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Foundations of Mathematical Analysis (Oxford Science Publications)
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, S \Bbb NS , S \Bbb ZS , S \Bbb QS , S \Bbb RS
, and S \Bbb CS , 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.
Contents:
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
Brief Description:
The primary concern of this text is the development of the different number systems, N, Z, Q, R and C, and their consideration leads to specific branches of mathematics.
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