I'm a Polish high school student (in Poland education is like this: preschool → primary school → middle school → high school (entrance age 16) → graduate school (entrance age 19~20)). My school is very good (in top 2.2% in Poland). I don't have problems with mathematics in school, but I have the impression that focus falls more often on computation by mechanical following of memorized algorithms than on theory or problem-solving.(adsbygoogle = window.adsbygoogle || []).push({});

I recently became interested in mathemathics beyond school level (my main hobby (and probably future major) is computer science -- I program in several languages). I'd like to improve my understanding (both intuitive and rigorous) of already learned material, but also learn advanced concepts outside the curriculum. I think my proofwriting needs improvement too.

I'd like to buy some good books and start learning from them, but I don't know which direction to explore first. I'd be grateful if You suggested me 2 to 5 books (price is of small importance). Here are books suggested on the Internet to people in similar situation, divided into "directions", in no particular order:

General

- How to Solve It: A New Aspect of Mathematical Method, G. Polya
- How to Prove It: A Structured Approach, Daniel J. Velleman
- Solving Mathematical Problems: A Personal Perspective, Terence Tao
- What Is Mathematics? An Elementary Approach to Ideas and Methods, Richard Courant, Herbert Robbins
- The Princeton Companion to Mathematics, Timothy Gowers, June Barrow-Green, Imre Leader
- Problem-Solving Strategies, Arthur Engel
- The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems, Martin Gardner

Geometry

- Introduction to Geometry, H. S. M. Coxeter
- Geometry, Harold R. Jacobs
- Geometry: Euclid and Beyond, Robert Hartshorne
- Geometry: Seeing, Doing, Understanding, Harold R. Jacobs

Linear Algebra

- Linear Algebra Done Right, Sheldon Axler
- Linear Algebra, Kenneth M Hoffman, Ray Kunze
- Linear Algebra: A Geometric Approach, Ted Shifrin, Malcolm Adams

Calculus

Other

- Fifty Challenging Problems in Probability with Solutions, Frederick Mosteller
- Fundamentals of Number Theory, William J. LeVegue

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# Which direction to explore, books to buy for self-learning (high school student)

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