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Real Analysis

Real Analysis

$69.99

textbook
  • Date Published: August 2000
  • availability: Available
  • format: Paperback
  • isbn: 9780521497565

$ 69.99
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About the Authors
  • 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.

    • 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
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    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

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    Product details

    • Date Published: August 2000
    • format: Paperback
    • isbn: 9780521497565
    • length: 416 pages
    • dimensions: 254 x 178 x 22 mm
    • weight: 0.73kg
    • contains: 45 b/w illus.
    • availability: 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.

  • Author

    N. L. Carothers, Bowling Green State University, Ohio

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