A Course in Real Analysis book cover

A Course in Real Analysis

The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference.

Audience

One- or two-semester course in real analysis for upper-level undergraduate and graduate students in mathematics, applied mathematics, computer science, engineering, economics, and physics

Hardbound, 688 Pages

Published: January 2012

Imprint: Academic Press

ISBN: 978-0-12-387774-1

Reviews

  • "The exposition is very clear and unhurried and the book would be useful both as a text and a book for self-study. The last chapters go beyond what is usually covered in analysis courses and this is all to the good." -- Sigurdur Helgason, MIT
    **
    "There is a literary quality in the writing that is rare in mathematics texts. It is a pleasure to read this book. The exercises are a strong feature of the book and the examples are well chosen and plentiful." -- Peter Duren, University of Michigan
    **
    "The outstanding features of the book are the wealth of examples and exercises, the interesting biographical data, and the introduction to wavelets and dynamical systems." -- Duong H. Phong, Columbia University
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    "McDonald and Weiss have crafted a treasure chest of exercises in real analysis. Just an amazing and broad collection. Students and researchers will surely benefit from the enormous amount of superb exercises." -- Enno Lenzmann, University of Copenhagen
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    "I was very impressed by the motivating discussions of a number of difficult concepts, along with their fresh approach to the details following. Their general philosophy of starting with concrete ideas, and slowly abstracting, worked well in communicating even the most difficult concepts in the course." -- Todd Kemp, University of California, San Diego


Contents

    1. Set Theory
    2. The Real Number System and Calculus
    3. Lebesgue Measure on the Real Line
    4. The Lebesgue Integral on the Real Line
    5. Elements of Measure Theory
    6. Extensions to Measures and Product Measure
    7. Elements of Probability
    8. Differentiation and Absolute Continuity
    9. Signed and Complex Measures
    10. Topologies, Metrics, and Norms
    11. Separability and Compactness
    12. Complete and Compact Spaces
    13. Hilbert Spaces and Banach Spaces
    14. Normed Spaces and Locally Convex Spaces
    15. Elements of Harmonic Analysis
    16. Measurable Dynamical Systems
    17. Hausdorff Measure and Fractals

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