**Pure and Applied Undergraduate Texts**

Volume: 20;
2013;
362 pp;
Hardcover

MSC: Primary 15; 22; 26; 28; 42; 43; 46;

**Print ISBN: 978-0-8218-9141-4
Product Code: AMSTEXT/20**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-0-8218-9477-4
Product Code: AMSTEXT/20.E**

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

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# Fundamentals of Mathematical Analysis

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*Paul J. Sally, Jr.*

This is a textbook for a course in Honors Analysis (for
freshman/sophomore undergraduates) or Real Analysis (for junior/senior
undergraduates) or Analysis-I (beginning graduates). It is intended
for students who completed a course in “AP Calculus”, possibly
followed by a routine course in multivariable calculus and a
computational course in linear algebra.

There are three features that distinguish this book from many other
books of a similar nature and which are important for the use of this
book as a text. The first, and most important, feature is the
collection of exercises. These are spread throughout the chapters and
should be regarded as an essential component of the student's
learning. Some of these exercises comprise a routine follow-up to the
material, while others challenge the student's understanding more
deeply. The second feature is the set of independent projects
presented at the end of each chapter. These projects supplement the
content studied in their respective chapters. They can be used to
expand the student's knowledge and understanding or as an opportunity
to conduct a seminar in Inquiry Based Learning in which the students
present the material to their class. The third really important
feature is a series of challenge problems that increase in
impossibility as the chapters progress.

The foundational material contained in this book is published separately as Paul Sally's, "Tools of the Trade: Introduction to Advanced Mathematics," also available from the AMS.

#### Readership

Undergraduate and graduate students interested in learning and teaching real analysis.

#### Table of Contents

# Table of Contents

## Fundamentals of Mathematical Analysis

- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- Preface ix10 free
- Acknowledgments xiii14 free
- The construction of real and complex numbers 116 free
- Metric and Euclidean spaces 3348
- Complete metric spaces 7792
- Normed linear spaces 101116
- Differentiation 141156
- Integration 191206
- Fourier analysis on locally compact abelian groups 237252
- Sets, functions, and other basic ideas 271286
- Linear algebra 313328
- Bibliography 351366
- Index of terminology 353368 free
- Index of notation definitions 361376 free
- Back Cover Back Cover1378