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Fundamentals of Mathematical Analysis

Paul J. Sally, Jr. University of Chicago, Chicago, IL
Available Formats:
Hardcover ISBN: 978-0-8218-9141-4
Product Code: AMSTEXT/20
362 pp
List Price: $79.00 MAA Member Price:$71.10
AMS Member Price: $63.20 Electronic ISBN: 978-0-8218-9477-4 Product Code: AMSTEXT/20.E 362 pp List Price:$74.00
MAA Member Price: $66.60 AMS Member Price:$59.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $118.50 MAA Member Price:$106.65
AMS Member Price: $94.80 Click above image for expanded view Fundamentals of Mathematical Analysis Paul J. Sally, Jr. University of Chicago, Chicago, IL Available Formats:  Hardcover ISBN: 978-0-8218-9141-4 Product Code: AMSTEXT/20 362 pp  List Price:$79.00 MAA Member Price: $71.10 AMS Member Price:$63.20
 Electronic ISBN: 978-0-8218-9477-4 Product Code: AMSTEXT/20.E 362 pp
 List Price: $74.00 MAA Member Price:$66.60 AMS Member Price: $59.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$118.50
MAA Member Price: $106.65 AMS Member Price:$94.80
• Book Details

Volume: 202013
MSC: Primary 15; 22; 26; 28; 42; 43; 46;

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.

• Cover
• Title page
• Contents
• Preface
• Acknowledgments
• The construction of real and complex numbers
• Metric and Euclidean spaces
• Complete metric spaces
• Normed linear spaces
• Differentiation
• Integration
• Fourier analysis on locally compact abelian groups
• Sets, functions, and other basic ideas
• Linear algebra
• Bibliography
• Index of terminology
• Index of notation definitions
• Back Cover

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Volume: 202013
MSC: Primary 15; 22; 26; 28; 42; 43; 46;

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.

• Cover
• Title page
• Contents
• Preface
• Acknowledgments
• The construction of real and complex numbers
• Metric and Euclidean spaces
• Complete metric spaces
• Normed linear spaces
• Differentiation
• Integration
• Fourier analysis on locally compact abelian groups
• Sets, functions, and other basic ideas
• Linear algebra
• Bibliography
• Index of terminology
• Index of notation definitions
• Back Cover
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