Real analysis through modern infinitesimals / Nader Vakil.

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"Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external c...

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Bibliographic Details
Main Author: Vakil, Nader
Language:English
Published: Cambridge, UK : Cambridge University Press, 2011, ©2011.
Series:Encyclopedia of mathematics and its applications ; v. 140.
Subjects:
Mathematical analysis.
Set theory.
MATHEMATICS / Mathematical Analysis.
Physical Description:xix, 565 pages : illustrations ; 24 cm.
Format: Book
Contents:
  • Machine generated contents note: 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; A. Vector spaces; B. The b-adic representation of numbers; C. Finite, denumerable, and uncountable sets; D. The syntax of mathematical languages; References; Index.