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.
Table of 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