Bleg: Mathematics textbooks for high school self-study August 16, 2009Posted by Akhil Mathew in blegs, General, math education.
Tags: math books, self-study
Inspired by Martin’s latest entry, and the general difficulty of teaching oneself mathematics, I’m going to shamelessly copy imitate the the idea of a recent Ben Webster post about undergraduate summer reading to ask our readers:
What books would you recommend for self-study by a serious high school student interested in mathematics, physics, or computer science?
You can assume familiarity with, at least, reasonably rigorous multivariable calculus and linear algebra. Nevertheless, please do not suggest the proof of Fermat’s Last Theorem. Since we’re not exclusively a math blog, let’s leave the door open to books on physics and computer science as well.
For starters, I will suggest a few of my favorites:
- Principles of Mathematical Analysis, by Walter Rudin. As one professor I know would say, austere beauty. Very rigorous. Same for the sequel Real and Complex Analysis, also by Walter Rudin. Together these hooked me on analysis for a while.
- Algebra, by Herstein. Many fun exercises.
- Algebra, by Lang. It’s not as well-motivated as I would like in some places, and it does a lot, but it is an excellent reference. It also has exercises.
- Commutative Algebra, by Eisenbud. At first I disliked the style of this book, but I found myself coming back to it over and over. It covers quite a bit of material and is accessible. Eisenbud is also more fun to read than most other books on commutative algebra.
- A Comprehensive Introduction to Differential Geometry, by Spivak. I just started reading this. It is immensely fun to read, well-motivated, and rigorous. I already like it much better than Calculus on Manifolds (which I think is much weaker on these attributes). By contrast, I had difficulty with other differential geometry books such as Lang’s Differential and Riemannian Manifolds, since I could not understand the motivation behind all the mathematics, and the level was generally too high for me.