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Mathematics: A Very Short Introduction
Timothy Gowers
Table of Contents
1. Models
2. Proof
3. Algorithms
4. Generalization
5. Sameness and similarity
6. Invariants
7. Orders of Magnitude
8. Numbers
9. Limiting processes
10. Dimension
11. Manifolds
12. Differential equations
13. Probability
14. The life of a mathematician
15. The philosophy of mathematics