Good Pre-Calculus book? I was reading this article and the author mentioned I should come here and get some advice. I'm 17, currently taking Pre-Calc in high schooling doing really good, but I feel like I'm not getting the most out of it. The teacher feels like he's more interested in covering chapters than getting us to understand things deeply and that worries me. The article says:


  Try to find a book where the author treats you as the intelligent, independent person you are, not as someone who has to take a course for a degree requirement...go to some math forums (like Math Overflow) and ask for book recommendations, telling them you want to become good at math and not just pass a required course; give them specific details and they can help find a book perfect for you.


So yeah asked on Math Overflow and was suggested to come here. I want to get better at math and really understand the concepts deeply and appreciate it like it was intended to. Any help I can get will be appreciated. Thanks!
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.
There are many good textbooks for Calculus, such as

[1] Walter Rudin. Principles in Mathematical Analysis. Academic Press.

[2] Zorich. Mathematical Analysis, Vol. 1-2. Springer-Verlag.

[3] Григорий Михайлович Фихтенгольц. Course of Calculus. ?