Introduction to Analysis

Fifth Edition

Edward D. Gaughan, New Mexico State University, Las Cruces, NM

This book is designed to bridge the gap between the intui-tive calculus usually offered at the undergraduate level and the sophisticated analysis encountered at the senior or first-year graduate level. Through its rigorous treatment of standard topics, it offers a deeper understanding of the ideas in the calculus. A series of Projects at the end of each section consist of substantial mathematical problems and the guidance necessary to solve them.

Pure and Applied Undergraduate Texts, Volume 1; 1998; 240 pages; Hardcover; ISBN: 978-0-8218-4787-9; List US$62; AMS members US$49.60; Order code AMSTEXT/1

Differential Topology

Victor Guillemin, Massachusetts Institute of Technology, Cambridge, MA, and Alan PollackThis introduction to differential topology takes the clever

approach of using transversality to avoid advanced methods and demonstrate that mathematics can be done without big machinery. Use of this unifying idea allows for intelligent treatments of important theorems such as the Lefschetz fixed-point theorem and the Poincaré-Hopf index theorem. The 15 to 20 exercises in each section enhance the understanding of the material.

AMS Chelsea Publishing, Volume 370; 1974; 222 pages; Hardcover; ISBN: 978-0-8218-5193-7; List US$40; AMS members US$36; Order code CHEL/370.H

Partial Differential

Equations

Second Edition

Lawrence C. Evans, University of California, Berkeley, CA

This book would be invaluable for a graduate student preparing to do research in PDEs; I wish I had a copy in graduate school.

—MAA Reviews

This second edition of what has been called an essential text for every grad-uate student in analysis includes an array of new topics in partial differential equations, particularly in a new chapter on nonlinear wave equations. The author offers an unparalleled combination of insight and technical detail. The second edition includes 84 new exercises, many of which are elaborate.

Graduate Studies in Mathematics, Volume 19; 2010; 749 pages; Hardcover; ISBN: 978-0-8218-4974-3; List US$93; AMS members US$74.40; Order code GSM/19.R

What’s Happening in the

Mathematical Sciences,

Volume 8

Dana Mackenzie

The author’s way of presenting the material is vivid, simple and engaging. The narrative is illustrated [with] beautiful pictures. For those with a mathematical background ...it will make a fascinating read.

—Ilia Rushkin, Plus Magazine

This volume showcases the latest remarkable progress in pure and applied mathematics, written in an engaging style that conveys modern mathematics’ thrill of discovery. Among the stories in this volume are several showing mathematics’ significant role in current events, from the financial crisis to breast cancer screening. The book chronicles several important conjectures that mathematicians have settled in the past several years.

What’s Happening in the Mathematical Sciences, Volume 8; 2011; 129 pages; Softcover; ISBN: 978-0-8218-4999-6; List US$23; AMS members US$18.40; Order code HAPPENING/8

Advanced Calculus

Second Edition

Patrick M. Fitzpatrick, University of Maryland, College Park, MD

This book offers a rigorous but clear presentation of the fundamental concepts of mathematical analysis, emphasizing that this subject constitutes a coherent body of knowledge. It offers the reader a genuine understanding of the concepts at the heart of the computational algorithms. The book includes exercises that are challenging and in many cases foreshadow future developments.

Pure and Applied Undergraduate Texts, Volume 5; 2006; 590 pages; Hardcover; ISBN: 978-0-8218-4791-6; List US$82; AMS members US$65.60; Order code AMSTEXT/5

Random Walk and

the Heat Equation

Gregory F. Lawler, University of Chicago, IL

This book introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. By beginning with the concrete example of

random walk, the author builds up a structure that finishes with the powerful notion of Brownian motion. This is the first treatment of the connection between the heat equation and Brownian motion that is geared specifically to undergraduates.

Student Mathematical Library, Volume 55; 2010; 156 pages; Softcover; ISBN: 978-0-8218-4829-6; List US$29; AMS members US$23.20; Order code STML/55

AMS CHELSEA PUBLISHING

American Mathematical Society • Providence, Rhode Island

DifferentialTopology

Victor GuilleminAlan Pollack

Graduate Studiesin Mathematics

Volume 19

Partial Differential Equations

Lawrence C. Evans

American Mathematical Society

SECOND EDITION

AMERICAN MATHEMATICAL SOCIETY