that it will be very easy in the future to update their content.","clarity_rating":5,"clarity_review":"The text contains several paragraphs inside every section where they explain in every day English how the ideas presented are used in real life. They have done an excellent job using LaTeX. The graphs presented are of a superb quality. It is very easy to notice that the author took the extra time to make sure everything was presented in a very professional way.","consistency_rating":5,"consistency_review":"The text is self-consistent on its entirety. The notation, font type, etc. remains the same from section to section.","modularity_rating":5,"modularity_review":"The text clearly shows with headings and colors where sections, homework, applications, etc. are presented. The way it is organized makes it very easy to read for instructors and students alike.","organization_rating":5,"organization_review":"The topics are presented in the logical way any Linear Algebra course is typically presented. They have been very thoughtful about including a couple of introductory chapters before presenting the general idea of a Vector Space. This is of great help for students trying to understand the common properties behind every single Vector Space in Mathematics.","interface_rating":5,"interface_review":"The pdf shows no navigation problems when opening it in different browsers like Google Chrome, Safari and Internet Explorer. All book elements such as text, graphs, headings,... look extremely clear and neat.","grammatical_rating":5,"grammatical_review":"I have not found any grammatical errors after reading most of the pdf. The wording use is clear, consistent and to the point.","cultural_rating":5,"cultural_review":"I have not found any content that could be insensitivity or offensive to any culture. I have not found any references to race, sex or religion.","overall_rating":10,"overall_review":"The author made a SUPERB job when creating this text. Explanations are very clear. There are plenty of examples for the students to reference to. The homework assignment problems cover a wide variety of difficulty levels, from the most basic to the most advance. Above all, I have really liked the amount of real life applications presented in pretty much every single chapter of the book.","created_at":"2019-03-21T10:55:48.000-05:00","updated_at":"2019-03-21T10:55:48.000-05:00"},{"id":33629,"first_name":"suman","last_name":"balasubramanian","position":"Associate professor of mathematics","institution_name":"DePauw University","comprehensiveness_rating":4,"comprehensiveness_review":"The book is a well written standard textbook in linear algebra that covers all the topics essential for a one to two semester sequence of the course.","accuracy_rating":4,"accuracy_review":"The content is accurate and virtually error free..","relevance_rating":4,"relevance_review":"The book is a well written standard textbook in linear algebra that covers all the topics essential for a one to two semester sequence of the course. The applications are relevant and fairly up to date with current trends. A suggestion would be to consolidate the applied topics found in each chapter and introduce them as a stand-alone chapter at the end of the text.  This would help in the addition or updating of applied topics as and when necessary. It would also help in covering the necessary topics during the course and then introducing the  applications in the end.","clarity_rating":4,"clarity_review":"The material in the text is presented in detail in a logical and clear manner. Sometimes the author goes into greater depth than necessary in each section making it a bit difficult to navigate through them.","consistency_rating":5,"consistency_review":"The book is very consistent in its usage of terminology.","modularity_rating":3,"modularity_review":"No comments here.","organization_rating":3,"organization_review":"The material in the text is presented in detail in a logical and clear manner. Sometimes the author goes into greater depth than necessary in each section making it a bit difficult to navigate through them.","interface_rating":4,"interface_review":"No comments.","grammatical_rating":5,"grammatical_review":"No grammatical errors found so far.","cultural_rating":4,"cultural_review":"N/A","overall_rating":8,"overall_review":null,"created_at":"2021-12-31T20:02:09.000-06:00","updated_at":"2021-12-31T20:02:09.000-06:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/linear-algebra-with-applications?locale=es","updated_at":"2026-05-18T02:09:55.000-05:00"},{"id":210,"title":"Linear Algebra, Theory And Applications","edition_statement":null,"volume":null,"copyright_year":2012,"ISBN10":null,"ISBN13":null,"license":"Attribution-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"unknown","description":"This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants. The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.","contributors":[{"id":3661,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Kenneth","middle_name":null,"last_name":"Kuttler","location":"Bringham Young University","background_text":"Kenneth Kuttler, Professor of Mathematics at Bringham Young University. University of Texas at Austin, Ph.D. in Mathematics."}],"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":255,"url":"http://www.saylor.org/site/wp-content/uploads/2012/02/Linear-Algebra-Kuttler-1-30-11-OTC.pdf","year":null,"created_at":"2018-09-07T12:22:38.000-05:00","updated_at":"2018-09-07T12:22:38.000-05:00","name":"Saylor Foundation"}],"formats":[{"id":421,"type":"PDF","url":"http://www.saylor.org/site/wp-content/uploads/2012/02/Linear-Algebra-Kuttler-1-30-11-OTC.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2221,"type":"eBook","url":"https://books.apple.com/us/book/linear-algebra-theory-and-applications/id553290698","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":2,"reviews":[{"id":317,"first_name":"Leo","last_name":"Butler","position":"Associate Professor","institution_name":"North Dakota State University","comprehensiveness_rating":5,"comprehensiveness_review":"This is intended as a text for a second linear algebra course. In addition to covering the expected topics (in no particular order: linear transformations, matrices, row reduction, determinants, characteristic polynomial, spectral theory), the text starts with a chapter which could be used as a text for a course on the foundations of mathematics and it ends with chapters on analysis and algebra/number theory.\r\n\r\nThe text includes an index.","accuracy_rating":5,"accuracy_review":"The text is quite carefully written.","relevance_rating":5,"relevance_review":"The text is likely to be useful to students beyond this course as a reference. In many cases, it anticipates more general results and sets up the statement of results in R^n to mirror those more general results.","clarity_rating":5,"clarity_review":"Overall, the text is well-written. The author spends time introducing terminology. The only fault I find is the repeated editorializing, which is the author talking to the professor not the student.","consistency_rating":5,"consistency_review":"The text is consistent in its use of terminology and notation.","modularity_rating":5,"modularity_review":"The book has a clear skeleton which covers the content of a second course in linear algebra, along with more than enough material to add in as needed.","organization_rating":4,"organization_review":"The text is coherent and largely well-organized. However, I would not introduce determinants before row operations and factorizations.","interface_rating":5,"interface_review":"The text is easily viewed in a pdf reader.","grammatical_rating":5,"grammatical_review":"There are no grammatical errors.","cultural_rating":5,"cultural_review":"There are no obvious examples of offensive or insensitive material in the text.","overall_rating":10,"overall_review":"The author is to be commended for his work. He has clearly devoted a substantial amount of time and energy in preparing a text that is well-structured, easy to read, and free of typographical errors.","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":4144,"first_name":"Aida","last_name":"Galeb","position":"Assistant Teaching Professor","institution_name":"University of Massachusetts Lowell","comprehensiveness_rating":5,"comprehensiveness_review":"The book has detailed explanations of many topics in linear algebra. The theorems and proofs are well phrased. There are lot of examples to support the theory. Many problems are provided for additional practice.","accuracy_rating":5,"accuracy_review":"Without having enough time to go through every section in detail, the book is error-free.","relevance_rating":5,"relevance_review":"The content is very relevant. The application examples are well chosen to demonstrate the theory and will not be outdated.","clarity_rating":4,"clarity_review":"The text is clear, well written. The notation is sometimes a bit cumbersome but the author tries to give the most general form which requires more complex notation.","consistency_rating":5,"consistency_review":"The book is consistent and connected throughout.","modularity_rating":3,"modularity_review":"Because of the internal consistency and connectivity it would be difficult to pick and choose the topics out of the order. Notation, definitions, and the theorems throughout the book are related.","organization_rating":5,"organization_review":"The book is well organized by topics, prepares the reader for what is coming next.","interface_rating":5,"interface_review":"No issues in navigating through the book.","grammatical_rating":5,"grammatical_review":"No grammatical errors.","cultural_rating":5,"cultural_review":"The text is not culturally insensitive in any way.","overall_rating":9,"overall_review":"The book has very good approach to linear algebra. It covers many topics and there are a lot of great applications. The theorems and proofs are well presented. There is so much material in the book that it would be impossible to use it in a one semester LA undergraduate course. It can be used by someone interested in linear algebra topics as a self-study course or as a reference book.","created_at":"2020-06-29T15:52:32.000-05:00","updated_at":"2020-06-29T15:52:32.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/linear-algebra-theory-and-applications?locale=es","updated_at":"2026-05-18T02:08:40.000-05:00"},{"id":187,"title":"A Computational Introduction to Number Theory and Algebra","edition_statement":null,"volume":null,"copyright_year":2009,"ISBN10":null,"ISBN13":null,"license":"Attribution-NonCommercial-NoDerivs","language":"eng","accessibility_statement":null,"accessibility_features":"unknown","description":"All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well. The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures. There are a few sections that are marked with a “(∗),” indicating that the material covered in that section is a bit technical, and is not needed else- where. There are many examples in the text, which form an integral part of the book, and should not be skipped. There are a number of exercises in the text that serve to reinforce, as well as to develop important applications and generalizations of, the material presented in the text. Some exercises are underlined. These develop important (but usually simple) facts, and should be viewed as an integral part of the book. It is highly recommended that the reader work these exercises, or at the very least, read and understand their statements. In solving exercises, the reader is free to use any previously stated results in the text, including those in previous exercises. However, except where otherwise noted, any result in a section marked with a “(∗),” or in §5.5, need not and should not be used outside the section in which it appears. There is a very brief “Preliminaries” chapter, which fixes a bit of notation and recalls a few standard facts. This should be skimmed over by the reader. There is an appendix that contains a few useful facts; where such a fact is used in the text, there is a reference such as “see §An,” which refers to the item labeled “An” in the appendix.","contributors":[{"id":2858,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Victor","middle_name":null,"last_name":"Shoup","location":"New York University","background_text":"Victor Shoup is a Professor in the Department of Computer Science at the Courant Institute of Mathematical Sciences, New York University."}],"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":35,"name":"Applied","parent_subject_id":7,"call_number":"QA37.3","visible_textbooks_count":48,"url":"https://open.umn.edu/opentextbooks/subjects/applied?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":118,"url":"http://shoup.net/ntb/","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2019-12-29T15:53:58.000-06:00","name":"Cambridge University Press"}],"formats":[{"id":887,"type":"PDF","url":"http://shoup.net/ntb/ntb-v2.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":3,"reviews":[{"id":459,"first_name":"William","last_name":"McGovern","position":"Professor","institution_name":"University of Washingon","comprehensiveness_rating":5,"comprehensiveness_review":"As promised by the title, the book gives a very nice overview of a side range of topics in number theory and algebra (primarily the former, but with quite a bit of attention to the latter as well), with special emphasis to the areas in which computational techniques have proved useful.  There is a very good index and glossary and a good review of notation and basic facts in the first chapter.","accuracy_rating":5,"accuracy_review":"The content is very accurate ad up to date.  I see no signs of bias.","relevance_rating":5,"relevance_review":"The format of the book makes it especially easy to update as advances in the subjects occur, particularly computational advances.  References are given to websites as well as books.","clarity_rating":5,"clarity_review":"The prose is very lucid and easy to follow.  Many examples are given and difficult ideas are introduced gradually.  The many relationships between number theory and algebra are explored in detail, each subject yielding important insights into and applications of the other.  No jargon is used and terminology is carefully explained.","consistency_rating":5,"consistency_review":"The book has a very consistent framework and a nice flow from one chapter to the next.  As mentioned above, relationships between the two subjects of the title are emphasized.","modularity_rating":5,"modularity_review":"The book is nicely broken up into manageable sections that would fit well into a lecture course.  Interdependences among chapters are clearly indicated.","organization_rating":5,"organization_review":"The topics are presented clearly and logically with relationships among them clearly pointed out and discussed in detail.","interface_rating":5,"interface_review":"All pages display very well on my screen, with no legibility or distortion issues that I could see.","grammatical_rating":5,"grammatical_review":"The grammar seems fine.","cultural_rating":5,"cultural_review":"This is not relevant for a mathematics text, but I saw nothing that would be offensive to a reader of any ethnic background.","overall_rating":10,"overall_review":"I would be happy to teach a course out of this book.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":485,"first_name":"Michelle","last_name":"Manes","position":"Associate Professor","institution_name":"University of Hawaii","comprehensiveness_rating":4,"comprehensiveness_review":"The text is so comprehensive that it feels overwhelming.  The author wanted to include all of the mathematics required beyond a standard calculus sequence.  However, the mathematical maturity required to read and learn from this text is quite high.  \n\nThe first two chapters cover much of a standard undergraduate course in number theory, built up from scratch.  However, it almost completely lacks numerical examples and computational practice for the students, which would give those new to the material time and experience in which to digest, assimilate, and understand the material.  I would think that a book targeted at this level of mathematical sophistication would assume students are comfortable with (for example) the most basic notions of group theory or the idea of equivalence classes. \n\nI can't imagine an appropriate audience for this text: one with the ability to read and work entirely at this abstract level but without any (or most) of the mathematical preparation provided in at least half the chapters.","accuracy_rating":5,"accuracy_review":"I found no mathematical errors.  The mathematical presentation is rigorous, clear, and well-explained.  It can be terse at times, skipping steps and making conceptual leaps that will be challenging for all but the very best students.","relevance_rating":4,"relevance_review":"The book covers both standard background that will always be relevant for these topics: the number theory and algebra background, the probability theory.  The computational chapters use pseudocode, so they will not be quickly outdated when new languages become fashionable.  Most of the algorithms studied are quite \"classical\" (as much as that makes sense for computer science), with modern ideas and developments usually relegated to \"Notes\" at the end of the computational chapters.  This will, of course, become outdated with new research in computer science.  But any faculty member who keeps up with the relevant research will be able to mention new developments to students, and it will not interrupt the flow of the ideas at all.","clarity_rating":4,"clarity_review":"The book is exceedingly well written, though it is at a very high level.  It is not \"friendly\" or \"chatty\" as you will find with many number theory books targeted to undergraduates.  For many students this will detract from clarity because they do not yet have the mathematical sophistication to work at this level.","consistency_rating":5,"consistency_review":"The book does an excellent job of consistency of notation.  For example, it starts with a development of number theory concepts, and develops notation for residue classes in the integers modulo n.  Later in the chapters on groups and rings, this same notation is used in more general situations.  Whenever there is the potential for confusion (for example, in using \"a mod b\" as a binary operation as is common in computer science versus using \"a is congruent to x mod b\" as is more standard in mathematics) the author is careful to point out the dual meanings and to warn the reader that there is some overloading of terminology.  It is unavoidable that this will happen in any book that treats both subjects seriously, and the author is careful with notation and keeps potential confusion to a minimum.","modularity_rating":4,"modularity_review":"The book has 21 chapters, each with several sections.  Most, but not all, sections end with a set of exercises.  Essential exercises are underlined (a very nice feature!) and optional sections are indicated with an asterisk.  What would be helpful would be some suggested paths through the text for various purposes.  I don't think it would be appropriate in any class to start at Chapter 1 and and work through all (or even most) of the content.  I imagine that most classes would skip the background material and head straight for the computational chapters, with the background there \"as needed\" for the students.","organization_rating":4,"organization_review":"My main comment about the structure is that the mathematics chapters and the computational chapters seem to be separated.  For example, the chapter on \"Congruences\" covers a tremendous amount of number theory, not all of which falls naturally (in my mind) under that heading.  Chapter 1 has a section on \"Ideals and greatest common divisors,\" but Euclid's Algorithm is not tackled until Chapter 4 (a more computational chapter).  As I read, I often felt \"now we are doing mathematics... now we are concerned with computational questions.\"  There are natural places of overlap (like Euclid's algorithm), and they are separated rather than treated more holistically.","interface_rating":4,"interface_review":"I read a standard PDF file.  There were a few hyperlinks (from the table of contents to section headings, for example), but not much else in the way of interface.  Everything was rendered clearly.","grammatical_rating":5,"grammatical_review":"I found no errors.","cultural_rating":3,"cultural_review":"There is a lot of interesting history and \"cultural\" notes in the computing chapters, and almost none in the more mathematical chapters.  A student who studied from this text would miss a lot of the standard \"mathematics culture\" communicated in a more traditional number theory course.","overall_rating":8,"overall_review":"My primary comment is that I cannot pin down the audience for this book.  I could not use this in an undergraduate number theory class; it is at far too high a level and moves far too quickly.  I could not use it in a graduate number theory class; it assumes no background at all and does not do some standard topics.  I suppose it would be useful for self-study by a very advanced student who already knew a good deal of mathematics and wanted to explore the computational side.  I do think that the title \"A Computational Introduction to Number Theory and Algebra\" is misleading at best.  Lacking numerical examples (for examples, students never actually do any \"clock arithmetic\" type calculations when introduced to the integers mod n) and with a focus only on abelian groups and commutative rings with unity, the book is simultaneously too sophisticated and not sophisticated enough for my use.  It also has a bit of a \"joyless\" feel in the mathematics, with a development of ideas and a writing style that never brings students into any part of the discovery of the mathematics.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":552,"first_name":"Emily","last_name":"Witt","position":"Assistant Professor","institution_name":"University of Kansas","comprehensiveness_rating":5,"comprehensiveness_review":"This text is an introduction to number theory and abstract algebra; based on its presentation, it appears appropriate for students coming from computer science.  The book starts with basic properties of integers (e.g., divisibility, unique factorization), and touches on topics in elementary number theory (e.g., arithmetic modulo n, the distribution of primes, discrete logarithms, primality testing, quadratic reciprocity) and abstract algebra (e.g., groups, rings, ideals, modules, fields and vector spaces, some linear algebra, polynomial rings and their quotients).  The book also includes an introduction to probability.  This, and other topics, are tools for interesting computational applications.  The Table of Contents indicates a few sections that are not required for future material.  The text includes an effective index.","accuracy_rating":5,"accuracy_review":"From my research in writing this review, I have not come across any major errors.  The author has a list of errata on his webpage.","relevance_rating":5,"relevance_review":"The book appears to be up-to-date, and includes some interesting applications of theoretical material to topics relevant in cryptography (e.g., the RSA cryptosystem, and primality testing).","clarity_rating":4,"clarity_review":"The presentation of topics is accurate, and starts \"from scratch.\"  All material necessary in future sections is included in the appropriate section.  Some sections are terse, and an instructor may want to supplement the theoretical exercises with some more computational ones.  The Euclidean Algorithm is presented after sections on solving linear congruences modulo n, and the Chinese Remainder Theorem; applications of the Euclidean Algorithm to these topics are presented later.  An instructor may want students to become comfortable with these topics initially through computations, using the Euclidean Algorithm.  We should also point out that mathematical induction is a prerequisite for this text, and some of the material is presented using pseudocode, which is different than many texts on these topics.","consistency_rating":5,"consistency_review":"The book's terminology and mathematical frameworks appear to be consistent.","modularity_rating":3,"modularity_review":"Since the book is quite long, an instructor for a one-semester course would need to choose specific topics from the text to cover.  There are a few sections indicated that are not required for future material.  However, even among the remaining sections, an instructor would need to carefully choose sections that include all necessary prerequisite material.   Depending on a course's focus, this could be done fairly easily.","organization_rating":3,"organization_review":"Each chapter is written in a logical manner, referencing previous material as needed.  The book jumps from chapters on purely algebraic topics to those focused on applications.  For this reason, an instructor may want to choose certain sections in a chapter to cover as prerequisites for an application, instead of covering the material linearly.","interface_rating":5,"interface_review":"There do not appear to be any problems with the interface of the PDF of the text.","grammatical_rating":5,"grammatical_review":"There do not appear to be major grammatical errors in the text.","cultural_rating":5,"cultural_review":"Due to the topics in this text, this question does not appear to be applicable.","overall_rating":9,"overall_review":null,"created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/a-computational-introduction-to-number-theory-and-algebra?locale=es","updated_at":"2026-05-18T02:06:17.000-05:00"},{"id":213,"title":"A First Course in Linear Algebra","edition_statement":"10th Edition-2023-B-D","volume":null,"copyright_year":2023,"ISBN10":null,"ISBN13":null,"license":"Attribution","language":"eng","accessibility_statement":null,"accessibility_features":"unknown","description":"This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.","contributors":[{"id":3684,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Ken","middle_name":null,"last_name":"Kuttler","location":"Brigham Young University","background_text":"Ken Kuttler, Professor of Mathematics at Bringham Young University. University of Texas at Austin, Ph.D. in Mathematics."}],"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":403,"url":"https://collection.bccampus.ca/textbooks/a-first-course-in-linear-algebra-2023-b-d-vretta-lyryx-inc-448/","year":2017,"created_at":"2018-09-07T12:22:39.000-05:00","updated_at":"2025-03-12T08:55:54.000-05:00","name":"Lyryx"}],"formats":[{"id":689,"type":"PDF","url":"https://collection.bccampus.ca/textbooks/a-first-course-in-linear-algebra-2023-b-d-vretta-lyryx-inc-448/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":1407,"type":"Hardcopy","url":"https://opentextbook.docsol.sfu.ca/store/product/a-first-course-in-linear-algebra-2023-b-d-lyryx/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":4366,"type":"Online","url":"https://math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":9,"reviews":[{"id":234,"first_name":"Scott","last_name":"Kaschner","position":"Teaching Postdoctoral Fellow","institution_name":"University of Arizona","comprehensiveness_rating":4,"comprehensiveness_review":"This text covers all the material an instructor could want to include in an introductory Linear Algebra course.  The first three chapters (Systems of Equations, Matrices, and Determinants) are standard in any introductory Linear Algebra course, but the content of the remainder of such courses varies quite a bit.  The subsequent chapters of this book are each pretty well self-contained, so it would be pretty easy to adapt the content to a particular curriculum.\r\n\r\nThere is no glossary, and the index, while short, seems to be comprehensive.","accuracy_rating":5,"accuracy_review":"The book is over 400 pages, so I have not proof-read the entire book.  However, a few hours of reading revealed no errors or inaccuracies.  It is clear the author took great care with the presentation of the material, so I didn't expect there to be a significant number of errors.","relevance_rating":5,"relevance_review":"The material is so fundamental in mathematics, and this book covers all the important topics.  Relevance/longevity will not be an issue.","clarity_rating":5,"clarity_review":"The clarity of the writing is what I find most appealing about this book.  The proofs are all included and easy to read.  This book would be suitable for students' first exposure to proofs.  There are also plenty of thorough examples.  Terminology is always an issue with students in this subject, but the author has used a color scheme to identify definition boxes in the text and differentiate them from examples, theorems, etc.\r\n\r\nLinear Algebra texts often suffer from aggressive detail paid to procedure and computation.  This book includes a lot of prose to motivate technical procedures.  While it increases the length of the text, it is done very well.","consistency_rating":5,"consistency_review":"For this particular subject, consistency in terminology is essential.  There is some redundancy for the purposes of increasing modularity of the latter half of the book, but the consistency of the terminology and framework of the book is nonetheless first-rate.","modularity_rating":5,"modularity_review":"The modularity of this book is quite good, and this is of particular importance for this particular subject.  One could very easily reorder the chapters of the book to fit their curriculum.  ","organization_rating":4,"organization_review":"The presentation of the topics in this book is thorough almost to a fault.  While the exposition is quite clear and there are many great examples and explanations, the overall length could be intimidating to some students.  To cover all the material one in an average one semester introductory Linear Algebra course, one could have over 300 pages of mathematics text for their students to read.  Depending on the course/students, this could be an issue.  Despite its length, though, it is both extremely well-organized and easy to read.","interface_rating":3,"interface_review":"The diagrams in this book are great, though there aren't a lot of them in the first half of the book.  The geometric intuition in this subject is extremely important and difficult to convey, and this book does a sufficient job.  This is in part due to the great modularity of the book.  The geometric interpretations of matrices and determinants are left for the chapters in the second half of the book; it makes for a very algebra-heavy first three chapters.\r\n\r\nNavigation in the book is very good.  I would like to have all terminology hyperlinked to its definition box, but other than that, everything else is hyperlinked.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors.","cultural_rating":5,"cultural_review":"Cultural relevance is not an issue for this book.","overall_rating":9,"overall_review":"I like this book quite a lot.  For instructors dissatisfied with their ability to reorder standard Linear Algebra texts to suit their needs, this provides a very nice alternative.  It would be easy to adapt to any introductory curriculum.  There are plenty of very nice exercises.  The one missing element that I like in Linear Algebra exercises is True/False; aside from supplementing for that, one could use these exercises exclusively.  There is no use of technology (MATLAB, Maple, calculator, etc.) integrated into this text.","created_at":"2015-06-10T19:00:00.000-05:00","updated_at":"2015-06-10T19:00:00.000-05:00"},{"id":403,"first_name":"Joyce","last_name":"O'Halloran","position":"Professor","institution_name":"Portland State University","comprehensiveness_rating":4,"comprehensiveness_review":"The book includes all the topics we require in our introductory linear algebra course.","accuracy_rating":5,"accuracy_review":"I couldn't find any errors in accuracy.","relevance_rating":5,"relevance_review":"The content is up-to-date and includes applications that are relevant to many of the students' future plans.","clarity_rating":5,"clarity_review":"Very well written, clear explanations \u0026amp; lots of examples.","consistency_rating":4,"consistency_review":"I found no internal inconsistencies except for the notation used for \"solution set\" on p. 17.","modularity_rating":5,"modularity_review":"The sections of the book are of a reasonable length and the organization makes sense.","organization_rating":5,"organization_review":"The topics flow very nicely.","interface_rating":5,"interface_review":"Easy to navigate \u0026amp; especially useful to have internal links. \nImages were nicely done.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors, but a typo on p. 70:\nAbove Example 2.20, it reads  ...product AB maybe be...","cultural_rating":3,"cultural_review":"Not offensive, but could have included examples/exercises that were multicultural.","overall_rating":9,"overall_review":"I plan to propose that we adopt this text as our required text for our introductory linear algebra course.\n\nOn p. 293, when defining basic eigenvectors, I would like to see them referred to as \"basic eigenvectors associated with lambda\".  Then the following sentence is true.\n\nI find the title of Cor. 9.28 confusing; maybe \"length of bases\" would work better.\n","created_at":"2016-01-07T18:00:00.000-06:00","updated_at":"2016-01-07T18:00:00.000-06:00"},{"id":989,"first_name":"Randolph","last_name":"Joe","position":"Assistant Professor ","institution_name":"Reynolds Community College","comprehensiveness_rating":5,"comprehensiveness_review":"In my experience, text book works extremely well with the learning outcomes defined by my institution for entry level linear algebra course. For my students, textbook provides a foundation for the course. Techniques to solve the problems are easy to follow and build upon as the topics gets harder","accuracy_rating":5,"accuracy_review":"Upon an initial review I found no obvious errors.","relevance_rating":5,"relevance_review":"Content is up-to-date and should stay relevant for a long while","clarity_rating":5,"clarity_review":"Text provides detailed instruction to solve the problems.","consistency_rating":5,"consistency_review":"Text stays consistent throughout with definitions, solutions and responses. Students get used to the pattern of solving the problems ","modularity_rating":5,"modularity_review":"Text book can be taught using sections and subsections without creating much confusion. Few chapters that are interconnected may need extra care to rearrange since students would need to have some basic understand of the concept. ","organization_rating":5,"organization_review":"Flow of the chapters fits the learning outcomes needed to incorporate. ","interface_rating":5,"interface_review":"I have viewed it online only and it works very well on a computer screen. ","grammatical_rating":5,"grammatical_review":"Upon initial review, No spelling or grammar errors were encountered. ","cultural_rating":5,"cultural_review":"Math has a great flexibility when it comes to being culturally relevant. An inclusion of socially conscious everyday problems may help students with the following question- when would I use this math in real life.  ","overall_rating":10,"overall_review":"N/A","created_at":"2017-02-08T18:00:00.000-06:00","updated_at":"2017-02-08T18:00:00.000-06:00"},{"id":1058,"first_name":"Joshua","last_name":"Shelor","position":"Instructor","institution_name":"Virginia Western Community College","comprehensiveness_rating":4,"comprehensiveness_review":"This book contains all of the material that would generally be covered in a Freshman or Sophomore Linear Algebra course. The section on vectors is quite extensive, and would be excellent to use in a Freshman course that needed to introduce vectors very early for use in Engineering courses. On the other hand, the sections on Linear Transformations and Eigenvalues are exactly what I would want to see in a Sophomore course that was designed more for mathematicians. The section on abstract vector spaces I find somewhat deficient for a more theoretical course.","accuracy_rating":5,"accuracy_review":"The content is fully accurate. The theorems and proofs that are provided in each section are presented with precision, and yet easy to read.","relevance_rating":5,"relevance_review":"The fundamental courses of mathematics are not generally given to change, but Linear Algebra perhaps more than the rest does need to keep itself updated with the rapidly changing field of Numerical Analysis. I think that Kuttler has done an excellent job of keeping up with the current methods, but has not written in such a way as to make the text dependent on any particular numerical methods that are in vogue.","clarity_rating":5,"clarity_review":"I like very much the style of writing and even the formatting of headers and content titles. I found it very readable and easy to find what I was looking for.","consistency_rating":4,"consistency_review":"I did not detect any inconsistency in the way that the material was presented. The only thing that might be considered an inconsistency is that Subspaces and presented in the text prior to vector spaces. It is somewhat unnatural to define the subspace of something that is not defined as yet, but sadly it has become somewhat commonplace to do things in this way.","modularity_rating":5,"modularity_review":"The sections of the book are easily adaptable. I did like the fact that the section on vector spaces was written in a way to be included earlier if desired.","organization_rating":4,"organization_review":"Other than this issue with the section on vector spaces, I found the organization and flow of topics to be quite natural. Each topic comes in its proper place, but not in such a way as to detract from its adaptability.","interface_rating":5,"interface_review":"I like the way that sections and headings and theorems all are very descriptive, but also numbered, so that they can be easily found.","grammatical_rating":5,"grammatical_review":"I did not find any grammatical errors.","cultural_rating":5,"cultural_review":"I don't think there was any instance of cultural insensitivity.","overall_rating":9,"overall_review":"Exercises are provided at the end of each major section, and I found them to be ample both in quantity and in terms of the level of difficulty.","created_at":"2017-04-11T19:00:00.000-05:00","updated_at":"2017-04-11T19:00:00.000-05:00"},{"id":2198,"first_name":"Ryan","last_name":"Hass","position":"Instructor","institution_name":"Oregon State University","comprehensiveness_rating":5,"comprehensiveness_review":"For the book's stated purpose of providing a first approach to linear algebra is met.  The rigor is appropriate and the author has gone to great lengths to cover the standard definitions, theorems, and examples that are at the heart of linear algebra.","accuracy_rating":5,"accuracy_review":"I have found no errors during the first time I taught from this book.","relevance_rating":5,"relevance_review":"The author has done an exceptional job providing a modern exposure to linear algebra that is accessible to students of all STEM disciplines.  The applications are appropriate for the audience and the theory of linear algebra will not become obsolete in the next twenty years.","clarity_rating":5,"clarity_review":"Consider the following passage from an example on row reduction:\n\n\"Notice that the first column is nonzero, so this is our first pivot column. The first entry in the first row, 2, is the first leading entry and it is in the first pivot position.\"\n\nThe text is clear, accurate and not verbose.  This style is consistent throughout the text and technical terminology is properly used.  I am also happy to say that the author sets a fine example of never abusing notation.","consistency_rating":5,"consistency_review":"This book provides a consistent and mature approach to the topics in each section.  In particular, the final section on vector spaces is written at a level that is appropriate for students that want to take a deeper look at the underlying frameworks of linear algebra.","modularity_rating":5,"modularity_review":"The challenge in a linear algebra text is that there are so many definitions to cover in order for the abstract theory to develop.  The first few section of the book, 1-4, are essential.  However every topic in sections 1-4 need not be assigned.  For example, section 2.2's discussion on LU factorization is not necessary and can be omitted without any disruption.\n\nOnce the first 4 chapters are covered it is trivial to reorder the later sections to fit the objectives of your own course.  Students at this level should have no problem filling in the small gaps caused by any reordering.","organization_rating":4,"organization_review":"The book takes a standard approach for covering systems of equations, developing matrix theory, determinants, properties of R^n, linear transformations, the eigen problem, and ends with a deeper dive into general vector space theory.\n\nEach section provides simple, leading examples that explore the new topic.  Theorems, and when necessary, their proofs are presented in a logical fashion.  There are a sufficient number of examples for each section covering the basic ideas and cases that one encounters in linear algebra.\n\nFrom a personal opinion, section 4, R^n, is dense and could easily be broken up into two parts.  The first on the geometry of R^n and the second on the notion of linear independence and orthogonality.","interface_rating":5,"interface_review":"Theorems, examples and figures are clearly denoted throughout the textbook.  The use of color is also consistent and makes it easy to skim the sections.  I appreciate that learning outcomes are well organized and appropriate for each section.\n\nI would suggest adding a link in the table of contents to the exercise section of each chapter.","grammatical_rating":5,"grammatical_review":"This book's style and grammar is consistent with the books found from the major textbook publishers.","cultural_rating":5,"cultural_review":"This book does not cover any topics about culture, race or ethnicities and is written in a respectful manner.","overall_rating":10,"overall_review":"I have taught from the author's related book, \"Elementary Linear Algebra\", and I find the refinements here of the material to be a positive change in every regard.  This book is an excellent example of a mature textbook for students in STEM fields.","created_at":"2018-06-19T19:00:00.000-05:00","updated_at":"2018-06-19T19:00:00.000-05:00"},{"id":2199,"first_name":"Torrey","last_name":"Johnson","position":"Instructor","institution_name":"Oregon State University","comprehensiveness_rating":5,"comprehensiveness_review":"The book is sufficiently comprehensive for its purpose as a first course in the subject.  The row reduced echelon form and its many consequences and applications are covered well in the first several chapters.  Later chapters on linear transformations and spectral theory are presented at a nearly ideal level for such a course and a reasonable selection of applications are included.","accuracy_rating":4,"accuracy_review":"Aside from a few minor typographical errors the content appears to be very accurate.  No substantive errors were noted.","relevance_rating":5,"relevance_review":"The notation and presentation is similar to other recent books on linear algebra.","clarity_rating":4,"clarity_review":"The book is written in a very conversational style, and for the most part this aids the presentation.  Dense paragraphs are mostly avoided and the text is broken up with examples, theorems, etc... in a similar manner to other modern textbooks.","consistency_rating":4,"consistency_review":"I found no inconsistencies aside from a few minor issues with incorrect references to theorem numbers (ex. theorem 9.35 is referenced in the proof of theorem 4.83 when the intended reference is clearly from chapter 4).","modularity_rating":4,"modularity_review":"The length of individual sections is reasonable and topics are as self-contained as they can be given the nature of the subject.  For example, a student who already knows about vectors in R^n from vector calculus or another course could start chapter 4 at section 10 with only minor difficulties.","organization_rating":4,"organization_review":"The order and presentation of topics are quite clear, with plenty of examples.  As noted by another reviewer, the overall length of the text may seem excessive to some readers.","interface_rating":4,"interface_review":"The small number of figures in the text serve their purposes well.  Overall, the text is very easy to navigate and visually attractive.","grammatical_rating":5,"grammatical_review":"No significant grammatical errors were noted.","cultural_rating":5,"cultural_review":"No issues here.","overall_rating":9,"overall_review":null,"created_at":"2018-06-19T19:00:00.000-05:00","updated_at":"2018-06-19T19:00:00.000-05:00"},{"id":2734,"first_name":"Adam","last_name":"Larios","position":"Assitant Professor","institution_name":"University of Nebraska - Lincoln","comprehensiveness_rating":5,"comprehensiveness_review":"This book covers a very large and comprehensive list of topics.  Aside from the leading topics in a standard linear algebra course, there are some less-standard but highly important topics covered, such as spectral theory, abstract vector spaces, curvilinear coordinates, and even a nice chapter on complex numbers (a topic which is often assumed even if students aren't so familiar with it).  I wish there was a little more about other methods for solving linear systems, that is, anything other than Gaussian elimination/LU-factorization which should only be used as a last resort for large matrices, and is rarely used in practice.  For example, a section on basic iterative methods (e.g., Jacobi or Gauss-Seidel) might be useful, if only to demonstrate to students that there are other, possibly better, methods out there.  However, this is a very minor point, as most textbooks on linear algebra do not cover these topics either.  ","accuracy_rating":5,"accuracy_review":"I did not find any major errors in the book.  ","relevance_rating":3,"relevance_review":"Linear algebra itself will be a subject of high relevance for the far foreseeable future, and this book does a good job of capturing the major important points of what is now consider the classical core of linear algebra, and even extends a bit beyond this.  However, modern linear algebra needs to be very mindful of cases in which matrices are extremely large (e.g., billion by billion or larger), as such matrices are becoming increasingly common in nearly all areas of science and engineering.  Therefore, in sections where methods which are inefficient or unstable for large matrices, major warning signs need to be given.  This text does not do a good job of this.  For example, in the discussion of Cramer's rule, the only line that puts things into context is \"Cramer’s Rule gives you another tool to consider when solving a system of linear equations.\"  This is a major overstatement, as Cramer's rule has computational complexity O(n*n!), making it completely useless for solving anything larger than a 3x3 system.  (Gaussian elimination, while still typically a bad choice, is at least only O(n^3)).  Moreover, Cramer's rule is unstable even for 2x2 systems.  Cramer's rule can occasionally be useful in theoretical applications, but the text does not discuss these nuances at all.  Many other examples like this occur in the book, but this is perhaps the most glaring one.","clarity_rating":5,"clarity_review":"The style of the book is nice and streamlined, cutting out much unnecessary fluff, while still clearly hitting the main points.","consistency_rating":5,"consistency_review":"The textbook follows a nice, consistent build-up of definitions and notation.  The colors and styles used (e.g., for the example boxes, the theorems, etc.) are also quite consistent.","modularity_rating":5,"modularity_review":"The author did a really excellent job of separating the sections and making the as independent as possible.  I also like that there seems to be modularity in terms of complexity.  For example, a beginner can spend time reading Chapter 4, discussing linear algebra on R^n without getting bogged down in abstractions, while a more experienced reader can skip to Chapter 9 on abstract vector spaces, without feeling like they need to constantly return to Chapter 4.  The exercises also seem independent.  For instance, I did not find any places where an exercise relies on you having completed an exercise from an earlier section, which is very nice from the standpoint of modularity.\r\n\r\nI have seen other reviewers complain about the length of the text, but I think this may be a consequence of having a text that is so modular, and also inclusive of advanced topics.  I would much rather have a long text from which I can extract the pieces I need, than a short text with topics all mashed together.  I think the author was wise to trade brevity for modularity in this book.","organization_rating":5,"organization_review":"This text has a clean, clear development of linear algebra.  Another reviewer said that the text introduces subspaces before Vector spaces, but this does not really seem quite the whole story: Subspaces of R^n are introduced, *then* much later, abstract vector spaces are introduced.  This seems to me to be a very reasonable way to build things up.  Even historically, people first started to understand subspaces in R^n before they understood the idea of an abstract vector space.  \r\n\r\nI think it really is a nicely organized text, with easy-to-find topics, a carefully layered build-up of topics, and with the main topics cleanly separated.","interface_rating":5,"interface_review":"I had no problems navigating the pdf.  Both text and graphics appeared very clear, rendered immediately, and were easy to read.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors.","cultural_rating":5,"cultural_review":"This is a book on abstract mathematics, and as expected, no material arises that would reasonably be considered to be ulturally insensitive or offensive.","overall_rating":10,"overall_review":"Very nice book, and I am considering using it in a classroom, but I wish it had a little more of a nod to the difficulties of handling large matrices.  For a classically-focused course though, the book is excellent.","created_at":"2019-04-05T14:03:24.000-05:00","updated_at":"2019-04-05T14:03:24.000-05:00"},{"id":4131,"first_name":"Timothy","last_name":"Mitchell","position":"Part-time Faculty","institution_name":"Bridgewater State University","comprehensiveness_rating":5,"comprehensiveness_review":"This book provides detailed coverage of the topics in a Linear Algebra Course.  It is written in such a way, that it could be used for students who need a formal theoretical course or a an introductory course tobe applied in other areas","accuracy_rating":5,"accuracy_review":"All examples were well written and free of errors","relevance_rating":5,"relevance_review":"Since this is a math texts, its topics will not change over a period of time","clarity_rating":5,"clarity_review":"The text reads easily. Diagrams are clear. Important information is highlighted so as to attract the students attention.","consistency_rating":5,"consistency_review":"Very consistent in its presentation.","modularity_rating":5,"modularity_review":"The author has has set up the booked by various topics. It is very easy to change the order of topics being taught.","organization_rating":5,"organization_review":"The author provides a clear, logical approach in each chapter with clear examples t support the topic.","interface_rating":5,"interface_review":"All diagrams, charts and examples are easy to navigate and read. The text is pleasing on the eyes.","grammatical_rating":5,"grammatical_review":"No grammar errors observed","cultural_rating":1,"cultural_review":"Not applicable","overall_rating":9,"overall_review":"I liked the clarity of the book.  Although the book provided some good practice example, depending on the class, the instructor may need to supplement the assignments","created_at":"2020-06-29T12:19:35.000-05:00","updated_at":"2020-06-29T12:19:35.000-05:00"},{"id":35345,"first_name":"Keaton","last_name":"Hamm","position":"Assistant Professor","institution_name":"University of Texas at Arlington","comprehensiveness_rating":5,"comprehensiveness_review":"This book covers all of the main topics that are typically covered in a mid-level undergraduate linear algebra course for STEM majors. It has enough theory to work for a proof-based math major course, but the proofs are nicely suppressed under links for those who do not wish to see them. Personally, I prefer a modern textbook to discuss the Singular Value Decomposition (SVD), as it is a key topic in machine learning and data science. However, other than this, the book does cover all of the usual topics.","accuracy_rating":5,"accuracy_review":"The book is quite precise in its writing, including its working out of examples and problems.","relevance_rating":5,"relevance_review":"The book topics are relevant and follow roughly the usual course of linear algebra instruction. Again, I would really prefer discussion of the SVD, and consider this a lack in this textbook.","clarity_rating":5,"clarity_review":"The writing is very clear and easy to follow. The figures are nicely done, clear, and add to the text to help students understand the concepts. If anything, there could be somewhat more figures in some sections.","consistency_rating":5,"consistency_review":"I found the book to be very consistent in its notation, terminology, and presentation.","modularity_rating":5,"modularity_review":"Overall, the book is divided into sufficiently small chunks to make it very easy to pick and choose sections to cover if one wanted to. Chapter 4 has very many sections and could perhaps be broken into two, but that is a minor preference thing. I think that it would be easy to go somewhat out of order in the text if one so desired, and to pick and choose which sections within the text one covered if there were particular pieces of less relevance to a given course.","organization_rating":5,"organization_review":"The organization of the book is good. There are many paths to the typical material of Linear Algebra, and this book offers a reasonable one. I would perhaps cover Determinants later on in the course, but the modularity of the chapters would make this possible.","interface_rating":5,"interface_review":"I primarily interacted with the web version of the book, and it is relatively easy to navigate. The pdf version is also easy to use.","grammatical_rating":5,"grammatical_review":"The book's grammar is great as far as I can tell.","cultural_rating":5,"cultural_review":"No issues.","overall_rating":10,"overall_review":null,"created_at":"2024-12-13T15:21:48.000-06:00","updated_at":"2024-12-13T15:21:48.000-06:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/a-first-course-in-linear-algebra-2017?locale=es","updated_at":"2026-05-18T02:10:33.000-05:00"},{"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":217,"title":"Abstract Algebra: Theory and Applications","edition_statement":null,"volume":null,"copyright_year":2016,"ISBN10":null,"ISBN13":"9781944325022","license":"Free Documentation License (GNU)","language":"eng","accessibility_statement":null,"accessibility_features":"unknown","description":"This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly. Until recently most abstract algebra texts included few if any applications. However, one of the major problems in teaching an abstract algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation. This text contains more material than can possibly be covered in a single semester. Certainly there is adequate material for a two-semester course, and perhaps more; however, for a one-semester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentation of topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical one-semester course might cover groups and rings while briefly touching on field theory, using Chapters 1 through 6, 9, 10, 11, 13 (the first part), 16, 17, 18 (the first part), 20, and 21. Parts of these chapters could be deleted and applications substituted according to the interests of the students and the instructor. A two-semester course emphasizing theory might cover Chapters 1 through 6, 9, 10, 11, 13 through 18, 20, 21, 22 (the first part), and 23. On the other hand, if applications are to be emphasized, the course might cover Chapters 1 through 14, and 16 through 22. In an applied course, some of the more theoretical results could be assumed or omitted. A chapter dependency chart appears below. (A broken line indicates a partial dependency.)","contributors":[{"id":3627,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Thomas","middle_name":"W.","last_name":"Judson","location":"Stephen F. Austin State University","background_text":"Thomas W. Judson, Associate Professor, Department of Mathematics and Statistics, Stephen F. Austin State University. PhD University of Oregon."}],"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":158,"url":"http://abstract.ups.edu/contact.html","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2019-05-29T11:22:50.000-05:00","name":"University of Puget Sound"}],"formats":[{"id":612,"type":"PDF","url":"https://scholarworks.sfasu.edu/ebooks/23/","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":613,"type":"Hardcopy","url":"http://www.barnesandnoble.com/w/abstract-algebra-thomas-w-judson/1101838049","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2306,"type":"LaTeX","url":"http://abstract.ups.edu/download.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2307,"type":"Online","url":"http://abstract.ups.edu/aata/aata.html","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"5","textbook_reviews_count":5,"reviews":[{"id":553,"first_name":"Daniel","last_name":"Hernández","position":"Assistant Professor","institution_name":"University of Kansas","comprehensiveness_rating":5,"comprehensiveness_review":"This book is introductory, and covers the basic of groups, rings, fields, and vector spaces.  In addition, it also includes material on some  interesting applications (e.g., public key cryptography).  In terms of covering a lot of topics, the book is certainly comprehensive, and contains enough material for at least a year-long course for undergraduate math majors.   A \"dependency chart\" in the preface should be very useful when deciding on what path to take through the text.  \n\nOne noteworthy feature of this book is that it incorporates the open-source algebra program Sage.  While the .pdf copy I found through the OTN website only included a not-very-serious discussion of Sage at the end of most exercise sets, the online textbook found at \n\nhttp://abstract.pugetsound.edu/aata/\n\nappears to contain a much more substantial discussion of how to use Sage to explore the ideas in this book.  I admit that I didn't explore this feature very much.","accuracy_rating":5,"accuracy_review":"Though I have not checked every detail (the book is quite long!), there do not appear to be any major errors.","relevance_rating":5,"relevance_review":"The topics covered here are basic, and will therefore not require any real updates.\n\nThe book is also written in such a way that it should be easy to include new sections of applications.","clarity_rating":5,"clarity_review":"I would say that this this book is well-written.  The style is somewhat informal, and there are plenty of illustrative examples throughout the text.  The first chapter also contains a brief discussion of what it means to write and read a mathematical proof, and gives many useful suggestions for beginners.  \n\nThrough I didn't read every proof, in the ones I did look at, the arguments convey the key ideas without saying too much.  The author also maintains the good habit of explicitly recalling what has been proved, and pointing out what remains to be done.  In my experience, it is this sort of mid-proof \"recap\" is helpful for beginners.","consistency_rating":5,"consistency_review":"The terminology in this text is standard, and appears to be consistent.","modularity_rating":5,"modularity_review":"Each chapter is broken up into subsections, which makes it easy to for students to read, and for instructors to assign reading.  In addition, this book covers modular arithmetic, which makes it even more \"modular\" in my opinion!","organization_rating":4,"organization_review":"It seems like there is no standard way to present this material.  While the author's choices are perfectly fine, my personal bias would have been to discuss polynomial rings and fields earlier in the text.","interface_rating":5,"interface_review":"The link on page v to \n\nabstract.pugetsound.edu\n\nappears to be broken.\n\nMy browser also had some issues when browsing the Sage-related material on the online version of this text, but this may be a personal problem.","grammatical_rating":5,"grammatical_review":"I did not notice any major grammatical errors.","cultural_rating":5,"cultural_review":"I'm not certain that this question is appropriate for a math textbook.  On the other hand, I'll take this as an opportunity to note that the historical notes that appear throughout are a nice touch.","overall_rating":10,"overall_review":"The problem sets appear to be substantial and appropriate for a strong undergraduate student.  Also, many sections contain problems that are meant to be solved by writing a computer program, which might be of interest for students studying computer science.\n\nI am also slightly concerned that the book is so long that students may find it overwhelming and hard to sift through.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":1093,"first_name":"Nicolae","last_name":"Anghel","position":"Associate Professor","institution_name":"University of North Texas","comprehensiveness_rating":5,"comprehensiveness_review":"This is a two-in-one book: a theoretical part and a computational part. Initially the OTL contained a 2014 version of the book, which only made tangential reference to the SAGE computational system. I downloaded from the author’s website the full, 2016 version, which eventually was also made into the OTL default.  \nThe theoretical part of the book is certainly adequately comprehensive, covering evenly the proposed material, and being supported by judiciously chosen exercises. The computational part also seems to me comprehensive enough, however one should not take my word for it as this side exceeds my areas of expertise and interest.","accuracy_rating":5,"accuracy_review":"The parts that I checked, at random, were very accurate, so I have no reason to believe that the book was not entirely accurate. However, only after testing the book in the classroom, which I intend to do soon, can I certify this aspect.","relevance_rating":5,"relevance_review":"The material is highly relevant for any serious discussion on math curriculum, and will live as long as mankind does.","clarity_rating":5,"clarity_review":"For me as instructor the book was very clear, however keep in mind that this was not the first source for learning the material. Things may be different for a beginning student, who sees the material for the first time. Again, a judgment on this should be postponed until testing the book in the classroom.","consistency_rating":5,"consistency_review":"The book is consistent throughout, all the topics being covered thoroughly and meaningfully.","modularity_rating":5,"modularity_review":"I have no substantive comments on this topic.","organization_rating":5,"organization_review":"The book, maybe a little too long for its own good, is divided into 23 chapters. The flow is natural, and builds on itself. The structure of each chapter is the same: After adequately presenting the material (conceptual definitions, theorems, examples), it proceeds to exercises, sometimes historical notes, references and further readings, to conclude with a substantial computational (based on SAGE syntax) discussion of the material, also including SAGE exercises. The applications to cryptography and coding theory highlight the practical importance of the material. I particularly liked the selection of exercises.","interface_rating":5,"interface_review":"Another big advantage of a free book is that the student does not have to print all of it, certainly not all of it at the same time. This is a big plus, since with commercial books most of the time a student buys a book and only a fraction of it is needed in a course.","grammatical_rating":5,"grammatical_review":"Written in a conversational, informal style the book is by and large free of grammatical errors. There are about a dozen minor mistakes, such as concatenated words or repeated words.","cultural_rating":5,"cultural_review":"The historical vignettes are sweet. Maybe adding pictures of the mathematicians involved would not be a bad thing.","overall_rating":10,"overall_review":"I liked the book, but I like more the concept of free access to theoretical and practical knowledge. Best things in life should essentially be free: air, water, …, education. I will make an effort to use open textbooks whenever possible.","created_at":"2017-04-11T19:00:00.000-05:00","updated_at":"2017-04-11T19:00:00.000-05:00"},{"id":2175,"first_name":"Andrew","last_name":"Misseldine","position":"Assistant Professor","institution_name":"Southern Utah University","comprehensiveness_rating":5,"comprehensiveness_review":"\r\n\tThis textbook is recommended for a upper division undergraduate course on abstract algebra and contains enough materials to cover a two-semester sequence, with particular emphasis placed on groups, rings, and fields. The group theory contains all the main topics of undergraduate algebra, including subgroups, cosets, normal subgroups, quotient groups, homomorphisms, and isomorphism theorems and introduces students to the important families of groups, with a particular emphasis on finite groups, such as cyclic, abelian, dihedral, permutation, and matrix groups. The textbook also includes more advanced topics such as structure of finite abelian groups, solvable groups, group actions, and Sylow Theory. The coverage of rings is equally comprehensive including the important topics of ideals, domains, fields, homomorphisms, polynomials, factorization, field extensions, and Galois Theory. The book is accompanied with a comprehensive index of topics and notation as well of solutions to selected exercises.\r\n","accuracy_rating":5,"accuracy_review":"\r\n\tThe content of the textbook is very accurate, mathematically sound, and there are only a few errors throughout. The few errors which still exist can be reported to the author via email who appears to be very welcoming to suggestions or corrections from others. The author updates the textbook annually with corrections and additions.\r\n","relevance_rating":5,"relevance_review":"\r\n\tThis textbook follows the classical approach to teaching groups, rings, and fields to undergraduate and will retain its value throughout the years as the theory and examples will not be changing. It is possible that some of the applications included, mostly related to computer science, could eventually become obsolete as new techniques are discovered, but this will probably not be too consequential to this text which is a math book and not a compute science textbook. The applications of algebra can still be interesting and motivating to the reader even if they are not the state-of-the-art. The author updates the textbook annually with corrections and is very welcoming to suggestions or corrections from others.\r\n","clarity_rating":4,"clarity_review":"\r\n\tOverall, the textbook is very clear to read for those readers with the appropriate background of set theory, logic, and linear algebra. Proofs are particularly easy to follow and are well-written. The only real struggle here is in the homework exercises. Occasionally, the assumptions of the homework are not explicit which can lead to confusion for the student. This is often the fault that the exercises are collected for the entire chapter and not for individual sections. It can sometimes be a chore for instructors to assign regular homework because they might unintentionally assign an exercise which only involves vocabulary from an early section but whose proofs required theory from later in the chapter.\r\n","consistency_rating":5,"consistency_review":"\r\n\tThe author is consistent in his approach to both the theory and applications of abstract algebra, which matches in style many available textbooks on abstract algebra. In particular, the book's definitions and names of important theorems are in harmony with the greater body of algebraists. It is also consistent with its notation, although sometimes this notations deviates from the more popular notations and often fails to mention alternative notations used by others. A comprehensive notation index is included with references to the original introduction of the notation in the text. Regrettably, no similar glossary of terms exists except the index, which is should be sufficient for most readers.\r\n","modularity_rating":4,"modularity_review":"\r\n\tThe textbook is divided into chapters, sections, and subsections, with exercises and supplementary materials placed in the back of each chapter or at the end of the book. These headings and subheadings lead themselves naturally to how an instructor might parse the course material into regular lectures, but, dependent of the amount of detail desired by the instructor, these subsections do not often produce 50-minute lectures. The textbook's preface includes a dependency chart to help an instructor decide on the order of topics if time restricts complete coverage of the topics. The textbook could be easily adapted for a two semester sequence with the first semester covering groups and the second covering rings and fields or a single semester course which introduces both groups and rings while skipping the more advanced topics. The application chapters/sections can easily be included into the course or omitted from the course based upon the instructor's interest and background with virtually no interruption to the students. Some chapters include a section of \"Additional Exercises\" which include exercises about topic not covered in the textbook but adjacent to the topics introduced. Although these sections are prefaced by some explanation of the exploratory topic, rarely are these topics thorough explained which might leave student grossly confused and require the instructor to supplement the textbook on any exercises assigned from here.\r\n","organization_rating":5,"organization_review":"\r\n\tAll sections follow the basic template of first introducing new definitions followed by examples, theorems, and proofs (although counterexamples are included, the presentation could benefit from additional counterexamples) and further definitions, examples, and theory are introduced as appropriate. Each chapter is concluded with a historical note, exercises for students, and references and suggested readings. Additionally, each chapter includes a section about programming in Sage relevant to the chapter contents with accompanying exercise, but this section is only available in the online version, not the downloadable or print versions. The first chapters review prerequisite materials including set theory and integers, which can be skipped by those students with a sufficient background without any loss. This book takes a \"group-first\" approach to introductory abstract algebra with rings, fields, vector spaces, and Boolean algebras introduced later. Throughout the textbook, in addition to the examples and theory, there are several practical applications of abstract algebra with a particular emphasis on computer science, such as cryptography and coding theory. These application sections/chapters can be easily included into the course without much extra preparation for the instructor or omitted at no real disruption to the student.\r\n","interface_rating":5,"interface_review":"\r\n\tThis textbook was authored using PreTeXt, which designed for typesetting mathematical documents and allow them to be converted into multiple formats. This textbook is available in an online, downloadable pdf, and print version. All three versions have solid format, especially in regard to the mathematical typesetting and graphics. The online version is available in both English and Spanish, where the interface and readability are equally of high quality.\r\n","grammatical_rating":5,"grammatical_review":"\r\n\tThe textbook appears to be absent of regular grammatical or mathematical errors, although a few might be present. The few errors which still might exist can be reported to the author via email who appears to be very welcoming to suggestions or corrections from others. The author updates the textbook annually with corrections and additions. For the purposes of this review, the English version of the textbook was reviewed. The reviewed makes no claim about the quality of the grammar of the Spanish version which was translated by Antonio Behn from the author's original English version.\r\n","cultural_rating":5,"cultural_review":"\r\n\tCulture is not really a concern for theoretical mathematics textbooks which focuses almost entire on mathematical content knowledge and theory and not so much on people or their relationships. The textbook is devoid of culturally insensitive of offensive materials. Many chapters end with historical notes about mathematicians who helped to develop the chapter's materials. These notes typically follow the traditional Western European narrative of abstract algebra's development and is fairly homogeneous. Efforts could be made to include a more diverse and international history of algebra beyond Europe. For example, there is no historical note about the Chinese Remainder Theorem other than a sentence to explain why its name includes the word \"Chinese.\" The textbook, originally written in English, now includes a complete Spanish edition, which is a massive effort for any textbook to be more inclusive.\r\n","overall_rating":10,"overall_review":"\r\n\tThis has been one of my absolute favorite textbooks for teaching abstract algebra. In fact, I think Judson's book is a golden standard for what a high-quality, mathematical OER textbook should be. It has created using the very impressive PreTeXt. In addition to the different formats, this book includes SAGE exercises. It has enough material to fill the usual two-semester course in undergraduate abstract algebra.\r\n","created_at":"2018-06-19T19:00:00.000-05:00","updated_at":"2018-06-19T19:00:00.000-05:00"},{"id":3014,"first_name":"Malik","last_name":"Barrett","position":"Assistant Professor","institution_name":"Earlham College","comprehensiveness_rating":5,"comprehensiveness_review":"Judson covers all of the basics one expects to see in an undergraduate algebra sequence. That is, some review from discrete math/intro to proofs (chapters 1-2), and elementary group theory including chapters on matrix groups, group structure, actions, and Sylow theorems. \r\n\r\nThe coverage of ring theory is slimmer, but still relatively \"complete\" for a semester of undergraduate study. Three chapters on rings, one on lattices, a chapter reviewing linear algebra, and three chapters on field theory with an eye towards three classical applications of Galois theory. I will note here that Judson avoids generators and relations.\r\n\r\nThe coverage is all fairly standard, with excepting the definition of Galois group (see accuracy), and the referencing system in the HTML version is extremely convenient. For example, Judson leverages HTML so that proofs are collapsed (but can be expanded) which allows him to clean up the presentation of each section and include full proofs of earlier results when useful as references. The index uses a similar approach, choosing to display a collapsed link to the first paragraph in which the term is used, which is often a formal definition. There are no pages displayed, but there is a google search bar to scan the book with. Given the searchability, the index style is an interesting choice.\r\n\r\nSince Judson includes _a lot_ of Sage which he uses to expand, clarify, or apply theory from the text, a fairly standard presentation of the theory, and includes hints/solutions to selected exercises, the textbook is very comprehensive. ","accuracy_rating":4,"accuracy_review":"I've noticed very few outright errors in the text proper. However, of primary note is Judson's non-standard (in my experience) definition of Galois group as the automorphism group Aut(E/F) of an arbitrary field extension E/F. He defines this before he's defined fixed fields (ala Artin), or normal/separable extensions. All of the exercises use this definition as well, and so I chose to (mostly) avoid the chapter on Galois theory in favor of a more standard presentation. \r\n\r\nThere _are_ some errors in the exercises, however, like the inclusion of unnecessary or irrelevant parts, or typos. But I came across very few of these in my problem sets.\r\n\r\n","relevance_rating":5,"relevance_review":"Modern applications are sprinkled throughout the text that informs the students of the value of the material beyond theoretical. Judson does this in practical ways given that Sage is such a big component of the book, and so there are many exercises and descriptions that stress this relevance. ","clarity_rating":4,"clarity_review":"Judson's writing is direct and effective. I find his style clean and easy to follow. However, there are instances where there are big jumps between what some beginning exercises assume and what was presented explicitly in the chapter which confused many of my students. For instance, there is a dearth of examples of how to compute minimal polynomials and extension degrees (and the subtleties involved), and so the instructor has to provide the strategies necessary to solve parts of the first two problems. ","consistency_rating":5,"consistency_review":"The book is consistent in language, tone, and style. The only inconsistencies I've noticed involve the occasional definition appearing inline (usually in a sentence motivating the definition) instead of set aside in a text box. Defined terms _are_ still shown in bold, though. Still, it can make it hard to locate the precise definition quickly by scanning the section, but happens so rarely I won't detract a point.","modularity_rating":5,"modularity_review":"Judson is very direct, and so his chapters are very focused. Moreover, many sections are punctuated, perhaps including no more than several definitions and propositions along with a historical note. So it's quite easy to divide the material into tight, bite-sized portions along the sections of the book, with a few exceptions, i.e., sections that run -much- longer and denser than average, like the section on field automorphisms. \r\n\r\nMany sections and some chapters are written in a way that relies minimally on previous material which allows one to omit them or change the order of presentation without too much fuss. For instance, it's easy to cover the material on matrix groups and symmetry (chapter 12) right after the intro coverage of groups (chapter 3) if you want more concrete examples. Or omit the chapters on integral domains (with some minimal adjustment), lattices, and linear algebra if one is making a push to fields and Galois theory.","organization_rating":5,"organization_review":"The text has a relatively linear progression, with some exceptions. The exceptions aren't detractions, though, and allow for modularity or digressions to applications.","interface_rating":5,"interface_review":"The UI of the text is amazingly clean and efficient. Google search makes scanning the book quick and easy, the collapsible table of contents and the sidebar makes jumping around in the text simple. Sage can be run on the page itself making the Sage section quite effective. One can even right-click on rendered LaTeX, like tables, and copy the underlying code (which is super convenient for Cayley tables).","grammatical_rating":5,"grammatical_review":"I recall no major grammatical errors.","cultural_rating":5,"cultural_review":"Judson sticks to the math, so the text is pretty impersonal. Even the historical notes are fact-based accounts.","overall_rating":10,"overall_review":"I used the book for a year-long algebra sequence and was fairly happy with the outcome. Beyond the first two sections of the Galois theory chapter being too non-standard for my tastes, I had few complaints and will very likely use the text again. The problem bank is also very good and they generally complement the material from the chapters quite well.","created_at":"2019-06-24T22:49:28.000-05:00","updated_at":"2019-06-24T22:49:28.000-05:00"},{"id":35556,"first_name":"Robert","last_name":"Kelvey","position":"Associate Professor","institution_name":"The College of Wooster","comprehensiveness_rating":5,"comprehensiveness_review":"Firstly, since this is the first thing you'll see: I love this book and give it 5 stars all-around! I've used it as a main reference text when teaching abstract algebra at The College of Wooster since 2018. Now on with the details.\n\nThis text covers the standard material for a typical undergraduate course in abstract algebra. Judson follows the Groups-\u003eRings-\u003eFields approach, with roughly the first half of the text devoted to group theory and the latter half to rings and fields. The content is exactly what one would expect to find in an introductory text on abstract algebra. \nIf you are used to an older text (e.g., Herstein or Gallian) then you should easily be able to translate to this textbook (and I would highly recommend that you do!). \n\nThe material on group theory introduces many examples early on. For instance, permutation groups, dihedral groups, and matrix groups are all introduced via examples in Chapter 3, and then are expanded upon in their own chapters (Chapters 5 and 12). Some specialized topics, such as simple alternating groups or wallpaper groups, can be found in related chapters. For those interested in covering more theoretical/advanced topics, Judson provides detailed chapters on group actions and the Sylow Theorems. And of course, there are several chapters devoted solely to specific applications, such as algebraic coding theory (much of the applications in the text are in the realm of coding theory).\n\nThe material on rings and fields is also standard for an introductory algebra text at the undergraduate level. At a glance, it might appear that there is not as much content in the latter half of the book when compared to the front half, but many of the applications for rings and fields are embedded within respective chapters. There are also \"Historical Notes\" spread throughout the book (I counted 17) giving brief details on famous mathematicians or significant advances in mathematics.\n\nThe index and glossary are very effective - especially when using the online version of the text (which is accessible here: http://abstract.pugetsound.edu). Note that there is a more up-to-date version of this text available for download directly from that site. The one linked here, at the time of this writing, is the 2020 version, and there has been a 2021 and 2022 versions made available.\n\nI would highly recommend using the online text, especially if you are interested in utilizing Sage. Each chapter in the online text comes with a section devoted to using Sage in relation to that chapters content. This is a really great value-add for those interested in employing more computation and programming into an abstract algebra course.","accuracy_rating":5,"accuracy_review":"In my almost eight years of using this textbook I have not noticed an error or inaccuracy. The author has regularly updated the text over many years. Note again that the most up-to-date version can be found on the text's webpage, http://abstract.pugetsound.edu, along with an online version. I think you can feel confident in adopting this book that it has been thoroughly revised and updated for accuracy.","relevance_rating":5,"relevance_review":"If you visit the author's webpage for this text, you'll see that there have been 14 updates to the text since 2009. Source code for the book can also be found there, and a publicly available GitHub repository exists as well (https://github.com/twjudson/aata). A quick glance at the repositories commits will show that it is frequently updated when appropriate. The author clearly welcomes collaboration and contributions to the text. I would say this text has certainly been arranged to allow for easy straightforward updates.\n\nAlso the content is indeed up-to-date, no worries there!","clarity_rating":5,"clarity_review":"The writing here is very clear and generally to the point. There are usually multiple examples given for any new definition. Around the examples and definitions is where most of the text is. Usually by the end of a chapter, the text is Theorem-\u003eProof, Theorem-\u003eProof, with less exposition in-between. Some readers might wish for more exposition at times, but in terms of clarity of writing, the lack of it here is a benefit (once the definitions and examples are done, you just want to get to the Theorems!).","consistency_rating":5,"consistency_review":"The numbering and mathematical notation is consistent throughout the text. Much of the notation is standard and comes with its own index appendix, which is additionally helpful in the online version of the text.","modularity_rating":5,"modularity_review":"This text is very well organized into various sections within each chapter. One can very easily divide chapters or sections into subunits for reading without disrupting the reader.","organization_rating":5,"organization_review":"As mentioned above on Comprehensiveness, this text follows the \"Groups First\" pedagogical approach, with Rings and Fields following afterwards. The material for each section builds in a logical manner and is pedagogically pleasing. But do note that if you are interested in teaching a course with a \"Rings First\" approach, then this text is not  easily adjustable for that purpose. Everything in the textbook builds towards future chapters, so it is not possible to, say, start with Chapter 16 instead of Chapter 2 or 3.\n\nThat being said, it is certainly possible to cover only the necessary material from the first few chapters on groups that is necessary for the material on rings. This would be roughly 5 to 6 weeks of a semester covering group theory material with the rest of the class devoted to rings and fields. A detailed summary of how to do a \"rings-intensive approach\" can be found via the Ohiolink OER Commons Abstract Algebra Course Content (made possible by a Ohio Department of Higher Education OER Innovation Grant). Disclosure: I worked on said content, which is how I know about it!","interface_rating":5,"interface_review":"The interface, in both the pdf and online book, are clear for the reader.","grammatical_rating":5,"grammatical_review":"There are no significant grammatical errors. At least, none that I noticed in the last many years that were significant enough to write down, nor any in my reading for this review. But as mentioned in the relevance section, the text is updated yearly and any noticed typos or small grammatical errors can be submitted for revision via GitHub.","cultural_rating":5,"cultural_review":"The text is available in English and Spanish. I would love to see continued translations.","overall_rating":10,"overall_review":null,"created_at":"2025-06-27T18:12:52.000-05:00","updated_at":"2025-06-27T18:12:52.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/abstract-algebra-theory-and-applications?locale=es","updated_at":"2026-05-18T02:09:37.000-05:00"},{"id":239,"title":"Algebra and Trigonometry 2e","edition_statement":null,"volume":null,"copyright_year":2021,"ISBN10":"1938168372","ISBN13":"9781951693404","license":"Attribution","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. The Algebra and Trigonometry 2e revision focused on improving relevance and representation as well as mathematical clarity and accuracy. Introductory narratives, examples, and problems were reviewed and revised using a diversity, equity, and inclusion framework. Many contexts, scenarios, and images have been changed to become even more relevant to students’ lives and interests. To maintain our commitment to accuracy and precision, examples, exercises, and solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates from the first edition were considered and unified across the different formats of the text. The first edition of Algebra and Trigonometry by OpenStax is available in web view here.","contributors":[{"id":4757,"contribution":"Author","primary":true,"corporate":false,"title":null,"first_name":"Jay","middle_name":null,"last_name":"Abramson","location":"Arizona State University","background_text":"Jay Abramson has been teaching Precalculus for over 35 years, the last 20 at Arizona State University, where he is a principal lecturer in the School of Mathematics and Statistics. His accomplishments at ASU include co-developing the university’s first hybrid and online math courses as well as an extensive library of video lectures and tutorials. In addition, he has served as a contributing author for two of Pearson Education’s math programs, NovaNet Precalculus and Trigonometry. Prior to coming to ASU, Jay taught at Texas State Technical College and Amarillo College. He received Teacher of the Year awards at both institutions."}],"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":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":98,"url":"https://openstaxcollege.org/textbooks/algebra-and-trigonometry","year":null,"created_at":"2018-09-07T12:22:37.000-05:00","updated_at":"2018-09-07T12:22:37.000-05:00","name":"OpenStax"}],"formats":[{"id":137,"type":"PDF","url":"https://assets.openstax.org/oscms-prodcms/media/documents/Algebra-and-Trigonometry-2e-WEB.pdf","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":138,"type":"Online","url":"https://openstax.org/details/books/algebra-and-trigonometry-2e?Book%20details","price":{"cents":0,"currency_iso":"USD"},"isbn":null},{"id":2951,"type":"eBook","url":"https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4.5","textbook_reviews_count":19,"reviews":[{"id":424,"first_name":"Mingshen","last_name":"Wu","position":"Professor","institution_name":"University of Wisconsin-Stout","comprehensiveness_rating":1,"comprehensiveness_review":"This book is a comprehensive textbook.  It does cover all the materials that we need to cover by our college mathematics course MATH-120 and MATH-121.\n\n  This book does not provide an effective index and glossary.  However, users can use the content list to find the section needed.  Yes, this is a good question: the authors should spend a little more time to develop an index and glossary that may help students and other learners.","accuracy_rating":5,"accuracy_review":"The contents in this book are basic algebra and trigonometry.  I did not find significant error.  I believe it is unbiased.","relevance_rating":4,"relevance_review":"The contents are fundamental algebra and trigonometry concepts/skills that have not been changed too much over long period of time.  So, it is fine.  The teachers who use this book may add in other application problems as needed -- this happen to my teaching all the time whenever what textbook I use.\n\nI do feel this book is a little bit too long though.  Properly shorten it may be a good idea.","clarity_rating":4,"clarity_review":"Yes, I think this book provides adequate context for the jargon/technical terminology used.\n\nBased on my experience this book is easy to read by students.","consistency_rating":5,"consistency_review":"I would say that it is not easy to keep internally consistent in terms of terminology and framework by these many authors.  I was surprised that it is just fine.  I feel it is quite consistent.","modularity_rating":5,"modularity_review":"Yes, the book contents are arranged into 13 chapters.  It is quite easy to select the topics needed to make a course with 3-credit, 4-credit, or 5-credit.  This book certainly provides enough optional contents for our sequence of two 4-credit courses (algebra and trigonometry)","organization_rating":5,"organization_review":"Yes, the topics in the text are presented in a logical, clear fashion.","interface_rating":4,"interface_review":"I reviewed this book using the online book version.  Book loading is relatively slow.   Navigating from chapter to chapter online takes a while to load.  This book has over a thousand pages!\n\nOnce it loaded up, the text is clear, the pictures are very nice, too.","grammatical_rating":3,"grammatical_review":"I didn't see grammatical errors.","cultural_rating":5,"cultural_review":"This book definitely is not culturally insensitive or offensive in any way.  This book should be acceptable by all races, ethnicities, and backgrounds including international usage.","overall_rating":8,"overall_review":"1. For convenience, I would suggest the authors to add an index and/or glossary that may help students to learn.\n2. Some chapters were a little bit too long.  Try to avoid including several quite similar examples.\n3. The online content list has no page number -- I am not sure the paper copy since I didn't see -- better add it on.  It would be nice if user can online navigate using page numbers.","created_at":"2016-08-21T19:00:00.000-05:00","updated_at":"2016-08-21T19:00:00.000-05:00"},{"id":1305,"first_name":"Robert","last_name":"Strozak","position":"Senior lecturer","institution_name":"Old Dominion University","comprehensiveness_rating":4,"comprehensiveness_review":"This book covers more than I require in PreCalculus I, and may be useful in our PreCalculus II course.","accuracy_rating":5,"accuracy_review":"I didn't find any mistakes or content irregularities.","relevance_rating":4,"relevance_review":"I think the homework sets will need to be expanded or updated.","clarity_rating":4,"clarity_review":"it is well written. I think my students can use it as a useful reference.","consistency_rating":5,"consistency_review":"This book matches or current text very closely, so it will follow the same terminology and style we already use.","modularity_rating":4,"modularity_review":"It has a series of \"mini lessons\" that can be used effectively.","organization_rating":5,"organization_review":"The topics follow our current text, which I find very logical.","interface_rating":5,"interface_review":"The book is very \"clean.\"","grammatical_rating":4,"grammatical_review":"None, as far as I have found.","cultural_rating":5,"cultural_review":"I see nothing that would be offensive.","overall_rating":9,"overall_review":null,"created_at":"2017-06-20T19:00:00.000-05:00","updated_at":"2017-06-20T19:00:00.000-05:00"},{"id":1462,"first_name":"Bill","last_name":"Heider","position":"Instructor","institution_name":"Hibbing Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers the topics you would typically expect to be covered in a combined college algebra/Trigonometry text.   The text does allow for students with varying levels of readiness, as the first two chapters covers topics typically encountered in an  \"Intermediate Algebra\" course.  Topics covered include all the algebra and trigonometry to prepare a student for an introductory level calculus course.   Contextual problems are included throughout.  A comprehensive index lists major topics and links to the appropriate page when utilizing the pdf file provided.","accuracy_rating":5,"accuracy_review":"Sampling homework sets and examples no errors were found.","relevance_rating":4,"relevance_review":"Applications are up to date.  In addition, technology is incorporated in a generic way so as to allow for various models of calculators or utilizing software, web- based calculators or spread sheets.   The book provides links to you tube videos and provides support for online homework using service including webassign, xyz homework and others.","clarity_rating":4,"clarity_review":"Examples are presented in a clear manner.   the book uses liberal diagrams and illustrations to facilitate understanding as appropriate.","consistency_rating":5,"consistency_review":"Each section and each chapter follows the same pattern to facilitate usage of the book.   Each chapter concludes with a summary and a set of practice problems in addition to problems at the end of each section of the text.  In addition the book divides chapters into major sections","modularity_rating":5,"modularity_review":"Each section of each chapter can be completed reasonably in a day or two of a typical course.  There is some option to re order chapters and topics.","organization_rating":5,"organization_review":"the book is well organized and laid out in a very understandable fashion.  Each section starts with some motivation of the content, examples of problems, followed by relevant applications.  Links to videos are included and the chapter ends with a comprehensive set of problems.   The PDF file conveniently links both the table of contents and index to the relvant section, simplifying navigation to the desired sections","interface_rating":5,"interface_review":"the interface of the book is excellent.  The pictures and diagrams are claer.  The pdf file links both the table of contents and index to the appropriate page in the text.","grammatical_rating":5,"grammatical_review":"No grammar issues.","cultural_rating":5,"cultural_review":"Examples are generally culture and gender neutral.   There is no bias in the presentation of material.","overall_rating":10,"overall_review":"This book would be an excellent choice for any combined college algebra/Trigonometry course.  Any course utilizing the text would be well prepared  for a claculus course aor any other program requiring a typical background in these topics of mathematics.","created_at":"2017-06-20T19:00:00.000-05:00","updated_at":"2017-06-20T19:00:00.000-05:00"},{"id":1531,"first_name":"John","last_name":"Salisbury","position":"Mathematics Instructor","institution_name":"Rogue Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers numerous subject's that would be covered in several different courses where I teach.  The book covers several more topics than the title would indicate.  There are glossaries at the end of each section of each chapter which I found to be effective and useful.","accuracy_rating":5,"accuracy_review":"I found the text to be accurate, error-free, and not biased.","relevance_rating":5,"relevance_review":"The applications and the introductory sections seem timely and unlikely to be obsolete any time soon.  Most of the material is unchanging and it would not be difficult to rewrite the introductory sections which tend to deal with real word situations.","clarity_rating":5,"clarity_review":"The book is really straightforward and clear and free from a lot of the razzle dazzle that current mathematics textbooks tend to have.  The glossary sections are a good innovation and the terminology is well explained.","consistency_rating":5,"consistency_review":"I found no problem with consistency of the terminology or framework of the book.","modularity_rating":5,"modularity_review":"The sections are not too long.  There are numerous subheadings and an instructor could pick and choose (and, indeed, would have to) topics to cover.  The book is over 1000 pages long so it could be used for several individual courses.  It covers elementary algebra, trigonometry, topics from precalculus, probability, and several other topics.","organization_rating":3,"organization_review":"It covers so many topics that it is a little hard to say that the topics appear in a logical, clear fashion.  Because so many topics are covered, it could be argued that the book is compelled to jump around a bit.","interface_rating":5,"interface_review":"The book is totally straightforward and simple in its presentation without trying to be flashy in any way.  I found this simple, straightforward interface appealing.","grammatical_rating":5,"grammatical_review":"No problem in the grammar at all that I found.","cultural_rating":3,"cultural_review":"I found nothing culturally insensitive or offensive, but on the other hand, I don't the that that book makes use of multiple races, ethnicities or backgrounds.","overall_rating":9,"overall_review":"It would could be used for many different courses at the community college where I teach.  Each department or teacher would have to know which sections of the book should go with which course.","created_at":"2017-08-15T19:00:00.000-05:00","updated_at":"2017-08-15T19:00:00.000-05:00"},{"id":1541,"first_name":"Cristina","last_name":"Hansen Ruiz","position":"Associate Lecturer","institution_name":"University of the West of England","comprehensiveness_rating":5,"comprehensiveness_review":"The text covers all areas related to algebra and trigonometry, starting from the very basics, such as numbers or plotting coordinates, and taking the student to a minimum level from which to start further studies. Added value are the final chapters regarding geometry, sequences and probability. An appropriate index has been added at the end of the book.\nAt the end of each chapter there is a glossary under the term “key terms”.","accuracy_rating":5,"accuracy_review":"The book seems to be accurate and very thorough.","relevance_rating":5,"relevance_review":"The book is relevant for students that are weak with their algebra and need to revise key areas in order to attempt further studies. Final chapters about geometry, sequences and probability, questions about real world applications make the content up to date. Examples and real world applications show that the book can be used by students that want to attempt further studies in very different areas, such as biology and physics. The clear sections within the text and questions makes it easy to update.\nThus the book seems to have a long longevity.","clarity_rating":5,"clarity_review":"Technical terminology is introduced with examples and stories. These stories relate to the abstract ideas that the student needs to learn. An example of this can be seen on page 74, where the use of coordinate axis is introduced with the story of where to position a fly within the ceiling with the use of perpendicular walls. Thus an adequate context is being provided, that will help the student go back and forward in order to learn the abstract ideas that are needed to progress.","consistency_rating":5,"consistency_review":"The same terminology and ideas are being used throughout the book. An example of this is the consistency between chapter 2, where the coordinate system is introduced , and the subsequent chapters, such as chapter 6, where the same coordinate system is used with other functions.","modularity_rating":5,"modularity_review":"The text has been divided into smaller reading sections with the use of different type of headings. It makes it easy to skip parts, or concentrate more on others.\nDue to the nature of Mathematics, it is clear that some ideas need to have been worked upon while progressing through the book. However, the clear index and headings make it easy to jump to a different section, and also give hints of where to find appropriate information, examples, and questions if needed.","organization_rating":5,"organization_review":"Topics in the text are presented in a logical fashion, starting from the very basics, building on top of them and reaching out for more difficult topics. This structure is clear in the index and throughout the chapters. Starting with examples to introduce the basic abstract ideas, makes the content flow.","interface_rating":4,"interface_review":"I downloaded the PDF version of the text. Navigating, making it smaller or bigger, writing a comment or highlighting parts of the text was very easy. However I did miss the same index that appears on the contents pages (iii to vi) on the left hand side of the PDF reader interface. That could be improved to make navigation throughout different topics easier.","grammatical_rating":5,"grammatical_review":"Grammar was fine.","cultural_rating":5,"cultural_review":"The text is not culturally insensitive.","overall_rating":10,"overall_review":"PDF version could be improved adding an index to the left of the interface.\nA chapter about statistics could be added and linked with probability.\nAll in all, it is a good introductory text to be used across faculties.","created_at":"2017-08-15T19:00:00.000-05:00","updated_at":"2017-08-15T19:00:00.000-05:00"},{"id":1965,"first_name":"G. Brock","last_name":"Williams","position":"Professor","institution_name":"Texas Tech University","comprehensiveness_rating":5,"comprehensiveness_review":"This book covers all the standard topics of both a college algebra and trigonometry course.  I could only find two topics that I wish were included (neither are typically included  college algebra and trigonometry texts).  \n\nThe first was a discussion of the importance of proof in mathematics.  Otherwise students can (and usually do) just see the trig identity section as \"a bunch of stuff to memorize and symbols to push around\" without understanding their importance.\n\nThe second was the inclusion of Euler's formula when covering the polar form of complex numbers.","accuracy_rating":5,"accuracy_review":"I could find no mistakes.","relevance_rating":5,"relevance_review":"The actual course material hasn't changed of course in the last 200 years, so there is little chance of the material itself rendering the text obsolete.  The greater danger is in examples that could seem dated in a few years.  Care seems to have been taken in this regard.  The only examples I noticed that I thought might seem out of place were problems that involved the cost of phone service.  They seem to have been written with land lines in mind, and might have been better expressed as costs for data plans.","clarity_rating":4,"clarity_review":"The book is clear and straightforward.  It could be described as \"no-nonsense\".  It doesn't \"sparkle\" or contain moments of humor that would draw students in. ","consistency_rating":5,"consistency_review":"Notation and assumed pre-requisites are consistent.","modularity_rating":4,"modularity_review":"Modularity is not very easy to achieve (and often not highly desirable) in a math text that by necessity builds step by step on prior knowledge.  However, this book does present the trigonometry in a way that could be separated from the algebra, making this a suitable book for a course on just college trigonometry.","organization_rating":5,"organization_review":"One of the things I most like about this text (especially the algebra half) is that topics are organized in a way that requires revisiting and deepening the understanding of earlier topics. \nFor example, the book introduces polynomials and factoring polynomials in chapter 1, then comes back to solving quadratic equations (completing the square, etc) in the middle of chapter 2, then graphing quadratics by completing the square in chapter 5, then graphs and roots of general polynomials.\n\nIts treatment of linear functions is similar beginning with solving (one-variable) linear equations at the beginning of chapter 2, then linear inequalities at the end of chapter 2, before graphing and linear regression in chapter 4.\n\nThis spiraling back to re-visit topics is one of the best features of the text.\n","interface_rating":4,"interface_review":"The online version of the book is reasonably easy to navigate with no significant problems.  The high-quality pdf version is a bit large, however, and slower machines may have trouble scrolling through the whole file.","grammatical_rating":5,"grammatical_review":"I noticed no grammatical errors.","cultural_rating":5,"cultural_review":"I noticed no culturally offensive material.","overall_rating":9,"overall_review":null,"created_at":"2018-03-27T19:00:00.000-05:00","updated_at":"2018-03-27T19:00:00.000-05:00"},{"id":2085,"first_name":"Meryem","last_name":"Abouali","position":"Adjunct lecturer","institution_name":"Laguardia Community College","comprehensiveness_rating":5,"comprehensiveness_review":"Algebra and Trigonometry text covers  a standard typical topics for Algebra course. Within each concept there is an appropriate level of critical thinking and application. There is a perfect level of comprehensiveness.","accuracy_rating":5,"accuracy_review":" Overall , the accuracy of the text was very good. The authors have  separate important definitions, results, concepts , and theorems in blue text boxes that direct the reader's attention. Notations and explanations seems fairly accurate .","relevance_rating":5,"relevance_review":"This text is adequately relevant to the  subject as it is taught today . The authors use  real world examples in the chapters and the homework. The real -life applications  provided in the book are general enough that changes would not be necessary . They are good for all time. ","clarity_rating":5,"clarity_review":"The text has a good clarity and it is very readable to students at this level. The use of common  fronts, text boxes, and overall the language and organization of the text is excellent . It is a user- friendly because the layout makes it easier for students .The text is very consistent in the language used from section to section as will as its terminology and symbols.","consistency_rating":4,"consistency_review":"The text is very consistent in its approach to explanation and students engagement . Additionally , the notations used  lead students  to strong comprehension. The flow is consistent and clear in each section in terms of how concepts are introduced . The authors used consistent terminology as in most other math textbooks.","modularity_rating":4,"modularity_review":"The text is breaking down the content  into easy parts . It is appropriately designed and ordered from section to section which makes the learning easier.","organization_rating":5,"organization_review":"Overall the organization of the text is logical and seems pedagogically justified. The layouts such as the transition from topic to topic from within a section and between sections is easy . Topics are organized from easier to more difficult in a logical manner.","interface_rating":5,"interface_review":"The navigation is a quite user- friendly. The links within the text that allow the user to jump to specific topic in the  text are useful. All the links work well. The text uses appropriate organization of graphics and text  highlights  important concepts. The  colors for text, front, and headings are all appropriate and help to focus the readers's attention to what is truly important.","grammatical_rating":5,"grammatical_review":"The text appears to be grammatically correct. It is error -free. It is obvious that the authors took their time to eliminate errors from this text.","cultural_rating":5,"cultural_review":"The text is not culturally insensitive or offensive in any way. The text doesn't have as many culturally inclusive examples as other traditional text books, it would be beneficial to incorporate more culturally diverse examples for our diverse student population.","overall_rating":10,"overall_review":"I would thank the authors for their great effort in putting together this text. I am planning on adapting this text for my classroom within the next year . It 's a well written , I like the format and the flow of the concepts.","created_at":"2018-05-21T19:00:00.000-05:00","updated_at":"2018-05-21T19:00:00.000-05:00"},{"id":2263,"first_name":"Cecilia","last_name":"Weingartner","position":"Lecture of Mathematics","institution_name":"Southern Utah University","comprehensiveness_rating":4,"comprehensiveness_review":"The text book is comprehensive, covering most of the materials for College Algebra and Trigonometry in a standard, traditional way. It has an introduction, learning objectives, contents with definitions, key points, graphs, and examples with similar practice questions. It lacks the integrated connection between concepts within the book.","accuracy_rating":5,"accuracy_review":"I did not come across any mistakes while skimming the text.","relevance_rating":4,"relevance_review":"The concept does not change.  The applications could be broader.","clarity_rating":4,"clarity_review":"Examples and graphic displays are quite standard and clear.  I especially like the video using the wolfram graphic to illustrate the polar graphs in trigonometry functions.","consistency_rating":4,"consistency_review":"The notations are quite consistent throughout the book.   \nThe online version of the textbook and the pdf version of the textbook are a little different.\nIn the pdf version, the highlighted region is mainly for the definition, formulas and key points, which are very consistent.  However, in the online version, the highlighted region is also including the special feature with show/hide solution button, which has lessen the important of the highlighted definitions, formulas and key points.","modularity_rating":4,"modularity_review":"The textbook is written in a way that can be subdivided into smaller sections.  I created a module called Solving Zero for Polynomial Equation in degree two.  I combined parts from chapter 1, 2, 5, 6, and 9.  I added few examples or graphs for the completeness to some topics.  I also added some examples requiring software to estimate the zero.  It works well.","organization_rating":4,"organization_review":"The topics are presented in a logical and clear fashion.\nIn the textbook, Linear Equations in Two Variables are in the same section of Linear Equation in One Variable.","interface_rating":4,"interface_review":"This book covered many topics. It is not easy to navigate the reference materials within the textbook. For example, there are no links between key terms and definitions within shaded boxes.\n\nFor the online version, it contains a good feature for having the “show solution” options for the examples. However, they are in shaded boxes as well as the definitions. It is a little bit confusing. And the sizes of graphs and fonts for those examples in shaded boxes are not consistent. It looks a little odd sometimes.","grammatical_rating":5,"grammatical_review":"I have not found any grammatical errors.","cultural_rating":5,"cultural_review":"I do not think there is any culturally insensitive or offensive content in the text.","overall_rating":9,"overall_review":"I did not care much for the calculator explanations. Aside from this, the textbook is easy to adapt into one to two courses.  I like the wolfram YouTube video on polar graphing. The textbook can implement more application-based questions to increase some challenging exercises for students to explore.","created_at":"2018-08-02T19:00:00.000-05:00","updated_at":"2018-08-02T19:00:00.000-05:00"},{"id":2265,"first_name":"Stacy","last_name":"Jurgens","position":"Instructor","institution_name":"Mesabi Range College","comprehensiveness_rating":5,"comprehensiveness_review":"The text was very thorough. In fact, when using it in my Advanced Algebra course I skipped many sections. The homework problems were plentiful and offered a lot of variety. However, the word problems all felt a little too similar. A student doing a few problems in a row could settle into a \"routine\" versus apply their problem solving skills. As for the index and glossary, they were comprehensive and useful. However, when a student downloaded the text as a PDF, the numbers in the index/glossary did not match the page numbers of the PDF, causing confusion. Also, the math type often downloaded garbled.","accuracy_rating":5,"accuracy_review":"I never found an Instructors Manual so I can't comment on accuracy. However, the different sections with examples were accurate.","relevance_rating":5,"relevance_review":"Math is Math, it doesn't require updates. However, I wish that the complex number sections and hmwk problems requiring the use of complex numbers was seperated from the main content. If an instructor does not have complex numbers in their course content, they run the risk in later sections of assigning problems that use them.","clarity_rating":5,"clarity_review":"Minimal text is how I prefer to teach Algebra and Trig. I focus on the symbolic language. The text in this book was adequate and not superfluous.","consistency_rating":5,"consistency_review":"Very good consistency.","modularity_rating":4,"modularity_review":"Please see the above comments on Complex Numbers. \nOther than that, I thought the topics were maybe broken down too far. It at times felt like it was less than College or even Advanced Algebra level.","organization_rating":3,"organization_review":"See above about Complex Numbers.","interface_rating":2,"interface_review":"Some of the math text did not download correctly, preventing students from being able to do assigned homework.","grammatical_rating":5,"grammatical_review":"Looked good to me, but I am a Math person...","cultural_rating":5,"cultural_review":"Mathematics is the universal language and shows no bias.","overall_rating":9,"overall_review":"It was my first experience with an OER and I intend to use it again. I believe the second time around will be as insightful as the first.","created_at":"2018-08-02T19:00:00.000-05:00","updated_at":"2018-08-02T19:00:00.000-05:00"},{"id":2833,"first_name":"Brandy","last_name":"Williams","position":"Instructor ","institution_name":"Northshore Technical Community College","comprehensiveness_rating":4,"comprehensiveness_review":"All areas of the subject are covered.  The index is easy to use.  Each section contains a glossary which can be helpful and convenient, but for instructors who limit their teaching to specific sections, a comprehensive glossary that is easily identified in the index would be much more helpful.  ","accuracy_rating":4,"accuracy_review":"I have not found inaccuracies.   I found the introductions to the material and real world applicable examples to be unbiased.  However, the explanation of factoring trinomials with leading coefficients not 1 only explains one method (grouping) instead of explaining the general principle.  Some instructors prefer to teach factoring trinomials using trial and error with a focus on students understanding the general principle as the publisher explains for factoring trinomials with coefficients of 1 and factoring by pulling out the GCF.  I also disagree with the explanation of power functions in that variables raised to fractional powers were said to also be power functions.  ","relevance_rating":4,"relevance_review":"I really appreciated the fact that the text has links to youtube videos in some sections.  This will make the text much more interactive and relevant to the student.  The real life examples seemed quite relevant to today's culture.   However, one example in section 1.1 talked of using money to purchase MP3's.  To my knowledge, that term is not used in this current generation of graduating high school students.  ","clarity_rating":5,"clarity_review":"The text is well written, and the examples are interactive.  The real-life examples do not contain technical terminology which would be difficult for the average reader to understand. ","consistency_rating":5,"consistency_review":"The text is consistent in how it presents material.  Each section has an introduction to material, interactive examples, practice problems, and a glossary at the end.  ","modularity_rating":4,"modularity_review":"While I do feel the text is well organized, some sections contain an enormous amount of material.  If considering the book for a Pre-Calculus or Trigonometry course, the layout is appropriate to give a brief overview of previously taught Algebra topics.  I would not prefer this book for College Algebra. ","organization_rating":5,"organization_review":"The topics are appropriately structured; concepts flow from simple to complex. ","interface_rating":4,"interface_review":"The links work well; the images/charts contain no errors.  I have a great appreciation for the interactive examples.  However, some examples do not state the solutions as others do, which could be confusing to some readers. ","grammatical_rating":5,"grammatical_review":"I did not observe any grammatical errors. ","cultural_rating":5,"cultural_review":"The introduction to each section uses material from a variety of cultures throughout history such as Egyptians, Grecians, Haitians.  The introduction also explains applications in a variety of fields such as business, science, engineering, and architecture. ","overall_rating":9,"overall_review":"I appreciated many qualities about this book.  I enjoyed Section 1.1 which did a great job of explaining our number system in an understandable and relate able way.   The interactive examples are set up in a way that it gives students a chance to consider solutions before they are told what they are.  Students can then click on the link to receive either validation or correction for their thoughts.  As stated earlier, the youtube links make the text user friendly to students today.  Improvements to the text could include more common types of factoring examples in Section 1.5 (particularly the factoring by grouping example) instead of ones that are hardly encountered in the general practice of factoring.  The explanation of factoring trinomials with a leading coefficient not 1 could explain the general principle of factoring as was done for factoring by grouping and factoring trinomials with leading coefficient of 1 before describing a particular method.  The explanation of converting degrees to radians and radians to degrees could be more straightforward by offering a formula early one instead of using the concept of rotations.  The examples for this are also quite complicated.  All in all, it is a great option for a Trigonometry class.  ","created_at":"2019-04-24T18:04:17.000-05:00","updated_at":"2019-04-24T18:04:17.000-05:00"},{"id":2902,"first_name":"Marissa","last_name":"Ford","position":"Assistant Professor","institution_name":"Trine University","comprehensiveness_rating":4,"comprehensiveness_review":"I did not see a glossary, but there was an effective index.  From what I see, you cannot get to the index unless you download the book from the website.  Once I downloaded it, I could see the index.","accuracy_rating":5,"accuracy_review":"The problems I saw had no errors and were unbiased.  The content was accurate.","relevance_rating":5,"relevance_review":"There were some real-world applications considered, some real objects in life, but none that would be considered obsolete any time soon.","clarity_rating":5,"clarity_review":"The book was very clear.  There are definitions were they need to be. ","consistency_rating":5,"consistency_review":"The textbook is consistent in how it is written.","modularity_rating":5,"modularity_review":"The book is not hard to read.  Students can read through this without much difficulty.","organization_rating":5,"organization_review":"The topics are in a logical order, there is nothing I would change.  This is how I would teach the class.","interface_rating":5,"interface_review":"There were no navigation problems that I ran into.  The pictures were nice and there was no distortion.","grammatical_rating":5,"grammatical_review":"I did not see any grammatical errors.","cultural_rating":5,"cultural_review":"The book is not insensitive or offensive.","overall_rating":10,"overall_review":"There were some formatting things I noticed in the online version.  Specifically, on page 605, any time there is a formula, after it, there is a space that is missing between it and the next word.  However, when I downloaded the PDF version, that formatting error is gone.  ","created_at":"2019-05-13T10:43:50.000-05:00","updated_at":"2019-05-13T10:43:50.000-05:00"},{"id":2903,"first_name":"Matt","last_name":"Brown","position":"Director, Quantitative Reasoning Center","institution_name":"Earlham College","comprehensiveness_rating":5,"comprehensiveness_review":"I use this text for a semester course. There is more than enough content for a semester course. I doubt there is enough for a full year.","accuracy_rating":5,"accuracy_review":"No issues with accuracy at all.","relevance_rating":5,"relevance_review":"The content is practical and engaging for the students.","clarity_rating":5,"clarity_review":"The clarity is very accessible even for ESL students.","consistency_rating":5,"consistency_review":"I found no circumstances of inconsistent terminology in this text.","modularity_rating":5,"modularity_review":"Every time that I use this text I change something in the order of the content delivery, and the book is written in a way works.","organization_rating":5,"organization_review":"I particularly like the way the concept of functions is presented.","interface_rating":5,"interface_review":"While I still like to have a words-on-paper textbook, the students almost exclusively used the ebook version with no complaints.","grammatical_rating":5,"grammatical_review":"I found no grammatical errors.","cultural_rating":5,"cultural_review":"I use this book in a highly diverse setting and have never had an issue raised to me regarding insensitivity.","overall_rating":10,"overall_review":"I use this book in foundational math class.  There are three things in particular that make this book appeal to me.  I like the modularity of this book as it allows me jump around to shape each class based on the students' needs. I also utilized the accompanying PowerPoints as a foundation for my presentations.  Lastly and most importantly is the connection to WebAssign for online homework.  The ability of WebAssign to deliver additional content to supplement this text in the modality that each student desires based on their learning style makes a huge impact in outcomes. I highly recommend this text.","created_at":"2019-05-14T07:32:24.000-05:00","updated_at":"2019-05-14T07:32:24.000-05:00"},{"id":2926,"first_name":"Babul","last_name":"Saha","position":"Adjunct Lecturer","institution_name":"LAGCC","comprehensiveness_rating":5,"comprehensiveness_review":"This book is perfect to teach one semester course. It has all the material that we cover in a semester.","accuracy_rating":5,"accuracy_review":"The author maintained all the topics and sequence for this book.","relevance_rating":5,"relevance_review":"There is no issue for the relevance of the book. It full fill the requirement.","clarity_rating":5,"clarity_review":"This book is clearly readable for all level of students including non native speaker.","consistency_rating":5,"consistency_review":"I have seen the author maintained the consistency of the topics.","modularity_rating":5,"modularity_review":"It maintained the order of the topics. There is no need to shuffle the topics of this book.","organization_rating":5,"organization_review":"I like the book the way it is organized. First, the author explained the theoretical concept, then example and finally the exercise. I think most of our students need this pattern to succeed the course.","interface_rating":5,"interface_review":"I strongly agree that students can easily access the e book and they also can download the pdf version of this book. ","grammatical_rating":5,"grammatical_review":"I did not find any grammatical mistake.","cultural_rating":5,"cultural_review":"This book can be used for diverse group of students.","overall_rating":10,"overall_review":"Overall, I like this this book.","created_at":"2019-05-17T21:35:55.000-05:00","updated_at":"2019-05-17T21:35:55.000-05:00"},{"id":3642,"first_name":"Laura","last_name":"Stapleton","position":"Instructor","institution_name":"Marshall University","comprehensiveness_rating":5,"comprehensiveness_review":"The textbook is comprehensive.  I've used the Algebra and Trigonometry textbook in a face-to-face co-requisite College Algebra class for 2 years without problems.  Most students utilize the textbook digitally.  The textbook is set up as a traditional textbook with definitions, examples, objectives, and practice questions.  Very easy to follow.\r\n\r\nThere is a variety of problems to keep the learner engaged.  The textbook is helpful for learners who have differing levels of readiness.","accuracy_rating":5,"accuracy_review":"I've had no issues with inaccuracies.","relevance_rating":5,"relevance_review":"Applications and word problems are engaging and interesting.  The content is up-to-data and relevant.","clarity_rating":5,"clarity_review":"The book does a wonderful job of presenting the material in a logical manner.  Diagrams and illustrations are clear and understandable.  The book is written in an appropriate manner for learners of varying levels of readiness.","consistency_rating":5,"consistency_review":"Notations are consistently used throughout the book.  The book uses a consistent format for each chapter which assists learners as they use the book.","modularity_rating":5,"modularity_review":"The textbook can be subdivided into smaller sections.  I have changed the order of topics covered to match my individual style of teaching.  The subheadings break the material down into logical units so that the instructor can pick and choose topics.","organization_rating":5,"organization_review":"The organization of topics are logically ordered.  Topics are revisited, much like a spiral curriculum, where students see concepts in several places.   Students are able to see the relevancy of the topics and deepen understanding as the course progresses.","interface_rating":5,"interface_review":"The online version is easy to navigate.  Images and charts are clear and do not distract.  I like that students who use the online version can click on the Show Solution option to display the answer.  This allows the learner to try the problem on their own without seeing the solution.  Many of my students routinely use this interactive feature.","grammatical_rating":5,"grammatical_review":"I did not view any grammatical errors within the textbook.","cultural_rating":5,"cultural_review":"The textbook contains no cultural insensitive material.","overall_rating":10,"overall_review":"This is an excellent textbook and is used in more than one course at my institution.  It is well written with good flow.  \r\n\r\nAn index or glossary would be a helpful addition to the textbook.  I would also like the selection of practice problems to be expanded in varying degree of difficulty so that learners, who are at different levels of readiness, can practice.","created_at":"2020-03-10T18:44:56.000-05:00","updated_at":"2020-03-10T18:44:56.000-05:00"},{"id":3815,"first_name":"Carl","last_name":"Yao","position":"Math Instructor","institution_name":"Portland Community College","comprehensiveness_rating":5,"comprehensiveness_review":"The textbook coveres all possible topics in Precalculus.","accuracy_rating":5,"accuracy_review":"I didn't find any error.","relevance_rating":5,"relevance_review":"The textbook is general enough not to be outdated soon.","clarity_rating":5,"clarity_review":"The textbook is easily readable.","consistency_rating":5,"consistency_review":"The textbook uses good terminology.","modularity_rating":5,"modularity_review":"The textbook is in traditional sequence.","organization_rating":5,"organization_review":"The textbook is in a traditional sequence.","interface_rating":5,"interface_review":"No navigation issues at all.","grammatical_rating":5,"grammatical_review":"I didn't find too many grammar errors.","cultural_rating":4,"cultural_review":"n/a","overall_rating":10,"overall_review":"This is a great resource for Precalculus classes. Instructors passionate about saving students money should choose this textbook. Highly recommended!","created_at":"2020-05-14T16:47:31.000-05:00","updated_at":"2020-05-14T16:47:31.000-05:00"},{"id":4192,"first_name":"Valeria","last_name":"D'Orazio","position":"Assistant Professor","institution_name":"Massachusetts Maritime Academy","comprehensiveness_rating":5,"comprehensiveness_review":"This book covers all topics and more of a standard Precalculus  course.","accuracy_rating":5,"accuracy_review":"No errors were found in the online version. An errata document is provided for early editions of the textbook.","relevance_rating":5,"relevance_review":"Many examples from different fields of study are presented. They are classic problems arranged by level of difficulty.  In addition, the use of a graphing calculator to model real life data makes the problems interesting and real.","clarity_rating":5,"clarity_review":"The structure of his textbook makes it easy for students to follow the presentations of the topics. Important concepts and formulas are highlighted to promote easy access to information, understanding, and retention of the subject.","consistency_rating":5,"consistency_review":"The book is organized in a consistent format, common to other Precalculus textbooks,  so that its content can be easily accessed by both students and instructors.","modularity_rating":5,"modularity_review":"Topics are clearly explained and organized in subsections. Consistently, introductions and explanations of new concepts are backed up with examples explained in details and extra practice exercises. PowerPoint slides are also corresponding in pattern with the textbook","organization_rating":5,"organization_review":"The organization and choice of topics presented follow standard Precalculus textbooks.","interface_rating":5,"interface_review":"Interface is clear and offers a schematic and synthetic representation of the subject. Both textbook and additional resources can be easily located and downloaded.","grammatical_rating":5,"grammatical_review":"No errors found.","cultural_rating":5,"cultural_review":"I find course materials to be current, accurate, fair, and inclusive of a diverse population of students.","overall_rating":10,"overall_review":"n/a","created_at":"2020-06-30T15:48:03.000-05:00","updated_at":"2020-06-30T15:48:03.000-05:00"},{"id":4803,"first_name":"Tracy","last_name":"McCoy","position":"Math Instructor","institution_name":"Midlands Technical College","comprehensiveness_rating":5,"comprehensiveness_review":"I did not find any holes in the topics where a topic my college covers was not in this text.","accuracy_rating":5,"accuracy_review":"This book has been vetted.  I did not find errors.","relevance_rating":5,"relevance_review":"I found the examples relevant and the topics organized in a good way.  For instance, when teaching the Law of Sines, I was so happy to see Abramson included area.  Also, I liked the organization of the section on Vectors.  We are lucky in algebra and trigonometry where the topics are not changing.","clarity_rating":4,"clarity_review":"I am unsure if my confusion with the Identities chapter was just me or if others will feel the same.  I try to keep identities as simple as possible, but that is hard to do.  Many problems were set as true or false, so would have liked to have more true examples.  Well, I would have preferred to not have them set as true or false. Again, this may be just me.","consistency_rating":5,"consistency_review":"The text was consistent.","modularity_rating":5,"modularity_review":"I enjoyed experimenting with the html version and pdf version. Both have navigation panels for good movement through the text by section. In the HTML version of the book, the solutions of the examples in the section are hidden.  This feature will be helpful for anyone using a touchscreen device, and OpenStax has an App for this.","organization_rating":5,"organization_review":"I found the topics well organized.","interface_rating":5,"interface_review":"Nothing stands out.  The topics are organized in a coherent way.  The sections are easy to follow.  The examples make sense.","grammatical_rating":5,"grammatical_review":"This book has been vetted.  I did not find errors.","cultural_rating":4,"cultural_review":"I did not find any issues.  In fact, I have not read a problem with any gender.  It would be \"a scientist\" or \"a skateboarder.\"","overall_rating":10,"overall_review":"I found  Algebra and Trigonometry on OpenStax a while ago.  When I had to find a book quickly for a dual enrollment (DE) class this semester, I began using the book.  The class went well.  Students did not have any complaints with not having a book in hand.  Now that I have approval from my department chair to run a pilot in Fall 2021, I will have the book in our bookstore for purchase and copies in our library on reserve.  The pilot classes will use this text for MAT 110- College Algebra and MAT 111-Trigonometry, but could have used Precalculus as it has the same layout and text.\r\n\r\nThere are several support documents in Instructor Resources on OpenStax.  One is the Solutions Manual.  I used this regularly, which had good explanations. I did not like the formatting being in Word but it was easy to find what I needed.  Also, the site has recorded lectures and notes for you to use.  There are two support documents I will definitely use for the pilot, the PowerPoint slides and the Corequisite Skillsheets.  One caution, the PowerPoint slides are not whole presentations but instead are the slides of graphs to embed in your presentations. Since I change all presentations from books to my own style, this is perfect for me.  Finally, I cannot wait to utilize the Corequisite Skillsheets that provide a little more background for students who may need that. \r\n\r\nOverall, I enjoyed using this book and highly recommend checking it out.  I hope you will decide to use it.","created_at":"2021-04-20T12:01:31.000-05:00","updated_at":"2021-04-20T12:01:31.000-05:00"},{"id":33406,"first_name":"Yanwu","last_name":"Ding","position":"Associate Professor","institution_name":"Wichita State University","comprehensiveness_rating":4,"comprehensiveness_review":"The book explores the algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry","accuracy_rating":4,"accuracy_review":"The book provides good examples","relevance_rating":5,"relevance_review":"The book provides helpful resources for audience","clarity_rating":4,"clarity_review":"The book is clear about the concepts and calculations related","consistency_rating":4,"consistency_review":"The book provides solid explanations for the terms of terminologies.","modularity_rating":4,"modularity_review":"The book breaks down to small sections for easy to read","organization_rating":4,"organization_review":"The book is very organized","interface_rating":4,"interface_review":"it is good","grammatical_rating":5,"grammatical_review":"I did not notice grammatical errors","cultural_rating":5,"cultural_review":"The book uses example considering various backgrounds of audiences","overall_rating":9,"overall_review":"The examples in the book are very helpful","created_at":"2021-10-12T12:05:14.000-05:00","updated_at":"2021-10-12T12:05:14.000-05:00"},{"id":35818,"first_name":"Minna","last_name":"Mahlab","position":"Director","institution_name":"Grinnell College","comprehensiveness_rating":5,"comprehensiveness_review":"The text provides a thorough introduction to algebra and trigonometry and includes a review of requisite math skills leading into these subjects.  It is well organized for new students and returning students wishing to review.  The index entries could use refinement and clarification of terms for the new student.","accuracy_rating":5,"accuracy_review":"I did not find any content errors in the text, though I did not check all the examples and embedded videos for accuracy.  The examples are clear of cultural biases that generally impact international students unfamiliar with sports, in particular.","relevance_rating":5,"relevance_review":"Fortunately, the basics of algebra and geometry have not changed in recent history.  The embedded videos are an excellent addition for students unwilling or unable to use text exclusively, though the text is best suited for students willing to practice examples to develop proficiency.","clarity_rating":5,"clarity_review":"The author’s expertise in teaching these subjects is evident in the clarity of the text and explanations and organization of examples and problems, offering students the opportunity to develop skills and confidence with simpler examples before leading into more complicated problem solving.  The extensions and Real World applications provide connections to other disciplines.","consistency_rating":4,"consistency_review":"I did not find inconsistencies in terminology, and given the number of authors, there must have been a good editor.  Some sections offered more practice than others.  When there are many examples, it may be useful to separate repetitive practice problems into an “optional” section or category.","modularity_rating":5,"modularity_review":"I have suggested this text to students for review of concepts, and they report ease in locating the content needed using the index without having to page back and forth.","organization_rating":5,"organization_review":"There is a well-designed flow to this text such that I did not identify and concepts not already addressed as I worked through it.  Students with minimal exposure to these concepts may disagree.","interface_rating":4,"interface_review":"I found the PDF version quicker to load and easier to navigate when looking for specific topics, but the ebook version easier to use when reading as a student might.","grammatical_rating":5,"grammatical_review":"I did not find obvious errors in grammar, thought the subject matter does not lend itself to these errors.","cultural_rating":4,"cultural_review":"The text did not seem to rely, as some older texts do, on culturally specific references that might perplex unfamiliar students.  The introduction to each chapter is well documented, so that even students unfamiliar with, say, economics, can understand references to “the dot com bubble” without having heard it previously.  An explicit reference to inclusive teaching could be mentioned as important and beyond the scope of this text.","overall_rating":9,"overall_review":"I will confidently refer students to this text as a well vetted review of math skills, highlighting the video options for illustration and the wealth of practice offered.","created_at":"2026-03-08T13:33:27.000-05:00","updated_at":"2026-03-08T13:33:27.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/algebra-and-trigonometry?locale=es","updated_at":"2026-05-18T12:03:50.000-05:00"},{"id":850,"title":"Elementary Abstract Algebra: Examples and Applications","edition_statement":null,"volume":null,"copyright_year":2019,"ISBN10":null,"ISBN13":"9780359042111","license":"Attribution-NonCommercial-ShareAlike","language":"eng","accessibility_statement":null,"accessibility_features":"","description":"This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.","contributors":[{"id":5174,"contribution":"Editor","primary":false,"corporate":false,"title":null,"first_name":"Justin","middle_name":null,"last_name":"Hill","location":"Temple College","background_text":"Justin Hill, Temple College"},{"id":5175,"contribution":"Editor","primary":false,"corporate":false,"title":null,"first_name":"Chris","middle_name":null,"last_name":"Thron","location":"Texas A\u0026M University-Central Texas","background_text":"Chris Thron, Texas A\u0026M University-Central Texas"}],"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"}],"publishers":[{"id":829,"url":"http://abstractalgebra.altervista.org/index.html","year":2019,"created_at":"2020-06-27T10:18:50.000-05:00","updated_at":"2020-06-27T10:18:56.000-05:00","name":"Justin Hill and Chris Thron"}],"formats":[{"id":1489,"type":"Online","url":"https://sl2x.aimath.org/book/aafmt/","price":{"cents":0,"currency_iso":"USD"},"isbn":"9780359042111"},{"id":1490,"type":"PDF","url":"http://abstractalgebra.altervista.org/index.html","price":{"cents":0,"currency_iso":"USD"},"isbn":"9780359042111"},{"id":1988,"type":"Hardcopy","url":"https://www.printme1.com/","price":{"cents":0,"currency_iso":"USD"},"isbn":null}],"rating":"4","textbook_reviews_count":2,"reviews":[{"id":4451,"first_name":"Diana","last_name":"Morris","position":"Assistant Professor","institution_name":"University of Virginia","comprehensiveness_rating":5,"comprehensiveness_review":"At almost 1000 pages, this book certainly covers the basics comprehensively.  You might not find the Sylow Theorems or Jordan Canonical Form, but it accomplishes what it sets out to do, covering the basic background of numbers and set theory, the main examples of groups and rings, and then developing these concepts more formally.","accuracy_rating":4,"accuracy_review":"Given the trade-off between perfect mathematical clarity (think Rudin) and being intelligible to undergraduates, I think the book strikes a good balance.","relevance_rating":5,"relevance_review":"Abstract algebra books typically struggle to convince undergraduates of their relevance.  The sustained application in the book is Cryptography, but they did a beautiful job of relating basic concepts like modular arithmetic to practical applications that we do every day (e.g. if December 1st is on a Tuesday, what day of the week is Christmas?)","clarity_rating":5,"clarity_review":"Their basic wording of mathematical concepts was impressive, e.g. the explanation of multiplicative and additive identities is completely fool-proof, as were the every day examples of mathematical concepts, e.g. the notion of \"grandfather\" being a composition of \"parent\" and \"father\".  There is a real effort to guide students through proofs, e.g. how to justify each step and what qualifies as justification.  I also appreciated the generous hints on the exercises spread throughout the book and the Study Guides at the end of each chapter identifying competencies.","consistency_rating":4,"consistency_review":"The material has numerous different sources.  None of the transitions were jarring, but sometimes it felt more like a compendium than one flowing volume.","modularity_rating":4,"modularity_review":"Given the length of the text, an instructor would certainly want to pull out different chapters and make particular note of which leads to which.   There is actually a chart at the beginning of the text explaining how sections are related and which rely on previous sections.","organization_rating":4,"organization_review":"I could not decide if the organization of the book was confusing or brilliant.  For example, major examples of groups / rings are first defined in great depth without formally defining them as such, then in later chapters, one starts from the beginning with the definitions of groups and rings and discovers that they are already familiar.  \r\n\r\nI did feel that there was an overwhelming amount of material, more a reference book of basic abstract algebra topics than a simple narrative, but there were highly coherent sub-narratives throughout.","interface_rating":5,"interface_review":"The only thing that made it difficult to navigate was the sheer length of the document.","grammatical_rating":4,"grammatical_review":"The book had its share of misspellings, but not to the point of compromising or distracting from the meaning.","cultural_rating":5,"cultural_review":"The book did an excellent job of relating abstract mathematical concepts to practical examples familiar to any person.","overall_rating":9,"overall_review":"I would certainly recommend this book as a reference to any student wanting simple explanations and practical examples for the concepts of basic abstract algebra.  For most single semester introductory courses, it would make a fine basic textbook, with some selective pruning and perhaps a few additions where the instructor sees fit.","created_at":"2020-12-13T22:14:30.000-06:00","updated_at":"2020-12-13T22:14:30.000-06:00"},{"id":4712,"first_name":"Mark","last_name":"Koester","position":"Associate Professor","institution_name":"Metropolitan State University of Denver","comprehensiveness_rating":4,"comprehensiveness_review":"Extensive index is included. The book includes more topics than a semester course could study.","accuracy_rating":4,"accuracy_review":"There appears to be accuracy in the book.","relevance_rating":5,"relevance_review":"These topics in Abstract Algebra are appropriate for secondary preservice mathematics teachers.  Many of our state's  mathematics standards connect to the topics in the book.","clarity_rating":5,"clarity_review":"I enjoy the conversational style of the authors.  It is so important that textbooks are accessible for all.","consistency_rating":4,"consistency_review":"The same terminology is used throughout.","modularity_rating":4,"modularity_review":"There are twenty chapters. Of course, some ideas build on others, but often, it is noted in what chapter these other ideas can be found.","organization_rating":4,"organization_review":"There is a logical order to the text.","interface_rating":4,"interface_review":"I like having the ability to click on hints or propositions n the book rather than being inundated with text on a page.","grammatical_rating":4,"grammatical_review":"I didn't notice grammatical errors.","cultural_rating":4,"cultural_review":"I believe that this book is inclusive of others because it is so readable. There is not the inherent bias that one must be able to read cryptic symbols or to read the author's words obviously, clearly, or this is easy.  This was so damaging to having a positive identity as a mathematics major.","overall_rating":8,"overall_review":null,"created_at":"2021-03-26T17:21:00.000-05:00","updated_at":"2021-05-26T16:09:57.000-05:00"}],"url":"https://open.umn.edu/opentextbooks/textbooks/elementary-abstract-algebra-examples-and-applications-hill?locale=es","updated_at":"2026-05-18T12:03:53.000-05:00"}],"links":{"self":"https://open.umn.edu/opentextbooks/subjects/algebra.json?locale=es?page=1","total_pages":4,"total_count":35,"next":"https://open.umn.edu/opentextbooks/subjects/algebra.json?locale=es?page=2"}}