Hardcover ISBN:  9780883853443 
Product Code:  DOL/38 
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eBook ISBN:  9780883859162 
Product Code:  DOL/38.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853443 
eBook: ISBN:  9780883859162 
Product Code:  DOL/38.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 
Hardcover ISBN:  9780883853443 
Product Code:  DOL/38 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859162 
Product Code:  DOL/38.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853443 
eBook ISBN:  9780883859162 
Product Code:  DOL/38.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 38; 2009; 147 ppMSC: Primary 26
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 AscoliArzela 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.

Table of Contents

Chapters

Chapter 1. Basics

Chapter 2. Sequences

Chapter 3. Series

Chapter 4. The Topology of the Real Line

Chapter 5. Limits and the Continuity of Functions

Chapter 6. The Derivative

Chapter 7. The Integral

Chapter 8. Sequences and Series of Functions

Chapter 9. Advanced Topics


Reviews

Virtually every graduate program in the US, if not the world, requires its students to take a qualifying exam in real analysis....Mathematicians who are looking for a quick review of the subect of key facts will find this book a useful resource. Recommended.
J. T. Zerger, Choice


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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 AscoliArzela 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.

Chapters

Chapter 1. Basics

Chapter 2. Sequences

Chapter 3. Series

Chapter 4. The Topology of the Real Line

Chapter 5. Limits and the Continuity of Functions

Chapter 6. The Derivative

Chapter 7. The Integral

Chapter 8. Sequences and Series of Functions

Chapter 9. Advanced Topics

Virtually every graduate program in the US, if not the world, requires its students to take a qualifying exam in real analysis....Mathematicians who are looking for a quick review of the subect of key facts will find this book a useful resource. Recommended.
J. T. Zerger, Choice