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Precalculus: Stitz Zeager

textbook cover image
Below the Fragnée bridge (http://www.flickr.com/photos/jepoirrier/367405489/in/photostream/) by Jean-Etienne Minh-Duy Poirrier (http://www.flickr.com/photos/jepoirrier/) is used under a CC BY-SA license (http://creativecommons.org/licenses/by-sa/2.0/deed.en_CA)

Description: Precalculus is an introductory text. 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. Note: this book was updated on the BC Open textbook Project site on February, 17, 2015 to include the version of the textbook with chapters on Trigonometry.

Author: Carl Stitz, Ph.D., Jeff Zeager, Ph.D.

Original source: stitz-zeager.com

Adoption (faculty): Contact us if you are using this textbook in your course

Adaptations: Support for adapting an open textbook

Open Textbook(s):

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		Attribution 3.0 License. Copyright Yusuke Kamiyamane. Instructor/Student Resources: PPT Slides & Quizzes
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Attribution 3.0 License. Copyright Yusuke Kamiyamane. Print (.pdf) (11 MB)
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Reviews for 'Precalculus (formerly College Algebra)'

Number of reviews: 4
Average Rating: 3.75 out of 5

1. Reviewed by: Nora Franzova
  • Institution: Langara College
  • Title/Position: Assistant Chair for Math and Stats Department
  • Overall Rating: 4.5 out of 5
  • Date:
  • License: Creative Commons License

Q: The text covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary

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.

Comprehensiveness Rating: 5 out of 5

Q: Content is accurate, error-free and unbiased

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.

Content Accuracy Rating: 5 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

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.

Relevance Rating: 4 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

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.

Clarity Rating: 4 out of 5

Q: The text is internally consistent in terms of terminology and framework

I found no problems here.

Consistency Rating: 5 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.

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.

Modularity Rating: 4 out of 5

Q: The topics in the text are presented in a logical, clear fashion

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.

Organization Rating: 5 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

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.

Interface Rating: 3 out of 5

Q: The text contains no grammatical errors

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

Grammar Rating: 5 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds

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.

Cultural Relevance Rating: 5 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

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.

2. Reviewed by: Dr. Milan Frankl, MBA, PhD
  • Institution: University Canada West
  • Title/Position: Professor of Business
  • Overall Rating: 2.3 out of 5
  • Date:
  • License: Creative Commons License

Q: The text covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary

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.

Comprehensiveness Rating: 2 out of 5

Q: Content is accurate, error-free and unbiased

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.

Content Accuracy Rating: 2 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

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

Relevance Rating: 5 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

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.

Clarity Rating: 2 out of 5

Q: The text is internally consistent in terms of terminology and framework

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

Consistency Rating: 2 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.

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.

Modularity Rating: 2 out of 5

Q: The topics in the text are presented in a logical, clear fashion

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

Organization Rating: 2 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

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.

Interface Rating: 3 out of 5

Q: The text contains no grammatical errors

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.

Grammar Rating: 2 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds

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.

Cultural Relevance Rating: 1 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

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.

3. Reviewed by: Allyson Rozell
  • Institution: Kwantlen Polytechnic University
  • Title/Position: Math Instructor
  • Overall Rating: 4 out of 5
  • Date:
  • License: Creative Commons License

Q: The text covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary

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.

Comprehensiveness Rating: 4 out of 5

Q: Content is accurate, error-free and unbiased

Content seemed accurate.

Content Accuracy Rating: 5 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

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

Relevance Rating: 5 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

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.

Clarity Rating: 2 out of 5

Q: The text is internally consistent in terms of terminology and framework

I saw no inconsistencies in the text.

Consistency Rating: 5 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.

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

Modularity Rating: 4 out of 5

Q: The topics in the text are presented in a logical, clear fashion

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

Organization Rating: 5 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

I 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.

Interface Rating: 3 out of 5

Q: The text contains no grammatical errors

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.

Grammar Rating: 4 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds

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

Cultural Relevance Rating: 3 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

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.

4. Reviewed by: Karen Yeats
  • Institution: Simon Fraser University
  • Title/Position: Assistant Professor
  • Overall Rating: 4.2 out of 5
  • Date:
  • License: Creative Commons License

Q: The text covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary

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.

Comprehensiveness Rating: 4 out of 5

Q: Content is accurate, error-free and unbiased

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.

Content Accuracy Rating: 4 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

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.

Relevance Rating: 4 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

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.

Clarity Rating: 4 out of 5

Q: The text is internally consistent in terms of terminology and framework

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 "larger" for a negative number can sometimes mean larger in absolute value and sometimes greater than. The text makes some effort to be clear on this matter, see for instance the footnote on p304, but consistency without excess pedantry is near impossible in such cases.

Consistency Rating: 4 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.

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

Modularity Rating: 5 out of 5

Q: The topics in the text are presented in a logical, clear fashion

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.

Organization Rating: 4 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

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.

Interface Rating: 4 out of 5

Q: The text contains no grammatical errors

I saw no grammatical errors.

Grammar Rating: 5 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds

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.

Cultural Relevance Rating: 4 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

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.