Hardcover ISBN:  9780821891414 
Product Code:  AMSTEXT/20 
362 pp 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
Electronic ISBN:  9780821894774 
Product Code:  AMSTEXT/20.E 
362 pp 
List Price:  $74.00 
MAA Member Price:  $66.60 
AMS Member Price:  $59.20 

Book DetailsPure and Applied Undergraduate TextsVolume: 20; 2013MSC: 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 AnalysisI (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 followup 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.
ReadershipUndergraduate 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


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This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or AnalysisI (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 followup 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.
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