From the Book - Second edition.
Part I. The intuitive background
Part II. The beginnings of formalisation
Part III. The development of axiomatic systems
8. Natural numbers and proof by induction
10. Real numbers as a complete ordered field
11. Complex numbers and beyond
Part IV. Using axiomatic systems
12. Axiomatic systems, structure theorems, and flexible thinking
13. Permutations and groups
Part V. Strengthening the foundations
16. Axioms for set theory.
From the eBook - Second edition.
Cover; Preface to the Second Edition; Preface to the First Edition; Contents; Part I The Intuitive Background; 1 Mathematical Thinking; 2 Number Systems; Part II The Beginnings of Formalisation; 3 Sets; 4 Relations; 5 Functions; 6 Mathematical Logic; 7 Mathematical Proof; Part III The Development of Axiomatic Systems; 8 Natural Numbers and Proof by Induction; 9 Real Numbers; 10 Real Numbers as a Complete Ordered Field; 11 Complex Numbers and Beyond; Part IV Using Axiomatic Systems; 12 Axiomatic Systems, Structure Theorems, and Flexible Thinking; 13 Permutations and Groups; 14 Cardinal Numbers.
15 InfinitesimalsPart V Strengthening the Foundations; 16 Axioms for Set Theory; Appendix-How to Read Proofs: The 'Self-Explanation' Strategy; References and Further Reading; Index.