Good Pre-Calculus book?

Solution 1:

The series of books Algebra, Functions and Graphs, Trigonometry, and The Method of Coordinates by I. M. Gelfand and various co-authors is an excellent way to supplement a pre-calculus course. The books were written for advanced high school students taking correspondence courses with professors in the Soviet Union and are available in English translation. The books are clearly written, supplement topics found in the typical pre-calculus text, and provide challenging problems.

Another good source is a series of Japanese books edited by Kunihiko Kodaira. They include Mathematics I: Japanese Grade 10, Basic Analysis: Japanese Grade 11, and Algebra and Geometry: Japanese Grade 11. These books are also available in English translation. The grade 10 book is for a required course roughly equivalent to pre-calculus. Regular track students then take a course based on Mathematics II: Japanese grade 11. Mathematically inclined students take courses based on both the Algebra and Geometry and Basic Analysis texts. The texts are a good source of challenging problems and contain material that will supplement what you would learn in a pre-calculus course.

Solution 2:

I'm considerably older than you and failed miserably at math in high school so this may not apply to your case, but I found "Precalculus Mathematics in a Nutshell" by George F. Simmons to be a fantastic encapsulation of pre-calc topics when studying math as an adult. He really boils it down to the essentials. E.g. here's how he opens his chapter on Trig:

Most trigonometry textbooks have been written by people who appear to believe that the importance of the subject lies in its applications to surveying and navigation. Even though very few people become surveyors or navigators, the students who study these books are expected to undertake many lengthy calculations about the heights of flagpoles, the widths of rivers and the positions of ships at sea.

The truth is that the primary importance of trigonometry lies in a completely different direction - in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents and the orbits of the planets around the sun. What matters most in the subject is not making computations about triangles, but grasping the trigonometric functions as indispensable tools in science, engineering and higher mathematics. These functions and their properties are the sole subject matter of this chapter.

The entire book has that vibe. It's wonderful.

Solution 3:

I can recommend the Precalculus volume of a series called the CME Project. It's a high school textbook written by a team of thoughtful and savvy mathematicians. It works to make connections between topics, emphasizes making use of structure in calculation, and builds generalizations from concrete cases. It's a "habits of mind" approach that focuses on mathematical thinking and not just rote processes. I think you'll find in this book what is lacking from your class. Enjoy!