Real Analysis
1st Edition
Published on 2. August 2013
978-1-139-63243-0 (ISBN)
Description
This 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.
Reviews / Votes
'... 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 GazetteMore details
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
College/higher education
Illustrations
45 Line drawings, unspecified
File size
37,00 MB
ISBN-13
978-1-139-63243-0 (9781139632430)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
N. L. Carothers
Real Analysis
Book
08/2000
Cambridge University Press
€86.80
Article exhausted; check for reprint
N. L. Carothers
Real Analysis
Book
08/2000
Cambridge University Press
€77.30
Shipment within 15-20 days
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Content
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.
