Ebook: An Introduction to Analysis

As its title indicates, this book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form the book has been used in this way at the University of Michigan, Indiana University, and Texas A&M University, and has proved serviceable. In addition to its primary purpose as a textbook for a formal course, however, it is the authors' hope that this book will also prove of value to readers interested in studying mathematical analysis on their own. Indeed, we believe the wealth and variety of examples and exercises will be especially conducive to this end. A word on prerequisites. With what mathematical background might a prospective reader hope to profit from the study of this book? Our con­ scious intent in writing it was to address the needs of a beginning graduate student in mathematics, or, to put matters slightly differently, a student who has completed an undergraduate program with a mathematics ma­ jor. On the other hand, the book is very largely self-contained and should therefore be accessible to a lower classman whose interest in mathematical analysis has already been awakened.

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This book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form it has been used in this way at the University of Michigan, Indiana University, and Texas A&M University. The book addresses the needs of a beginning graduate student, that is a student who has completed an undergraduate program with a mathematics major.

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This book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form it has been used in this way at the University of Michigan, Indiana University, and Texas A&M University. The book addresses the needs of a beginning graduate student, that is a student who has completed an undergraduate program with a mathematics major.
Content:
Front Matter....Pages i-vii
The rudiments of set theory....Pages 3-24
Number systems....Pages 25-45
Linear algebra....Pages 46-64
Cardinal numbers....Pages 65-79
Ordinal numbers....Pages 80-95
Metric spaces....Pages 96-134
Continuity and limits....Pages 135-173
Completeness and compactness....Pages 174-223
General topology....Pages 224-276
Back Matter....Pages 277-300

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This book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form it has been used in this way at the University of Michigan, Indiana University, and Texas A&M University. The book addresses the needs of a beginning graduate student, that is a student who has completed an undergraduate program with a mathematics major.
Content:
Front Matter....Pages i-vii
The rudiments of set theory....Pages 3-24
Number systems....Pages 25-45
Linear algebra....Pages 46-64
Cardinal numbers....Pages 65-79
Ordinal numbers....Pages 80-95
Metric spaces....Pages 96-134
Continuity and limits....Pages 135-173
Completeness and compactness....Pages 174-223
General topology....Pages 224-276
Back Matter....Pages 277-300
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