What in the hell is "pre-calculus"? Apparently, I get to teach it next year. There's a book. Sure, I could just say what is in the book, but... the book is crap.
It's got a Chapter 0. I always cringe when I see a Chapter 0. This tells the students about sets, complex numbers, quadratic functions, linear equations, matrices, probability, and statistics. I think sets are a bit of a hard-on for Bourbaki that won't much relate to their next two years of math. Statistics seems better handled after Calculus, but some probability and combinatorics seems good. Matrices seems like a distraction, too.
Chapter 1 is about functions. Fine, but it includes continuity, end behaviour, and limits. Won't that be in the first semester of Calculus?
Chapter 2 is about Power, Polynomial, and Rational Functions. Fine.
Chapter 3 is Exponential and Logarithmic Functions. Great.
Chapter 4 is Trigonometric Functions. If one thing fucks over Calculus student in universities, it's that trigonometric functions are only vaguely understood. Shouldn't I spend more time with this?
Chapter 5 is Trigonometric Identities and Equations. Fine. This needs practice, but in none of this is there ever an introduction to the unit circle.
Chapter 6 is Systems of Equations and Matrices. Is this necessary?
Chapter 7 is Conic Sections, which frankly, seems like a better point of departure than Chapter 1. I mean, these kids just had conic sections in Algebra 2.
Chapter 8 is Vectors... okay... I guess it's pre-calculus with the assumption they'll see Calculus-based Physics....
Chapter 9 is Polar Coordinates and Complex Numbers. I'd pair this with the Conic Sections? Also, I'm not sure if they'll revisit this in Calculus.
Chapter 10 is Sequences and Series. Ok, this they need.
Chapter 11 is Inferential Statistics, which seems more related to other fields they may be studying.
Chapter 12 is Limits and Derivatives. Is this like all the "post WW2" stuff in the history book that the publisher was pretty sure you'd never make it to? It also seems to repeat Chapter 1.
I never had a "pre-calc" class. This book is problem based and my own formation was proof-based. Does anyone have a book they favored? Is there a standard set of knowledge for "pre-calc"? Is it supposed to coordinate with their other classes? What would be in your dream class for "pre-calc"? I'd rather just have one semester of trig, including spherical trig, then a semester of analysis with an emphasis on trigonometric functions.