This isn't a bad thing, just worth noting for those considering adopting the text.
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. 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.). That said, I taught with this book for three semesters and advocated its use for our department for a number of years. The text is very clear for someone who is well-prepared for the material. The footnotes add a fun element to the text but in a way that shouldn't wear out over time. The material has fun "weird dad" style of jokes with exercises involving Sasquatch, for example. The content is standard pre-calculus topics from algebra and trig. I didn't notice any glaring errors in the content. This book covers everything one would want to cover in a precalculus course though with more emphasis on the algebra topics rather than trigonometry. Reviewed by John Hammond, Senior Educator, Wichita State University on 10/14/21 Journalism, Media Studies & Communications +.I specifically picked Columbia’s department because it appears designed for math geniuses - you can’t even get credit for this course, as the normal math sequence begins with Calculus I and many many Columbia students start with Cal II or III. They do cover “polar coordinates, as time permits”, and they were the only syllabus I found that covered it. And Columbia’s class is called “College Algebra and Analytic Geometry (Pre-Calculus)”. In fact, most of the colleges I looked at would not grant students credit for both college algebra and pre-calculus, presumably because the material overlaps too much. (Neither Caltech nor MIT had a pre-cal class, and Carnegie Mellon’s pre-cal class did not address either topic, nor limits). Only one of the pre-cal syllabi I looked at addressed either vectors or conic sections, and that was Georgia Tech’s.
(In fact, that’s what I largely remember learning in HS precal, too.) None of the pre-cal syllabi I looked at talked about limits, although I would imagine some fast-paced or honors pre-cal classes probably introduce students to the topic. Pre-calculus seemed to focus on functions - polynomial, logarithmic, exponential, and rational - and trig.
A few college algebra classes included a treatment of conic sections, and several included basic trig. College algebra mainly seemed to deal with rational expressions, exponents, the quadratic formula, complex numbers, and functions (exponential, polynomial, and logarithmic). I looked at some college algebra and college-level precalculus syllabi available online, and there was a whole lot of overlap. This is entirely dependent upon the school and the specific course in question. I don’t think it’s correct to say that college algebra and precalc overlap.
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