# College Algebra

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

Pub Date: 2013

ISBN 13:

Publisher: Stitz Zeager Open Source Mathematics

## Read This Book

## Conditions of Use

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The textbook does not cover all the material one would need to address in college algebra, notably the trigonometric functions are absent … read more

The textbook does not cover all the material one would need to address in college algebra, notably the trigonometric functions are absent – even though they appear in the content. Moreover, formalism in theorem proving is absent or inappropriate in most situations.

Most of the theorems lack proper and formal proof – leaving the reader to find those in other sources. This is a major weakness for a math textbook.

No problem with longevity here. All the information has been (and will be) relevant for quite some time.

The writing style is colloquial and patronizing. The authors refer to some form of “inside jokes” about themselves. The students are addressed in a non-professional manner throughout the text. One needs to consider that in an online environment, mature students could form the majority of the reading audience.

Some inconsistencies appear in various chapters. The terminology is adequate but lacks formality – an essential element in mathematics.

The text consists mostly of exercises (more than 50 in each chapter) with little associated theory supporting the solution process. Some exercises are solved in a detailed and stepped way – easy to follow. Lack of formal rigour is present in most cases.

The theory is presented in short segments without proper substance – mostly referring the reader to outside sources. Again, lack of formality is a major weakness – this book is supposed to cover math material were rigour is essential

The text contains numerous grammar and style errors, including punctuations weaknesses not acceptable in an academic textbook. Most charts, graphs, and figures are OK and help understand the solutions provided.

The text contains numerous grammar and style errors, including punctuations weaknesses not acceptable in an academic textbook. The writing tone is informal, it contains colloquial language,slang and jargon which should be voided in formal writing.

I found the text offensive because of the condescending nature of some comments, irrelevant humour, inside jokes, and treatment of the reader in a non-professional way. One needs to consider that some readers (students) could be mature students, therefore not open to the patronizing nature of this type of the written material.

Summary: I do not recommend this textbook for various reasons detailed above. This textbook is mostly an exercise manual rather than a college textbook. Its content might be suitable for a face-to-face delivery method in a classroom with very young students. The writing style is condescending, colloquial, informal, and inadequate for mature audiences. If need be, I could attached more detailed comments – however they would cover every chapter of the 700+ pages of this eBook.

This review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.

I did not see specific coverage of scientific notation, and the text seemed weak in applications, particularly for lower level topics, like … read more

I did not see specific coverage of scientific notation, and the text seemed weak in applications, particularly for lower level topics, like linear and quadratic functions, which are quite important for a college algebra class. I believe it would benefit from a more extensive index.

Content seemed accurate.

Content was somewhat lacking in applications, but generally would not date quickly.

I found the language used to be too technical for our typical college algebra student. I personally enjoyed reading the text, but I think the style will be alienating for the student. I feel the level of exposition is more appropriate for a pre-calculus class than for a college algebra class. Also, the density of the text on the page, and the rather dry layout is also off-putting for the math-wary student.

I saw no inconsistencies in the text.

The modularity of the text was useful; it would be fairly easy to use only parts of the text.

The organization was clear, and the logical structure of the text was good.

I had no interface issues in dealing with the text, however, while the TeX formatting is familiar and clear for mathematicians, I think it is stark and unfriendly for the college algebra student.

The informal, conversational tone they use for much of the text tends to introduce a variety of extremely common and minor grammatical errors, which will not be noticed by most people. I saw no egregious grammatical errors. I would like more commas, but I believe they are currently out of grammatical fashion.

The names used in exercises seem to be largely of European extraction, so more diversity might be helpful.

The text is out of Washington State, and many of the examples are local to the area. This makes them still pretty local for the lower mainland of BC, and I like that. Examples and exercises primarily use imperial units; I would prefer to have a better balance of imperial and metric questions.

This review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.

The text definitely covers all topics that are covered in a usual College Algebra class, and actually it covers much more. The extensive … read more

The text definitely covers all topics that are covered in a usual College Algebra class, and actually it covers much more. The extensive coverage of Systems of Equations and Matrices can not be really squeezed into a one semester College Algebra class, but a 1st Linear Algebra class could definitely take that chapter and spend almost a month on it. Similar comment would describe the Sequences and Binomial Theorem chapter. Since according to the Open Textbook project, one can use any parts of the book, according to their needs, then I believe the book provides more than enough to choose from and covers ideas of the subject exactly as needed for our College Algebra class. Index and Glossary are detailed and the links worked well for me.

Content is accurate to such a point where even the most likely trouble spots for the students are picked out and presented and explained. The authors do not try to avoid the trouble spots, while many other books do. Exercises are abundant, and full solutions follow each group of exercises. That is of course great, but at the time of adoption of this book, we would have to remove the solutions to the even number problems and then collect those in some “Instructor’s Supplement”. Also the fact that full solutions immediately follow the exercises would be something we would have to change. Even though authors claim that they cut down on endless “drill and kill” questions, I feel there is really a lovely group of exercises (I'd even called some of them "cute".) and students will get good level of practice once they tackle these. All the graphs are clean and clear, for some reason in the later chapters I noticed that there are 2 different “font types” under figures. I guess one is from the graphics itself and one from LaTeX. (see Example 6.4.2 or Example 8.1.1 and others) It is not a problem, just my observation. There are only very few colored images and those are not exactly spectacular, but I know that stuff is hard to make.

Since College Algebra is not likely to change in the near future, this should not become an issue for the text. One thing that can be mentioned is the endless issue of graphing calculator use in a College Algebra class. The book can be definitely followed without using graphing calculators, but . . . there is enough exercises to make one feel that students will feel shortchanged if graphing calculators are not allowed. (That is the case at our college.) These are usually the more challenging exercises and they often come from Calculus with the promise that in Calculus, students will be able to solve them without a graphing utility. If we adopt the text, we might need to address this.

This is an interesting point. The text is clear, well written, technical terminology is used and explained. The text contains an endless line of “foot notes” in which the authors tease each other and comment on each others opinions. (For example we learn: “According to Carl, Jeff thinks symmetry is overrated.” (btw, I agree).) In any case there is a bit too many of these and when I started the reading of the book, this surprised me. The humorous foot notes, are taking away the possibility of me adding humorous comments in class. Students now might think, I just read them from the book. If the book just has facts, the instructor can make them more personal, or funny, or more digestible. When the book has the facts and the jokes, it will make it harder for me (the instructor) to add something more. I still like the book. I like the jokes/comments too, I just worry about my role. Although “Hooked on Conics” as a chapter title was quite brave.

I found no problems here.

Some times the “paragraphs get to be too long” and thus more likely to be skipped by the students. These are all well written and correct, they just trail of to lengthy explanations. To be exact, the length is no more then 10-15 lines, but in a math text, that is usually a lot. I was already reading the text and looking which sections we can skip and which to include and it seemed to be fairly easy to do, since there are many separate sections that one can choose from. Since the book is typed in LaTeX the self-referencing issues will be automatically dealt with during the typesetting.

The flow is exactly as I would follow. Maybe the composition of functions being left only for Chapter5 (just in time for inverse functions) feels a bit late. Although it was not missing in the flow of the previous chapters. Sometimes the authors venture into more detail that is needed in a basic College Algebra class. (for example the discussion about minima and maxima). But that does not harm the clarity of the text.

There were no navigation or distortion issues. The only problem I had that when I downloaded the .pdf file to my Mac it was not complete. Just the first 9 chapters.

I did not observe any grammatical errors, but I do not consider myself an appropriate judge of this.

The text uses in its examples “imaginary” characters and places. Chewbacca and Sasquatch (like Sasquatch Tonic or Sasquatch Berry Pies ) are frequently mentioned as well as dOpis media players. This is a dilemma all instructors have to address. Using real names and real places or imaginary ones? We all make our choice. Some feel that students will relate to reality better, I believe that imaginary places and names are well within the spirit of the book. The book does have real time data too – lets say from Federal Bureau of Transportation. All such data is from US of course, since the authors are from there.

The book uses imperial units, while Canada is on a metric system. This would take some effort to change. But textbooks that we normally use also mainly use imperial units.

This review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.

Cameron Morland

The version of the text we were provided had the trigonometry chapters cut out (This was done simply by clipping the pdf rather than … read more

The version of the text we were provided had the trigonometry chapters cut out (This was done simply by clipping the pdf rather than recompiling the latex, so the table of contents and index still reflect the full text, which is silly and unprofessional, but only a very minor point.). In order to cover the material we cover in precalculus the trigonometry sections would need to be put back in. Chapters 7,8, and 9 are unnecessary for our precalculus course; they are covered in other introductory math/macm courses. The index is comprehensive, and the pdf is searchable. The background assumed is generally appropriate. There are a few small exceptions, for example students are expected to know polynomial division. Some common student points of confusion are clarified, though others are not. For example in 1.1.2 the distinction between (a,b) as interval notation and (a,b) as a point in the cartesian plane is not clarified. There are some important issues with regard to intended audience, which will be dealt with more substantially in a later question, but in summary this text seems to be targeted to mathies in spirit (not in difficulty) despite the fact that in our system such people will have covered this material before university and so will not be in our precalculus classes.

Accuracy seems very good. I did not see any errors; however, I did not give a line by line reading so may have missed some errors.

There are some cultural references which will not age well, but they are more stylistic issues than content issues. For example the movie "8.99999..." is a joke which will not resonate once the original movie (from 2009) has been largely forgotten, and "hooked on conics" is a joke for those of us who grew up in the '90s and watched some American TV. I would not view this as a major issue. All computational examples expect a graphing calculator. As far as I have seen these single purpose devices are not used out in the real world, their only benefit seeming to be that some jurisdictions require them in high school so students from these jurisdictions already have them. An open text might be favourable to discussing an open CAS (computer algebra system) which students could use no matter where they go next, but the standard commercial CASs are also good and widely available choices, and as graphing calculator apps for smart phones mature they will become increasingly viable, not to mention web tools like Wolfram Alpha. On the positive side, there are many weblinks, to Wikipedia as well as to other sources, particularly to support asides and problems with data.

The authors voices come through loud and clear in a very charming way. It is quite conversational, and commendable in how well it puts the jargon in context and avoids unnecessary jargon. It has many asides and comments, mostly in footnotes, which enrich the text but can also be distracting or confusing. Similarly, the conversational style, while generally increasing readability, will be a challenge for some ESL students, particularly along with the jokes and asides which require American cultural knowledge. I feel that the prose and style of this book is simultaneously its greatest strength and its greatest weakness. I liked reading this book; I would have liked learning out of it when I was first encountering this material. Although very much itself (particularly the way the authors banter with each other), its style has some similarities to Spivak's calculus, which has a great cult following in the mathie crowd. However, the mathie crowd is very much not the audience of our precalculus courses, and I think the typical precalculus student's response to the style would be half confusion and half eye-rolling. I am particularly mystified by this as the authors are both at community colleges. Is their education system sufficiently different from ours that they get the sort of geeky audience who would appreciate this book? Do I misestimate our students' interests and abilities? Do the authors' students largely not get it? Ultimately I can only recommend that an instructor looking at this text look at the style and consider whether it fits with their own style and whether it is likely to be appreciated by their students.

The text is generally consistent. It makes explicit reference to itself in useful but not excessive ways. It is well structured. When the consistency is weaker it is in places where standard usage is often inconsistent, for example in colloquial usage

The sections are of a reasonable length. The dependencies within the text make sense given the material, and are generally clear.

Notwithstanding the style comments mentioned in a previous question, the presentation is sensible and is appropriately rigorous for the level; the proofs of many results are beyond the scope of such a course but the authors make efforts to motivate and contextualize the results so that the reader can largely see how they can be natural and important even though they cannot prove them. The order is fairly standard and the authors explain their reasoning behind those deviations from standard order which they use. There are some cases where sections do not flow well, for example section 1.1 begins with sets of numbers and moves onto interval notation which together form 1.1.1, and then jumps in 1.1.2 to cartesian coordinates. These initial sections are essentially developing background for use in the upcoming chapters on functions, and so by their nature are somewhat disjointed.

While not glossy like commercial textbooks, the book is clean and professional. The pdf contains useful internal links and external links. The one exception to the professionalism of the text is that certain sections were cut in the pdf we were given, but the latex was not recompiled, so the table of contents and index did not reflect the cuts.

I saw no grammatical errors.

The book is not insensitive or offensive in any way. The core material and most problems are purely mathematical. Only some problems and asides touch cultural issues at all. The problems based on real world data are all based on American data. Broadening the sources of data would improve the book. The occasional problems involving units are imperial, not metric. The book makes American cultural references, but generally ones which would also be familiar to Canadian students, such as popular movies.

Two final comments. First, the authors leave some unanswered questions (such as some well placed "why?"s) for the reader to think about. These are great for stronger students but will frustrate those who aren't getting it. Second, I find the matrix chapter weak, but it is not relevant to the precalculus course we offer in any case. Generally, I find the book very charming, but am concerned that the intended audience may not have the same response to it.

This review originated in the BC Open Textbook Collection and is licensed under CC BY-ND.

The textbook covers all of the traditional College Algebra content. If some institutions of higher education would embed the trigonometry within the … read more

The textbook covers all of the traditional College Algebra content. If some institutions of higher education would embed the trigonometry within the College Algebra / Pre-Calculus, these authors have another text to cover the trigonometry. The content is covered accurately and succinctly allowing the mainstream student an opportunity to engage in gaining a better understanding of the content.

From the mainstream students' perspective, the content is very accurate. From a faculty perspective, some of the content lacks proof; however, any quality faculty member can supplement the proof.

This content will stand the test of time as the text is arranged in a way which concisely and comprehensively covers the content with breadth and depth.

The text's clarity is nicely done. One item which could better be addressed are some of the examples - many times Sasquatch is referenced. More real-world examples would enhance the quality of the text.

The text constantly adheres to similar terminology and delivery of content.

This text would quite easily be parceled into units or be adjusted so that the text's content could be covered in a different order or utilized with other resources

The text's flow was thoughtfully-done starting with some basic and traditional content pertaining to all functions and moving through more specific types of functions.

There are no issues with distorted images nor are there any navigation problems with the downloadable .pdf eBook.

I observed very few grammatical errors.

Some of the examples containing Sasquatch or the Star Wars character Chewbacca take away from the real-world relevance of the text; however, there are no culturally insensitive or offensive remarks in the text in any way.

Certainly there are some College Algebra texts which are written with a more formal focus; however, the concise nature by which this text was penned is respectable.

This text does cover all of the topics that are presented in a typical College Algebra course. The chapter covering Systems of Equations and Matrices … read more

This text does cover all of the topics that are presented in a typical College Algebra course. The chapter covering Systems of Equations and Matrices is more in-depth than is common. The chapter on Conics is often-times included and is very useful. The number of topics and their depth would prove challenging to complete in one semester. The text could be used with chapters and/or sections omitted, which would give instructors ample material to choose from and use in their classrooms. My copy did not include chapters that I believe were in other pdfs, covering topics such as Trigonometry. Also, although referenced in my copy, Chapters 10 and 11. The index seemed completed and useful. There was no glossary in my version.

Content seemed accurate. Solutions follow each exercise set. Examples are abundant with thorough explanations. I was surprised at the number of problems in the exercise sets. In the Preface, the authors asserted that endless "drill and kill" questions are not productive, while there is a good number of problems in each set. The diagrams and graphs are clear.

I enjoyed some of the cultural references in the text. They seem to arise from US popular culture. I do wonder if they would be relevant to students outside of this culture. There also seemed to be local/geographical references which may be puzzling for many students. Although a graphing calculator is mentioned in the Preface as not a necessary tool for the text, there are numerous examples of its use throughout. This particular calculator may not be in use in the near future, while other less-costly options may be utilized. The content itself is relevant and will be for some time. The text uses English units, which would only be useful in the US and a few other countries.

The text is clearly written and terminology is explained and defined. I was pleasantly surprised, initially, at the tone of the text. While clear, it is friendly and conversational. The numerous footnotes, however, are distracting. Some enrich the text with references to linked material and are useful. Others seem to be inside jokes and teasing between the authors. I feel that students would be distracted by these and start to avoid them. Some students may find this condescending. An instructor would have to consider this prior to adoption.

The text is consistent. I saw no problems with this.

I find the modularity useful. This text could be divided into smaller sections or rearranged. I did find that some of the explanations were long. Many students will disregard a lengthy explanation. The writing is accurate and complete, but in some areas lengthy.

I found the flow and organization clear. I was surprised at the introduction of functions in the first chapter, but felt it may be a useful order. The authors explain their reasoning for this in the Preface. The sections are of a reasonable length.

The text is professional in its interface. Since the version I received was missing some chapters that had been referenced, this was a bit problematic in that they were referenced in footnotes. The diagrams and figures were adequate. Although lacking in the color of commercial texts, the graphics were useful.

I found no grammatical errors in the text, although I did examine it line-by-line. I also do not consider myself an expert in this.

The use of English units is only pertinent to a certain audience. Much of the data was from US sources. Many of the footnotes and cultural references are from US culture. More diversity would be useful. The book is not offensive. Again, some students may find some of the footnotes condescending.

I found the textbook friendly and accessible, with a strong organization and modularity. The textbook would be more useful in a classroom situation with a certain audience and instructor.

The text book covered all the topics in college algebra. The only two sub topics which were not in detailed is Linear Functions and Quadratic … read more

The text book covered all the topics in college algebra. The only two sub topics which were not in detailed is Linear Functions and Quadratic Functions. Under the Linear functions sub topics, there should have been a sections which would talk more about solving linear equations in one variable,including solving linear equations involving fractions . The other issue is under the quadratic functions there is not a subsection which talks about solving quadratic equations algebraically using the factoring method, the square root method, completing of squares method and quadratic formula method. Also finding the equations of lines with parallel line and perpendicular lines should have been explained a little bit to refresh the students mind. Overall this is a good book and my students love it. Am using it in two of my classes this semester.

The content is accurate and unbiased. There are no errors.

The context is up to date but I would recommend having different application questions from different fields added to the content so it can address questions in different student disciplines and career paths. Also the tex files are not included by the publisher to change or edit any content. Its a pdf and very hard to change anything.

The words, phrases, symbols, diagrams and graphs, and mathematical formulas used in the book were clear and precise and straight to the point. The questions and solutions to the questions were clear and students understood each question. Since using this book from the beginning of the semester I have never had complains from students about the clarity and technical terms used in the book. The clarity is good

The textbook has a very good consistency in terms of terminolgy and Framework. Alot of times the book made reference to some other techniques used in the previous sections.

The book can easily be divisibles into smaller reading sections that can be assigned at different points in the course. You can easily break up some sections to different modules during the course. For examples, in chapter 3 you break up some of the different subsections and connect or combine with other subsections in chapter 3. Also because the author used Latex its very much easy to create modules from it.

Overall the organization/structure wasn't bad, but my recommendations would be there authors moving chapter 5.1 and 5.2 to chapter. The composition of functions should have been added the arithmetric operations of function section 1.5. So the author should have combines 5.1 and 1.5 together. Adding inverse functions to chapter 1 would be also a good idea.

The interface of the book is fine and there are no issues with interface. Thats the best quality you can get from using Latex.

There were no grammatical errors.

The authors did a great job in writing this book in that the book is not insensitive or offensive in any way. I think there should more application questions from different cultures around the world.

More application questions would be very helpful to students. Am using this book in two of my classes and my students love the book. I type my own homework questions and exams questions. My recoomendations to the authorsn is to add a review section to each chapter with different questions as a review for that chapter.

The textbook covers a full range of subjects expected in most college algebra classes, including some topics--such as systems of equations and … read more

The textbook covers a full range of subjects expected in most college algebra classes, including some topics--such as systems of equations and matrices--that delve into Linear Algebra. It is worth noting that while the text includes large numbers of exercises for students to solve, formal proofs are largely ignored, so the text is not suitable for a class with an emphasis on the latter. The text has several calculator-specific problems, complete with display printouts, for those who allow or encourage calculator usage in class.

There did not appear to be any errors in the chapters I reviewed.

Since the material is foundational for many subsequent subjects, there is no danger of the mathematics losing relevance. Updates should be simple to perform.

Some of the solutions provided for example problems are rather verbose and potentially confusing for students depending on their experience level. At times the casual tone of the explanations, problems, and footnotes can be distracting as well. The somewhat informal style of several sections and questions may be hit-or-miss among both students and instructors, depending on the classroom.

Terminology and tone remain consistent throughout, with no notable exceptions.

There are many questions at the end of each section, allowing instructors to narrow down a preferred list or to separate specific problems to be used for review materials. The sections themselves can be easily reordered or modified to suit the class at hand if instructors prefer to focus more or less on individual sections in a chapter.

We typically switch the order of the first two chapter subjects, introducing the basics of linear and quadratic equations before defining functions and transformations in more detail, but the order can work as given too. The answers for section exercises would be better placed in a separate index rather than directly after the corresponding problems so students do not need to flip or scroll through pages of solutions between sections, though this is more of an issue in the physical text than the digital one.

An excellent feature of the digital version is the hyperlinks to previous definitions in the book or separate webpages for concepts like the Pythagorean Theorem or Newton’s Law of Cooling. It is a very useful way to review or learn about recurring formulas without flipping back through physical pages constantly or bookmarking several sections. Even the Index has direct links to appropriate pages. No issues exist with graphs and images, which are typically clear and relevant.

I did not notice any glaring grammar mistakes in the text.

There is somewhat of a focus on US data, units, and references, which could be expanded to other countries, systems, or cultures without needing to alter the writing style too much.

The text is solid in its given form, but it may need extensive modification to fit a particular course more effectively. Thankfully, the ease in doing so makes it a reasonable base for a college text.

## Table of Contents

- Chapter 1: Relations and Functions
- Chapter 2: Linear and Quadratic Functions
- Chapter 3: Polynomial Functions
- Chapter 4: Rational Functions
- Chapter 5: Further Topics in Functions
- Chapter 6: Exponential and Logarithmic Functions
- Chapter 7: Hooked on Conics
- Chapter 8: Systems of Equations and Matrices
- Chapter 9: Sequences and the Binomial Theorem

## About the Book

*College Algebra *is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely.

Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it.

The authors also offer a Precalculus version of this text, which has two extra chapters covering Trigonometry.

## About the Contributors

### Author(s)

**Carl Stitz, Ph.D.** is a Professor of Mathematics at Lakeland Community College outside of Kirtland, Ohio.

**Jeff Zeager, Ph.D.** is an Associate Professor of Mathematics at Lorain County Community College in Elyria, Ohio.

Dr. Stitz and Dr. Zeager co-wrote this college algebra textbook with the vision of creating a high-quality, open-source textbook that is within reach and accessible to the average college student. In recognition of their work, both authors received the prestigious Faculty Innovator Award from the University System of Ohio in 2010.