A mathematician’s bookshelf is probably more informative than his resume.
The idea of ‘book’ has been recently challenged by the advent of technology. Outstanding authors such as Hatcher (of ‘Algebraic Topology’ fame) prefers to keep an electronic copy of his book. This electronic copy is updated from time to time.
Legendary mathematician Terence Tao religiously publishes through his blog. Blogs allow comments from readers and usage of other forms of content such as Java applets, GeoGebra applets (for demonstrations), video content and so on.
It is possible that in near future, we will experience a new generation of ‘books’. The e-ink technology is coming of age. A combination of written account and interactive activities may replace the traditional ‘static’, ‘uni-directional’ books of past. Until that time, we have the treasure trove of mathematics literature, for readers of all age.
Not a book!
The following resources are not ‘books’. However, it makes sense to begin the discussion with them, as they will compliment the books in our list.
- Python and SageMath
- Terence Tao’s Blog
- n-Category Cafe
- Bigyan dot org
GeoGebra is a “graphing calculator for functions, geometry, algebra, calculus, statistics and 3d math!”. Though the creators of GeoGebra describes it as a ‘graphing calculator’, it is undoubtedly much more than that. Coupled with GeoGebra script, the software is capable of producing outstanding demonstrations of mathematical concepts.
Python is a programming language. SageMath is an open-source, free software for mathematical computation (an alternative to Wolfram, Maple, Matlab etc). SageMath allows programming in Python to perform complex mathematical computations.
Latex is useful for ‘writing mathematics in computer’. As a young mathematician, it is almost as important to write down your proofs, as is to ‘do them’. This makes ‘latex’, an un-ignorable friend for a mathematics student. Internet blogging platforms like WordPress has inbuilt support for Latex.
Terence Tao is a Fields medal-winning mathematician. He regularly publishes in his blog. If not for anything else, this is a great place for getting inspired.
Cut-the-knot is another great place to ‘see’ beautiful pre-college mathematics. It contains Java applets that demonstrate the concepts and adds interactivity to the site.
The following titles are useful for beginners:
- Mathematics can be fun by Yakov Perelman
- Algebra for fun by Yakov Perelman
- The Moscow Puzzles: 359 Mathematical Recreations by Boris A. Kordemsky
- Mathematical Circle; Russian Experience by Fomin
- Figures for Fun: Stories, Puzzles, and Conundrums by Yakov Perelman
These titles are useful for a math olympiad aspirant, typically at the entry level.
- Challenges and thrills of pre-college mathematics by Venkatchala
- Principles and Techniques in Combinatorics by KHEE-MENG KOH
- Inequalities by Little Mathematical Library
These books are useful for students aiming at the highest level of math olympiads.
- Geometric Transformation by Yaglom
- Secrets in Inequalities by FAN JIAN XIONG
- Complex Numbers from A to Z by Titu Andreescu
- Elementary Theory of Numbers by Sierpinsky