A Guide to Real Variables

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Brand new. We distribute directly for the publisher. The purpose of A Guide to Real Variables is to provide an aid and conceptual support for the student studying for the ... qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated.The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. Read more Show Less

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Overview

A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland's A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis. Together these books provide a concise guide to the subject at all levels, ideal for student preparation for exams.

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Product Details

  • ISBN-13: 9780883853443
  • Publisher: Mathematical Association of America
  • Publication date: 8/3/2009
  • Pages: 163
  • Product dimensions: 6.10 (w) x 9.10 (h) x 0.50 (d)

Meet the Author

Steven G. Krantz was born in San Francisco, California and grew up in Redwood City, California. He received his undergraduate degree from the University of California at Santa Cruz and the Ph.D. from Princeton University. Krantz has held faculty positions at UCLA, Princeton University, Penn State University, and Washington University in St. Louis. He is currently Deputy Director of the American Institute of Mathematics. He has written 160 scholarly papers, over 50 books and is the holder of the Chauvenet Prize and the Beckenbach Book Award.

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Table of Contents

Preface; 1. Basics; 2. Sequences; 3. Series; 4. The topology of the real line; 5. Limits and the continuity of functions; 6. The derivative; 7. The integral; 8. Sequences and series of functions; 9. Advanced topics; Glossary of terms from real variable theory; Bibliography; Index.

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