Real Analysis
Real Analysis
£54.99
GBPThis is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.
- Many more exercises than are commonly found at this level
- Historical commentary
- Many references to both original and secondary sources, including expository and survey articles which are accessible to students
Reviews & endorsements
'… extremely well written: very entertaining and motivating.' Adhemar Bultheel, Bulletin of the London Mathematical Society
'The author writes lucidly in a friendly, readable style and he is strong at motivating, anticipating and reviewing the various themes that permeate the text … The overwhelming impression is that Real analysis was a labour of love for the author, written with a genuine reverence for both its beautiful subject matter and its creators, refiners and teachers down the ages. As such - and high praise indeed - it will sit very happily alongside classics such as Apostol's Mathematical analysis, Royden's Real analysis, Rudin's Real and complex analysis and Hewitt and Stromberg's Real and abstract analysis.' The Mathematical Gazette
Product details
November 2000Paperback
9780521497565
416 pages
254 × 178 × 22 mm
0.73kg
45 b/w illus.
Available
Table of Contents
- Preface
- Part I. Metric Spaces:
- 1. Calculus review
- 2. Countable and uncountable sets
- 3. Metrics and norms
- 4. Open sets and closed sets
- 5. Continuity
- 6. Connected sets
- 7. Completeness
- 8. Compactness
- 9. Category
- Part II. Function Spaces:
- 10. Sequences of functions
- 11. The space of continuous functions
- 12. The Stone-Weierstrass theorem
- 13. Functions of bounded variation
- 14. The Riemann-Stieltjes integral
- 15. Fourier series
- Part III. Lebesgue Measure and Integration:
- 16. Lebesgue measure
- 17. Measurable functions
- 18. The Lebesgue integral
- 19. Additional topics
- 20. Differentiation
- References
- Index.
