A Guide to Real Variables

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MAA, Aug 13, 2009 - Mathematics - 147 pages
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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.
 

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Contents

Sequences
13
Series
23
The Topology of the Real Line
41
Limits and the Continuity of Functions
55
The Derivative
71
The Integral
85
Sequences and Series of Functions
103
Advanced Topics
115
Glossary of Terms from Real Variable Theory
129
Bibliography
141
About the Author
147
Copyright

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About the author (2009)

Steven Krantz is well-known for his skill in expository writing. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize.

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