Foundations of mathematical analysis
著者
書誌事項
Foundations of mathematical analysis
（Oxford science publications）
Clarendon Press , Oxford University Press, 1997
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内容説明・目次
内容説明
Foundations of Mathematical Analysis covers a wide variety of topics that will be of great interest to students of pure mathematics or mathematics and philosophy. Aimed principally at postgraduates and well-motivated undergraduates, its primary concern is a discussion of the fundamental number systems, $\Bbb N$, $\Bbb Z$, $\Bbb Q$, $\Bbb R$, and $\Bbb C$, in the context of the branches of mathematics for which they form a starting point; for example, a study of the natural numbers leads on to logic (via G\"odel's theorems), and of the real numbers (as constructed by Cauchy) to metric spaces and topology. Prof. Truss offers a refreshingly original approach to these matters, presenting standard material in new ways, and incorporating less mainstream topics such as long real and rational lines and the p-adic numbers. With a discussion of constructivism and independence questions including Suslin's problem and the continuum hypothesis, Prof. Truss completes a wide-ranging consideration of the development of mathematics from the very beginning, concentrating on the foundational issues particularly related to analysis.
The book is presented in such a manner as to be accessible to non-specialists.
目次
- 1. The natural numbers
- 2. Some set theory
- 3. The integers
- 4. The rational numbers
- 5. The real numbers
- 6. Metric spaces
- 7. Beginnings of analysis
- 8. The complex numbers
- 9. Irrational numbers
- 10. Classical spaces associated with R
- 11. Measure and category
- 12. The continuum problem
- 13. Constructive analysis
- References
- Index
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