Precalculus

Reviewed by John Hammond, Senior Educator, Wichita State University on 10/14/21

Comprehensiveness rating: 5 see less

This book covers everything one would want to cover in a precalculus course though with more emphasis on the algebra topics rather than trigonometry.

Content Accuracy rating: 4

I didn't notice any glaring errors in the content.

Relevance/Longevity rating: 4

The content is standard pre-calculus topics from algebra and trig. The material has fun "weird dad" style of jokes with exercises involving Sasquatch, for example. The footnotes add a fun element to the text but in a way that shouldn't wear out over time.

Clarity rating: 4

The text is very clear for someone who is well-prepared for the material. That said, I taught with this book for three semesters and advocated its use for our department for a number of years. Many students reported that it was too much much for them - the book is exhaustive - and they found the presentation in the sections too verbose(!) (I personally disagree, but I'm not the student...).

New teachers of precalc also had trouble extracting a 16 week course from the 1000+ pages and needed specific guidance for what sections to cover, what to omit. This isn't a bad thing, just worth noting for those considering adopting the text.

Consistency rating: 4

I have no comment - the book is internally consistent mathematically and comically - the footnotes almost tell a brief story of Carl which is a fun touch in a math book.

Modularity rating: 4

The text is very modular with the latex files allowing one to present either the entire book, just algebra, and just trigonometry.
Each section itself is its own latex file, so one could extract any individual section easily for repurposing.

Organization/Structure/Flow rating: 4

The material is presented in a logical fashion, though I personally rearranged and expanded the trigonometry section to match my personal pedagogical preference.

Interface rating: 5

PDF is easy to read and scales well at different resolutions.

Grammatical Errors rating: 3

The grammar seemed fine to me.

Cultural Relevance rating: 4

I didn't see anything that was culturally insensitive and examples tend not use humans at all but instead Sasquatch, Fritzy the Fox, Chewbacca the Bunny, and other silly characters.

Comments

As I noted above, I used the text for three semesters. I enjoyed the book and my students responded to it positively (it replaced a text that had cost at the time $306 for a one semester course).

It took some extra work on the part of my department to get everyone on board, but we're still using the text in our sections of precalculus after five years, which makes me rate this book quite highly.

Reviewed by Mike Weimerskirch, Lower Division Coordinator, University of Minnesota on 7/15/14

Comprehensiveness rating: 4 see less

The book is thorough in its treatment of topics. It assumes some algebra skills, the first five chapters will go too quickly for a student that needs a comprehensive college algebra course, but the pace is appropriate for a two semester course designed to get students ready for calculus. Had this been a hard copy text, students would complain about its length (over 1000 pages). That's the beauty of open-source .pdf file texts, and the authors made use of it, including deep topics like rotated conics. It contains a discussion of matrices in the chapter on solving equations and dot products (but not cross products).

Content Accuracy rating: 3

I haven't used the text yet myself, and therefore can't verify that the solution to the problems are correct, but it is in its 3rd edition, so it is likely that lots of these kinks have been worked out. The presentation of the mathematics seems fairly standard.

Relevance/Longevity rating: 2

The text has almost no color and is lacking in graphics by today's standards. For example, it is noted that the integers, rationals, reals ... are 'nested' like Matryoshka dolls, but there is no picture, nor even a Venn diagram to illustrate the nesting. Other will contend I am wrong on this, but the degree-minute-second method of measuring angles is a thing of the past. This is one example of where the authors could have examined the standard ways we have taught things for decades and brought them up-to-date. Many of the graphics use a TI-8x series calculator. I am finding that a majority of my students use an online graphing utility (wolframalpha or desmos).

Clarity rating: 3

The authors attempt to let their personality show in their writing with their humor, but it often comes off as an inside joke. If you have either of the authors as your professor, it probably seems like natural conversation, but I could see it as a bit distracting for most students. The mathematical content is very formal, (ordered pairs as defined as 'abscissa and ordinate') but presented in a very standard way. The graphs support the mathematics clearly.

Consistency rating: 5

The format is similar to most formal mathematical texts. The authors have done a good job providing links to references. For example, when a theorem from a previous chapter is referenced, you can click on the link to go back and see the theorem. Unfortunately, you may not be able to get back. Problems are linked in a similar way. It is handy be alerted to a future problem that uses the current material, but if you take the link to look at the problem, you may not be able get back.

Modularity rating: 3

Since the chapters and problem sections are numbered, it's not clear how the links could be reorganized. Otherwise, the material is subdivided in a fairly standard chapter/section/subsection hierarchy. Those that prefer to do trigonometry early could easily move chapter 10 ahead four chapters.

Organization/Structure/Flow rating: 5

Very standard for a math text, with one exception: The solutions to the exercises are given at the end of the section, not at the end of the book. Again, a great feature of open-source material is that if you prefer to have the answers at the end of the book, or in a separate volume all-together, it could be easily done.

Interface rating: 3

There are many links within the text, taking the reader to statements of previous theorems, previous examples, particular exercises which is a handy feature. Unfortunately, when you follow the link, you may not be able to get back. It seems to work back-and-forth in Firefox, but not in GoogleChrome. There are also links to more detailed work if necessary. The main text works out problems at a standard and appropriately small number of steps. For those whose algebra skills are weaker, there are links to more detailed work, which is handy.

Grammatical Errors rating: 3

At times, sentences run on, with the sentence looking more like a paragraph and having multiple commas. Otherwise, the writing looks clean, although at quite a high level.

Cultural Relevance rating: 4

The authors use standard wording to problems and don't try to personalize the material. For example, they say that 'a car is travelling at ...' rather than trying to name the person driving the car in a shallow attempt to include diversity. The book is neutral in this sense.

Comments

Overall, the book is very formal in its definitions, which may be good for advanced high school students who will pursue degrees in math and science, but is likely beyond the level of college students taking precalculus. Composition of functions and one-to-one function are dealt with in a very formal algebraic way, and supported with brief graphical representations. The derivation of formulas is quite formal, leading to the formula being highlighted in a box, leaving the reader to believe that the result is an important formula to be memorized, and thus works well if you believe in memorization. If you want your students to pay attention to the process of creating the formula and the underlying concept, the layout of the book will be a hindrance.