Nader Vakil is a Professor of Mathematics at Western Illinois University. He received his PhD from the University of Washington, Seattle, where he worked with Edwin Hewitt. His research interests centre on the foundation of mathematical analysis and applications of the theory of modern infinitesimals to topology and functional analysis.
Preface
Introduction
Part I. Elements of Real Analysis: 1. Internal set theory
2. The real number system
3. Sequences and series
4. The topology of R
5. Limits and continuity
6. Differentiation
7. Integration
8. Sequences and series of functions
9. Infinite series
Part II. Elements of Abstract Analysis: 10. Point set topology
11. Metric spaces
12. Complete metric spaces
13. Some applications of completeness
14. Linear operators
15. Differential calculus on Rn
16. Function space topologies
Appendix A. Vector spaces
Appendix B. The b-adic representation of numbers
Appendix C. Finite, denumerable, and uncountable sets
Appendix D. The syntax of mathematical languages
References
Index.
