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HardcoverISBN:  9780821889848 
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Hardcover ISBN:  9780821889848 
Product Code:  AMSTEXT/18 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
eBook ISBN:  9780821891902 
Product Code:  AMSTEXT/18.E 
List Price:  $74.00 
MAA Member Price:  $66.60 
AMS Member Price:  $59.20 
Hardcover ISBN:  9780821889848 
eBookISBN:  9780821891902 
Product Code:  AMSTEXT/18.B 
List Price:  $153.00$116.00 
MAA Member Price:  $137.70$104.40 
AMS Member Price:  $122.40$92.80 

Book DetailsPure and Applied Undergraduate TextsVolume: 18; 2012; 398 ppMSC: Primary 26; 03;
Foundations of Analysis is an excellent new text for undergraduate students in real analysis. More than other texts in the subject, it is clear, concise and to the point, without extra bells and whistles. It also has many good exercises that help illustrate the material. My students were very satisfied with it.
—Nat Smale, University of Utah
I have taught our Foundations of Analysis course (based on Joe Taylor.s book) several times recently, and have enjoyed doing so. The book is wellwritten, clear, and concise, and supplies the students with very good introductory discussions of the various topics, correct and wellthoughtout proofs, and appropriate, helpful examples. The endofchapter problems supplement the body of the text very well (and range nicely from simple exercises to really challenging problems).
—Robert Brooks, University of Utah
An excellent text for students whose future will include contact with mathematical analysis, whatever their discipline might be. It is contentcomprehensive and pedagogically sound. There are exercises adequate to guarantee thorough grounding in the basic facts, and problems to initiate thought and gain experience in proofs and counterexamples. Moreover, the text takes the reader near enough to the frontier of analysis at the calculus level that the teacher can challenge the students with questions that are at the ragged edge of research for undergraduate students. I like it a lot.
—Don Tucker, University of Utah
My students appreciate the concise style of the book and the many helpful examples.
—W.M. McGovern, University of Washington
Analysis plays a crucial role in the undergraduate curriculum. Building upon the familiar notions of calculus, analysis introduces the depth and rigor characteristic of higher mathematics courses. Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system.
The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section.
The list of topics covered is rather standard, although the treatment of some of them is not. The several variable material makes full use of the power of linear algebra, particularly in the treatment of the differential of a function as the best affine approximation to the function at a given point. The text includes a review of several linear algebra topics in preparation for this material. In the final chapter, vector calculus is presented from a modern point of view, using differential forms to give a unified treatment of the major theorems relating derivatives and integrals: Green's, Gauss's, and Stokes's Theorems.
At appropriate points, abstract metric spaces, topological spaces, inner product spaces, and normed linear spaces are introduced, but only as asides. That is, the course is grounded in the concrete world of Euclidean space, but the students are made aware that there are more exotic worlds in which the concepts they are learning may be studied.ReadershipUndergraduate students interested in real analysis.

Table of Contents

Cover

Title page

Contents

Preface

The real numbers

Sequences

Continuous functions

The derivative

The integral

Infinite series

Convergence in Euclidean space

Functions on Euclidean space

Differentiation in several variables

Integration in several variables

Vector calculus

Degrees of infinity

Bibliography

Index

Back Cover


Additional Material

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Foundations of Analysis is an excellent new text for undergraduate students in real analysis. More than other texts in the subject, it is clear, concise and to the point, without extra bells and whistles. It also has many good exercises that help illustrate the material. My students were very satisfied with it.
—Nat Smale, University of Utah
I have taught our Foundations of Analysis course (based on Joe Taylor.s book) several times recently, and have enjoyed doing so. The book is wellwritten, clear, and concise, and supplies the students with very good introductory discussions of the various topics, correct and wellthoughtout proofs, and appropriate, helpful examples. The endofchapter problems supplement the body of the text very well (and range nicely from simple exercises to really challenging problems).
—Robert Brooks, University of Utah
An excellent text for students whose future will include contact with mathematical analysis, whatever their discipline might be. It is contentcomprehensive and pedagogically sound. There are exercises adequate to guarantee thorough grounding in the basic facts, and problems to initiate thought and gain experience in proofs and counterexamples. Moreover, the text takes the reader near enough to the frontier of analysis at the calculus level that the teacher can challenge the students with questions that are at the ragged edge of research for undergraduate students. I like it a lot.
—Don Tucker, University of Utah
My students appreciate the concise style of the book and the many helpful examples.
—W.M. McGovern, University of Washington
Analysis plays a crucial role in the undergraduate curriculum. Building upon the familiar notions of calculus, analysis introduces the depth and rigor characteristic of higher mathematics courses. Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system.
The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section.
The list of topics covered is rather standard, although the treatment of some of them is not. The several variable material makes full use of the power of linear algebra, particularly in the treatment of the differential of a function as the best affine approximation to the function at a given point. The text includes a review of several linear algebra topics in preparation for this material. In the final chapter, vector calculus is presented from a modern point of view, using differential forms to give a unified treatment of the major theorems relating derivatives and integrals: Green's, Gauss's, and Stokes's Theorems.
At appropriate points, abstract metric spaces, topological spaces, inner product spaces, and normed linear spaces are introduced, but only as asides. That is, the course is grounded in the concrete world of Euclidean space, but the students are made aware that there are more exotic worlds in which the concepts they are learning may be studied.
Undergraduate students interested in real analysis.

Cover

Title page

Contents

Preface

The real numbers

Sequences

Continuous functions

The derivative

The integral

Infinite series

Convergence in Euclidean space

Functions on Euclidean space

Differentiation in several variables

Integration in several variables

Vector calculus

Degrees of infinity

Bibliography

Index

Back Cover