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The foundations of mathematics /
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
[2015]
|
| Edición: | Second edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.