Text for honors college algebra and trigonometry

Question

I am looking for suggestions on algebra and trigonometry for students who are interested in majoring in mathematics. So typical texts written for average freshman who is forced to take math as a core course is not suitable.

Answer 1

You might want to look at Basic Mathematics by the ever productive Serge Lang. The title is definitely understatement compared to other "college algebra" and precalculus texts, but it's quite accurate from the perspective of a mathematician. As a bonus, it's considerably cheaper than standard College Algebra / Precalculus texts (including the ones my university uses for college algebra).

From the Foreward:

Years ago, the colleges used to give courses in “college algebra” and other subjects which should have been covered in high school. More recently, such courses have been thought unnecessary, but some experiences I have had show that they are just as necessary as ever.

[...]

If only preparatory material for calculus is needed, many portions of this book can be omitted, and attention should be directed to the rules of arithmetic, linear equations (Chapter 2), quadratic equations (Chapter 4), coordinates (the first three sections of Chapter 8), trigonometry (Chapter 11), some analytic geometry (Chapter 12), a simple discussion of functions (Chapter 13), and induction (Chapter 16, §1). The other parts of the book can be omitted.

It seems to have, more or less, the standard stuff (condensed fairly significantly), plus some flourishes like isometries (in general, significantly more geometry than is standard) and permutations. I couldn't find the Table of Contents online or I would have included a link.

Answer 2

Precalculus, Mathematics for Calculus, 4th edition by James Stewart, Lothar Redlin, and Saleem Watson. This edition is a little old so you might be interested in a newer one, but this is the book which I learned precalc from and it was challenging. At the end of some chapters it has "problem solving"sections which should give most precalc student a headache (I know it gave me one), at least if they are not already involved in math competitions or what not.