The books listed below are appropriate for all ages, depending on the mathematical experience of the student. All of them would be interesting to a senior high-school student or adult who is interested in math. Levels 4-5 are subjects normally taught at university. Where possible I have chosen books that emphasize intuition along with rigorous logic.
Level 1
- Marilyn Burns, Math for Smarty Pants
- Anna Weltman, This is Not a Maths Book: A Smart Art Activity Book
- Alex Bellos, Patterns of the Universe: A Colouring Adventure in Math and Beauty
- Daniel Shiffman, Learning Processing (Programming)
Level 2
- Harold Jacobs, Geometry: Seeing, Doing Understanding
- Apostolos Doxiadas & Christos Papadimitriou, Logicomix: An Epic Search for Truth (Graphic Novel)
- Allen Downey, Think Python: How to Think Like a Computer Scientist (Programming)
Level 3
- Daniel Shiffman, The Nature of Code (Programming)
- Paul Zeitz, The Art and Craft of Problem Solving
- Douglas Ensley & J. Winston Crawley, Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games
- Hong Bing-Yu, Problems of Number Theory in Mathematical Competitions
Level 4
- Nathan Carter, Visual Group Theory
- Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid
- Michael Spivak, Calculus
- Harry Gensler, Introduction to Logic
- V.V. Prasolov, Intuitive Topology
- Gilbert Strang, Introduction to Linear Algebra
Level 5
- Michael Artin, Algebra
- Sheldon Axler, Linear Algebra Done Right
- Tristan Needham, Visual Complex Analysis
- Kenneth Ireland & Michael Rosen, A Classical Introduction to Modern Number Theory
