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Fundamentals of Mathematical Analysis
 
Paul J. Sally, Jr. University of Chicago, Chicago, IL
Front Cover for Fundamentals of Mathematical Analysis
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
Front Cover for Fundamentals of Mathematical Analysis
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  • Front Cover for Fundamentals of Mathematical Analysis
  • Back Cover for Fundamentals of Mathematical Analysis
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
     
     
    Pure and Applied Undergraduate Texts
    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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Additional Material
     
     
  • Request Exam/Desk Copy
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  • Get Permissions
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.

Readership

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

  • 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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