Ebook: A Problem Book in Real Analysis
- Tags: Analysis
- Series: Problem Books in Mathematics
- Year: 2010
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.
The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis.
Prerequisites for the reader are a robust understanding of calculus and linear algebra.
Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.
The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis.
Prerequisites for the reader are a robust understanding of calculus and linear algebra.
Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.
The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis.
Prerequisites for the reader are a robust understanding of calculus and linear algebra.
Content:
Front Matter....Pages i-vii
Elementary Logic and Set Theory....Pages 1-19
Real Numbers....Pages 21-39
Sequences....Pages 41-62
Limits of Functions....Pages 63-76
Continuity....Pages 77-96
Differentiability....Pages 97-126
Integration....Pages 127-158
Series....Pages 159-180
Metric Spaces....Pages 181-195
Fundamentals of Topology....Pages 197-221
Sequences and Series of Functions....Pages 223-247
Back Matter....Pages 1-6
Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.
The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis.
Prerequisites for the reader are a robust understanding of calculus and linear algebra.
Content:
Front Matter....Pages i-vii
Elementary Logic and Set Theory....Pages 1-19
Real Numbers....Pages 21-39
Sequences....Pages 41-62
Limits of Functions....Pages 63-76
Continuity....Pages 77-96
Differentiability....Pages 97-126
Integration....Pages 127-158
Series....Pages 159-180
Metric Spaces....Pages 181-195
Fundamentals of Topology....Pages 197-221
Sequences and Series of Functions....Pages 223-247
Back Matter....Pages 1-6
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