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  A TeXas Style Introduction to Proof

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  Product Code: TEXT/35

  Published in 2017
  A TeXas Style Introduction to Proof
  Base Product Code Keyword List: text; TEXT; text/35; TEXT/35; text-35; TEXT-35
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  Title (HTML): A TeXas Style Introduction to Proof
  Author(s) (Product display): Ron Taylor; Patrick X. Rault
  Affiliation(s) (HTML):
  Imprint Blurb: MAA Press: An Imprint of the American Mathematical Society
  Abstract:

  A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the “bridge course”) that also introduces TeX as a tool students can use to communicate their work. As befitting “textless” text, the book is, as one reviewer characterized it, “minimal.” Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult.

  Book Series Name: AMS/MAA Textbooks
  Volume: 35
  Publication Month and Year: 2017-12-31
  Copyright Year: 2017
  Page Count: 161
  Cover Type: Softcover
  Print ISBN-13: 978-1-93951-213-0
  Online ISBN 13: 978-1-61444-625-5
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  Online Sale Terms: Sale price: $30.00
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  Print Add to Cart URL: /some/url/at/AMS/TEXT-35
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-61444-625-5&pisbn=978-1-93951-213-0&epc=TEXT/35.E&ppc=TEXT/35&title=A%20TeXas%20Style%20Introduction%20to%20Proof&author=Ron%20Taylor%3B%20Patrick%20X.%20Rault&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-61444-625-5&pisbn=978-1-93951-213-0&epc=TEXT/35.E&ppc=TEXT/35&title=A%20TeXas%20Style%20Introduction%20to%20Proof&author=Ron%20Taylor%3B%20Patrick%20X.%20Rault&type=R
  Reviews:

  A lovely little book for beginning mathematics majors and other students encountering proofs for the first time. Students should find the text appealing, and it contains many good exercises that a professor can build a course around. … Overall, a most satisfying book for a beginning class in mathematical proofs.

  -- Curt Bennett, Professor of Mathematics at Loyola Marymount University and 2010 Haimo Award Winner

  A TeXas Style Introduction to Proof by Ron Taylor and Patrick X. Rault is truly delightful-full of humanizing charm that softens the hard edge of mathematical rigor. It is gentle, lively, clear, and warm. … From this book, students and their instructors will find many proofs of the joy of mathematics.

  -- Michael Starbird, University Distinguished Teaching Professor ofMathematics at The University of Texas at Austin and 2007 Haimo Award Winner

  Taylor and Rault skillfully guide students through basic proof-writing techniques so that the student createsand discovers the content. The book is well-written, the integration of LaTeX is unique, and the authors have a fantastic sense of humor.

  -- Amanda Croll, Assistant Professor of Mathematics, Concordia University, Irvine

  Cover Image URL: ~~FreeAttachments/text-35-cov.jpg
• 

  Mathematical Interest Theory: Second Edition

  Online: Sale price: $55.20

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  Product Code: TEXT/14

  Published in 2009
  Mathematical Interest Theory: Second Edition
  Base Product Code Keyword List: text; TEXT; text/14; TEXT/14; text-14; TEXT-14
  Print Product Code: TEXT/14
  Online Product Code: TEXT/14.E
  Title (HTML): Mathematical Interest Theory: Second Edition
  Author(s) (Product display): Leslie Jane Federer Vaaler; James W. Daniel
  Affiliation(s) (HTML):
  Imprint Blurb: MAA Press: An Imprint of the American Mathematical Society
  Abstract:

  Mathematical Interest Theory gives an introduction of how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. On the other hand, Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The content is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course.
  
  Mathematical Interest Theory includes more than 240 carefully worked examples. There are over 430 problems, and numerical answers are included in an appendix. A companion student solution manual (see TEXT/15) has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to the Texas Instruments BA II Plus and BA II Plus Professional calculators can be used to efficiently solve the problems. This is important for readers wishing to pass the SOA/CAS joint financial mathematics exam FM/2. However, this part of the book can be skipped without disturbing the flow of the exposition.
  
  Most questions from this textbook are available in WebAssign. WebAssign is a leading provider of online instructional tools for both faculty and students.

  Book Series Name: AMS/MAA Textbooks
  Volume: 14
  Publication Month and Year: 2009-12-31
  Copyright Year: 2009
  Page Count: 475
  Cover Type: Hardcover
  Print ISBN-13: 978-0-88385-754-0
  Online ISBN 13: 978-1-61444-600-2
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  Online Sale Terms: Sale price: $55.20
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-61444-600-2&pisbn=978-0-88385-754-0&epc=TEXT/14.E&ppc=TEXT/14&title=Mathematical%20Interest%20Theory%3A%20Second%20Edition&author=Leslie%20Jane%20Federer%20Vaaler%3B%20James%20W.%20Daniel&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-61444-600-2&pisbn=978-0-88385-754-0&epc=TEXT/14.E&ppc=TEXT/14&title=Mathematical%20Interest%20Theory%3A%20Second%20Edition&author=Leslie%20Jane%20Federer%20Vaaler%3B%20James%20W.%20Daniel&type=R
  Reviews:

  This is an excellent book on interest theory; one of the four books recognized by the Society of Actuaries and the Casualty Actuarial Society as a basis of study for the interest theory component of their joint Financial Mathematics (FM) exam. What I particularly like about 'Mathematical Interest Theory' is that many problems are intrinsically multi-stepped requiring use of several core functions. By providing a multitude of superior problems, the authors are able to familiarize the student, not only with core actuarial function, but also develop their skills in studying the interaction between these functions and real-world problems.

  -- Russell Jay Hendel, UMAP Journal

  Students pursuing an actuarial career as well as those seeking a mathematically based finances course stand to benefit from this informative, up-to-date, and above all, skillfully written treatise. Instructors and students of interest theory owe Daniel and Vaaler a debt of gratitude for their fine efforts.

  -- Susan Staples, Texas Christian University

  We use the Vaaler and Daniel text as our primary learning resource for actuarial science majors as they prepare for the SOA FM/CAS2 financial mathematics exam. Each concept is followed by several illustrative and detailed examples that help students master the big ideas in interest theory.

  -- Mark Maxwell, Director of Actuarial Science, Robert Morris University

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• 

  Common Sense Mathematics

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  Product Code: TEXT/33

  Published in 2016
  Common Sense Mathematics
  Base Product Code Keyword List: text; TEXT; text/33; TEXT/33; text-33; TEXT-33
  Print Product Code: TEXT/33
  Online Product Code: TEXT/33.E
  Title (HTML): Common Sense Mathematics
  Author(s) (Product display): Ethan D. Bolker; Maura B. Mast
  Affiliation(s) (HTML):
  Imprint Blurb: MAA Press: An Imprint of the American Mathematical Society
  Abstract:

  Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions.
  
  We asked ourselves what we hoped our students would remember about this course in ten years' time. From that ten year perspective, thoughts about syllabus—"what topics should we cover?"—seemed much too narrow. What matters more is our wish to change the way our students' minds work the way they approach a problem, or, more generally, the way they approach the world. Most people skip the numbers in newspapers, magazines, on the web, and, more importantly, even in financial information. We hope that in ten years our students will follow the news, confident in their ability to make sense of the numbers they find there and in their daily lives.
  
  Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we've chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics.
  
  An instructor's manual is freely available electronically: click here.
  
  A solutions manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.

  Book Series Name: AMS/MAA Textbooks
  Volume: 33
  Publication Month and Year: 2016-12-31
  Copyright Year: 2016
  Page Count: 308
  Cover Type: Hardcover
  Print ISBN-13: 978-1-93951-210-9
  Online ISBN 13: 978-1-61444-621-7
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-61444-621-7&pisbn=978-1-93951-210-9&epc=TEXT/33.E&ppc=TEXT/33&title=Common%20Sense%20Mathematics&author=Ethan%20D.%20Bolker%3B%20Maura%20B.%20Mast&type=R
  Reviews:

  The authors present a remarkable collection of problem situations gleaned from public media and supplemented by topics of personal finance. The problem situations are not only central to students' everyday lives but also provide a venue for continuing learning beyond a course and beyond school. Based on years of teaching quantitative reasoning, the book offers a clear model for such a course for the inexperienced teacher as well as opportunities for localizing and extending the material for the more experienced teacher.

  -- Bernard L. Madison, University of Arkansas, Fayetteville

  Cover Image URL: ~~FreeAttachments/text-33-cov.jpg
• 

  Ordinary Differential Equations: From Calculus to Dynamical Systems

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  Product Code: TEXT/25

  Published in 2014
  Ordinary Differential Equations: From Calculus to Dynamical Systems
  Base Product Code Keyword List: text; TEXT; text/25; TEXT/25; text-25; TEXT-25
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  Title (HTML): Ordinary Differential Equations: From Calculus to Dynamical Systems
  Author(s) (Product display): Virginia W. Noonburg
  Imprint Blurb: MAA Press: An Imprint of the American Mathematical Society
  Abstract:

  This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences.
  
  The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered, side-by-side with the analytic methods, and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily into a discussion of bifurcation of solutions with respect to parameters. The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations, using several compelling examples, many of which are drawn from population biology. In this chapter the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project, involving a problem recently appearing in the mathematical literature on dynamical systems, is included at the end of Chapter 5. A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises.
  
  The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being "flipped." The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.
  
  An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.
  
  Most questions from this textbook are available in WebAssign. WebAssign is a leading provider of online instructional tools for both faculty and students.

  Book Series Name: AMS/MAA Textbooks
  Volume: 25
  Publication Month and Year: 2014-12-31
  Copyright Year: 2014
  Page Count: 315
  Cover Type: Hardcover
  Print ISBN-13: 978-1-93951-204-8
  Online ISBN 13: 978-1-61444-614-9
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-61444-614-9&pisbn=978-1-93951-204-8&epc=TEXT/25.E&ppc=TEXT/25&title=Ordinary%20Differential%20Equations%3A%20From%20Calculus%20to%20Dynamical%20Systems&author=Virginia%20W.%20Noonburg&type=R
  Reviews:

  This is a textbook that could be used for a standard undergraduate course in ordinary differential equations. It is substantially cheaper than most of the alternatives from commercial publishers, it is well-written, and it appears to have been carefully proofread. The target audience seems to be students whose background in mathematics is not particularly strong. … The approach is modern in the sense that computer algebra systems are presented as important tools for the student, and also in the sense that geometric treatment of nonlinear equations gets substantial attention.

  -- Christopher P. Grant, Mathematical Review Clippings

  Although Noonburg's book is slim, it covers (and covers well) all of the familiar topics one expects to find in a first semester sophomore-level ODE course, and then some. It also has some interesting features that distinguish it from most of the existing textbook literature … The author's writing style is very clear and should be quite accessible to most students reading the book. There are lots of worked examples and interesting applications, including some fairly unusual ones. … This book offers a clean, concise, modern, reader-friendly approach to the subject, at a price that won t make an instructor feel guilty about assigning it. It is certainly worth a very serious look.

  -- Mark Hunacek MAA Reviews

  … The writing is clear, the problems are good, and the material is well motivated and largely self-contained. Some previous acquaintance with linear algebra would, however, be helpful. In summary, this new book is highly recommended for students anxious to discover new techniques.

  -- SIAM Review

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• 

  Modern Cryptography and Elliptic Curves: A Beginner's Guide

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  Product Code: STML/83

  Published in 2017
  Modern Cryptography and Elliptic Curves: A Beginner's Guide
  Base Product Code Keyword List: stml; STML; stml/83; STML/83; stml-83; STML-83
  Print Product Code: STML/83
  Online Product Code: STML/83.E
  Title (HTML): Modern Cryptography and Elliptic Curves: A Beginner’s Guide
  Author(s) (Product display): Thomas R. Shemanske
  Affiliation(s) (HTML): Dartmouth College, Hanover, NH
  Abstract:

  This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC).
  
  Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bézout's theorem as well as the construction of projective space. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollard's method of factorization, Diffie–Hellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstra's elliptic curve factorization method and ECC.
  
  The only real prerequisite for this book is a course on one-variable calculus; other necessary mathematical topics are introduced on-the-fly. Numerous exercises further guide the exploration.

  Book Series Name: Student Mathematical Library
  Volume: 83
  Publication Month and Year: 2017-07-31
  Copyright Year: 2017
  Page Count: 252
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-3582-0
  Online ISBN 13: 978-1-4704-4123-4
  Print ISSN: 1520-9121
  Online ISSN: 1520-9121
  Primary MSC: 11; 68; 14; 91; 81
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4123-4&pisbn=978-1-4704-3582-0&epc=STML/83.E&ppc=STML/83&title=Modern%20Cryptography%20and%20Elliptic%20Curves%3A%20A%20Beginner%26rsquo%3Bs%20Guide&author=Thomas%20R.%20Shemanske&type=R
  Readership:

  Undergraduate and graduate students interested in elliptic curves with applications to cryptography.

  Reviews:

  The main objective of this book, which is mainly aimed at undergraduate students, is to explain the arithmetic of elliptic curves defined over finite fields and to show how those curves can be used in cryptography. In order to do that, the author purposely avoids complex mathematical demonstrations and, instead, presents the concepts in a more descriptive way, suggesting some topics for further exploration by the reader.

  -- Victor Gayoso Martíinez, Mathematical Reviews

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• 

  Game Theory: A Playful Introduction

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  Product Code: STML/80

  Published in 2016
  Game Theory: A Playful Introduction
  Base Product Code Keyword List: stml; STML; stml/80; STML/80; stml-80; STML-80
  Print Product Code: STML/80
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  Title (HTML): Game Theory: A Playful Introduction
  Author(s) (Product display): Matt DeVos; Deborah A. Kent
  Affiliation(s) (HTML): Simon Fraser University, Burnaby, BC, Canada; Drake University, Des Moines, IA
  Abstract:

  This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning. Designed as a textbook for an undergraduate mathematics class and with ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the generous sets of exercises at various levels.

  Book Series Name: Student Mathematical Library
  Volume: 80
  Publication Month and Year: 2016-12-27
  Copyright Year: 2016
  Page Count: 343
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-2210-3
  Online ISBN 13: 978-1-4704-3597-4
  Print ISSN: 1520-9121
  Online ISSN: 1520-9121
  Primary MSC: 91
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3597-4&pisbn=978-1-4704-2210-3&epc=STML/80.E&ppc=STML/80&title=Game%20Theory%3A%20A%20Playful%20Introduction&author=Matt%20DeVos%3B%20Deborah%20A.%20Kent&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3597-4&pisbn=978-1-4704-2210-3&epc=STML/80.E&ppc=STML/80&title=Game%20Theory%3A%20A%20Playful%20Introduction&author=Matt%20DeVos%3B%20Deborah%20A.%20Kent&type=R
  Readership:

  Undergraduate students, graduate students, and researchers interested in game theory.

  Reviews:

  'Game theory: a playful introduction' is exactly as the title claims: an interactive introduction to the subject. It is a well-written text which starts with a thorough analysis of combinatorial game theory before smoothly transitioning to classical game theory...Not only is the text readable, but there are also an adequate number of exercises at the end of each chapter. These exercises are structured as a scaffold beginning with a check of basic skills and building up to challenging proofs...Overall, this text is a well-structured, well-written introduction to game theory.

  -- Brittany Shelton, Mathematical Reviews

  The topics covered here are chosen for a broad and versatile look at the subject, the writing style is clear and enjoyable, examples are plentiful, and there is a good selection of exercises, both computational and proof-oriented...In addition to clear and engaging writing, and a good selection of exercises, this book also boasts an excellent bibliography...I have no hesitation whatsoever recommending it as a text for an introductory undergraduate course.

  -- Mark Hunacek, MAA Reviews

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• 

  Matrix Groups for Undergraduates: Second Edition

  Online: Sale price: $29.40

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  Product Code: STML/79

  Published in 2016
  Matrix Groups for Undergraduates: Second Edition
  Base Product Code Keyword List: stml; STML; stml/79; STML/79; stml-79; STML-79
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  Title (HTML): Matrix Groups for Undergraduates: Second Edition
  Author(s) (Product display): Kristopher Tapp
  Affiliation(s) (HTML): Saint Joseph’s University, Philadelphia, PA
  Abstract:

  Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups.
  
  Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots.
  
  This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.

  From reviews of the First Edition:

  This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. … The book combines an intuitive style of writing with rigorous definitions and proofs, giving examples from fields of mathematics, physics, and other sciences where matrices are successfully applied. The book will surely be interesting and helpful for students in algebra and their teachers.

  —European Mathematical Society Newsletters

  This is an excellent, well-written textbook which is strongly recommended to a wide audience of readers interested in mathematics and its applications. The book is suitable for a one semester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.

  —MathSciNet (or Mathematical Reviews)

  Book Series Name: Student Mathematical Library
  Volume: 79
  Publication Month and Year: 2016-04-07
  Copyright Year: 2016
  Page Count: 239
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-2722-1
  Online ISBN 13: 978-1-4704-2938-6
  Print ISSN: 1520-9121
  Online ISSN: 1520-9121
  Primary MSC: 20
  Secondary MSC: 22
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2938-6&pisbn=978-1-4704-2722-1&epc=STML/79.E&ppc=STML/79&title=Matrix%20Groups%20for%20Undergraduates%3A%20Second%20Edition&author=Kristopher%20Tapp&type=R
  Readership:

  Undergraduate and graduate students and research mathematicians interested in teaching and learning Lie groups, in particular, classical Lie groups.

  Reviews:

  This book offers a very nice introduction to the theory of matrix groups and their Lie algebras. The background is kept to a minimum, only basics of calculus, linear algebra and group theory are assumed, while background on topology (of subsets of Euclidean space) is developed in the text. While the text gives complete and exact proofs, it is easy to read, appeals to intuition, and contains many pictures and helpful exercises.

  -- A. Cap, Monatshefte für Mathematik

  [T]he second edition is an expanded and improved version of the original. It can be strongly recommended for an undergraduate course in Lie groups, or as complementary reading for a course in group theory. Prerequisites are basic: knowledge of algebra, geometry, and analysis at an undergraduate level. Hence the book is suitable for a wide audience of readers who are meeting applications of group theory in other areas of mathematics and physics, or even further afield.

  -- Alla S. Detinko, Mathematical Reviews

  The author gives an inspiring presentation of the topics presented in this book.

  -- Erich W. Ellers, Zentralblatt Math

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• 

  Differential Geometry: Curves -- Surfaces -- Manifolds, Third Edition

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  Product Code: STML/77

  Published in 2015
  Differential Geometry: Curves -- Surfaces -- Manifolds, Third Edition
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  Title (HTML): Differential Geometry: Curves — Surfaces — Manifolds, Third Edition
  Author(s) (Product display): Wolfgang Kühnel
  Affiliation(s) (HTML): University of Stuttgart, Stuttgart, Germany
  Abstract:

  This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and—as a new feature—a good number of solutions to selected exercises.

  This new edition is an improved version of what was already an excellent and carefully written introduction to both differential geometry and Riemannian geometry. In addition to a variety of improvements, the author has included solutions to many of the problems, making the book even more appropriate for use in the classroom.

  —Colin Adams, Williams College

  This book on differential geometry by Kühnel is an excellent and useful introduction to the subject. … There are many points of view in differential geometry and many paths to its concepts. This book provides a good, often exciting and beautiful basis from which to make explorations into this deep and fundamental mathematical subject.

  — Louis Kauffman, University of Illinois at Chicago

  Book Series Name: Student Mathematical Library
  Volume: 77
  Publication Month and Year: 2015-12-22
  Copyright Year: 2015
  Page Count: 403
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-2320-9
  Online ISBN 13: 978-1-4704-2675-0
  Print ISSN: 1520-9121
  Online ISSN: 1520-9121
  Primary MSC: 53
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2675-0&pisbn=978-1-4704-2320-9&epc=STML/77.E&ppc=STML/77&title=Differential%20Geometry%3A%20Curves%20%26mdash%3B%20Surfaces%20%26mdash%3B%20Manifolds%2C%20Third%20Edition&author=Wolfgang%20K%FChnel&type=R
  Readership:

  Undergraduate and graduate students interested in differential geometry.

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• 

  Winding Around: The Winding Number in Topology, Geometry, and Analysis

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  Product Code: STML/76

  Published in 2015
  Winding Around: The Winding Number in Topology, Geometry, and Analysis
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  Title (HTML): Winding Around: The Winding Number in Topology, Geometry, and Analysis
  Author(s) (Product display): John Roe
  Affiliation(s) (HTML): Pennsylvania State University, State College, PA
  Abstract:

  The winding number is one of the most basic invariants in topology. It measures the number of times a moving point \(P\) goes around a fixed point \(Q\), provided that \(P\) travels on a path that never goes through \(Q\) and that the final position of \(P\) is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can

  • help us show that every polynomial equation has a root (the fundamental theorem of algebra),
  • guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem),
  • explain why every simple closed curve has an inside and an outside (the Jordan curve theorem),
  • relate calculus to curvature and the singularities of vector fields (the Hopf index theorem),
  • allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators),
  • generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem).

  
  
  All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses.

  This book is published in cooperation with Mathematics Advanced Study Semesters

  Book Series Name: Student Mathematical Library
  Volume: 76
  Publication Month and Year: 2015-09-03
  Copyright Year: 2015
  Page Count: 269
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-2198-4
  Online ISBN 13: 978-1-4704-2625-5
  Print ISSN: 1520-9121
  Online ISSN: 1520-9121
  Primary MSC: 55
  Secondary MSC: 57; 47; 58
  Textbook?: true
  Applied Math?: false
  MAA Book?: false
  Electronic Media?: false
  Apparel or Gift: false
  Publisher (non-AMS): Published in cooperation with Mathematics Advanced Study Semesters
  SXG Subject: GT
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/stml-76
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2625-5&pisbn=978-1-4704-2198-4&epc=STML/76.E&ppc=STML/76&title=Winding%20Around%3A%20The%20Winding%20Number%20in%20Topology%2C%20Geometry%2C%20and%20Analysis&author=John%20Roe&type=R
  Readership:

  Undergraduates and beginning graduate students interested in (and trying to learn) ideas concentrated around the notion of the winding number and its appearance in such areas of mathematics as analysis, differential geometry, and topology.

  Reviews:

  This book covers a lot of ground. But it does so in a clear and careful manner that would make a terrific read for the prepared undergraduate. It is a study in how an intuitive idea can transport one into some deep waters of mathematics, and that is an important story to tell.

  -- John McCleary, Mathematical Reviews

  People who teach university-level mathematics for a living often find themselves reading lots of books on the subject. But even for the book-lovers among us, after you've just read about ten linear algebra texts, all of which look like they were stamped from the same cookie cutter, the process can occasionally wear thin. It's very pleasant, then, to stumble across a book that is genuinely unique, that addresses a topic in a way not found elsewhere, and that teaches you something that you didn't know before. It's even nicer when the book in question does a really good job of it, as is the case with the book under review. ...Roe's writing style is succinct, but clear and quite elegant; I could practically hear a British accent as I read the book. This clarity of writing and the numerous appendices help make the book accessible.

  -- MAA Online

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• 

  A First Course in the Calculus of Variations

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  Product Code: STML/72

  Published in 2014
  A First Course in the Calculus of Variations
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  Title (HTML): A First Course in the Calculus of Variations
  Author(s) (Product display): Mark Kot
  Affiliation(s) (HTML): University of Washington, Seattle, WA
  Abstract:

  This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields.
  
  The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics.
  
  Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.

  Book Series Name: Student Mathematical Library
  Volume: 72
  Publication Month and Year: 2014-10-06
  Copyright Year: 2014
  Page Count: 298
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-1495-5
  Online ISBN 13: 978-1-4704-1961-5
  Print ISSN: 1520-9121
  Online ISSN: 1520-9121
  Primary MSC: 49
  Textbook?: true
  Applied Math?: true
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  SXG Subject: DE; AP
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1961-5&pisbn=978-1-4704-1495-5&epc=STML/72.E&ppc=STML/72&title=A%20First%20Course%20in%20the%20Calculus%20of%20Variations&author=Mark%20Kot&type=R
  Readership:

  Undergraduate students interested in the calculus of variations.

  Reviews:

  The author addresses several subtle aspects of the subject that are traditionally not covered in texts that are geared to the interests of applied mathematicians, physicists, and engineers ... What distinguishes this book from others is the author's style of introducing each topic with a practical example that serves to motivate the subsequent theory. Rather than presenting a prosaic collection of lemmas and theorems, the author demonstrates the practical need for addressing the more subtle aspects of the theory, which is well suited for an applications-oriented audience. The text also includes historical notes that are fascinating to read.

  -- Joel Storch, IEEE Control Systems Magazine

  The text follows the historical development of the subject and offers the reader a mixture of theory, techniques, and applications. This nice book is likely to be especially successful. [The] author has managed admirably to bring to light both the beauty and the usefulness of the calculus of variations in many problems arising in applied sciences, thus creating a beautiful introduction to this field. All the details are included in a way that is both attractive and easy for students to follow.

  -- Zentralblatt Math

  This text follows the historical development of the subject and offers the reader a mixture of theory, techniques and applications. ...The author integrates theory and applications quite deftly with the historical background and gives us a very attractive book. ...The introductory chapter gives a good indication of what's to come: clear writing, a carefully laid out development, well-chosen line drawings, and a thoughtful selection of recommended reading. ...This would serve admirably as the text for a course or as a tool for self-study. The exercises are first rate...

  -- MAA Reviews

  Kot displays more than a pedagogical sensitivity to notation (a traditional pitfall!); he inculcates the appreciation of notational nuance in his readers. Everyone who wants to learn this subject should start by investing the few hours necessary to read this book.

  -- CHOICE

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• 

  Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction

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  Product Code: STML/69

  Published in 2014
  Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction
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  Title (HTML): Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction
  Author(s) (Product display): Mark Levi
  Affiliation(s) (HTML): Pennsylvania State University, University Park, PA
  Abstract:

  It is hard to imagine a more original and insightful approach to classical mechanics. Most physicists would regard this as a well-worn and settled subject. But Mark Levi's treatment sparkles with freshness in the many examples he treats and his unexpected analogies, as well as the new approach he brings to the principles. This is inspired pedagogy at the highest level.

  —Michael Berry, Bristol University, UK

  How do you write a textbook on classical mechanics that is fun to learn from? Mark Levi shows us the way with his new book: “Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction.” The combination of his unique point of view with his physical and geometrical insights and numerous instructive examples, figures and problem sets make it a pleasure to work through.

  —Paul Rabinowitz, University of Wisconsin

  This is a refreshingly low key, down-to-earth account of the basic ideas in Euler-Lagrange and Hamilton-Jacobi theory and of the basic mathematical tools that relate these two theories. By emphasizing the ideas involved and relegating to the margins complicated computations and messy formulas, he has written a textbook on an ostensibly graduate level subject that second and third year undergraduates will find tremendously inspiring.

  —Victor Guillemin, MIT
  
  This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark.
  
  Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the “tennis racket paradox”; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more.
  
  In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems.
  
  With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

  This book is published in cooperation with Mathematics Advanced Study Semesters

  Book Series Name: Student Mathematical Library
  Volume: 69
  Publication Month and Year: 2014-03-07
  Copyright Year: 2014
  Page Count: 299
  Cover Type: Softcover
  Print ISBN-13: 978-0-8218-9138-4
  Online ISBN 13: 978-1-4704-1444-3
  Print ISSN: 1520-9121
  Online ISSN: 1520-9121
  Primary MSC: 34; 37; 49; 70; 00
  Textbook?: true
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1444-3&pisbn=978-0-8218-9138-4&epc=STML/69.E&ppc=STML/69&title=Classical%20Mechanics%20with%20Calculus%20of%20Variations%20and%20Optimal%20Control%3A%20An%20Intuitive%20Introduction&author=Mark%20Levi&type=R
  Readership:

  Undergraduate and graduate students interested in classical mechanics and ordinary differential equations.

  Reviews:

  This book can be recommended to students and also to everyone involved in preparing an introductory course in advanced classical mechanics, due to the well-selected material and, even more so, the clear presentation.

  -- Zentralblatt Math

  One of the most valuable aspects of the book — unfortunately rare among textbooks — is that we see an author in command of his subject who shares not just the bare facts but how he thinks about them and how all the pieces fit together.

  -- MAA

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• 

  Game Theory and Strategy

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  Product Code: NML/36

  Published in 1993
  Game Theory and Strategy
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  Title (HTML): Game Theory and Strategy
  Author(s) (Product display): Philip D. Straffin
  Imprint Blurb: MAA Press: An Imprint of the American Mathematical Society
  Abstract:

  This book is an introduction to mathematical game theory, which might better be called the mathematical theory of conflict and cooperation. It is applicable whenever two individuals—or companies, or political parties, or nations—confront situations where the outcome for each depends on the behavior of all. What are the best strategies in such situations? If there are chances of cooperation, with whom should you cooperate, and how should you share the proceeds of cooperation? Since its creation by John von Neumann and Oskar Morgenstern in 1944, game theory has shed new light on business, politics, economics, social psychology, philosophy, and evolutionary biology.
  
  In this book, its fundamental ideas are developed with mathematics at the level of high school algebra and applied to many of these fields (see the table of contents). Ideas like “fairness” are presented via axioms that fair allocations should satisfy; thus the reader is introduced to axiomatic thinking as well as to mathematical modeling of actual situations.

  Book Series Name: Anneli Lax New Mathematical Library
  Volume: 36
  Publication Month and Year: 1993-12-31
  Copyright Year: 1993
  Page Count: 244
  Cover Type: Softcover
  Print ISBN-13: 978-0-88385-637-6
  Online ISBN 13: 978-0-88385-950-6
  Online ISSN:
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  Reviews:

  “Game Theory and Strategy” is an elegant, crystal-clear expository work. Key concepts are emphasized and clearly explained.

  -- Nature

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• 

  Euclidean Geometry: A Guided Inquiry Approach

  Online: Sale price: $23.40

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  Product Code: MCL/9

  Published in 2012
  Euclidean Geometry: A Guided Inquiry Approach
  Base Product Code Keyword List: mcl; MCL; mcl/9; MCL/9; mcl-9; MCL-9
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  Title (HTML): Euclidean Geometry: A Guided Inquiry Approach
  Author(s) (Product display): David M. Clark
  Affiliation(s) (HTML): State University of New York, New Paltz, New Paltz, NY
  Publisher Blurb: A co-publication of the AMS and the Mathematical Sciences Research Institute
  Abstract:

  Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation.
  
  Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry.
  
  The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority.
  
  This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers.
  
  In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

  Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

  Book Series Name: MSRI Mathematical Circles Library
  Volume: 9
  Publication Month and Year: 2012-06-26
  Copyright Year: 2012
  Page Count: 127
  Cover Type: Softcover
  Print ISBN-13: 978-0-8218-8985-5
  Online ISBN 13: 978-0-8218-9106-3
  Print ISSN: 1944-8074
  Online ISSN: 1944-8074
  Primary MSC: 97
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  SXG Subject: GT
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-0-8218-9106-3&pisbn=978-0-8218-8985-5&epc=MCL/9.E&ppc=MCL/9&title=Euclidean%20Geometry%3A%20A%20Guided%20Inquiry%20Approach&author=David%20M.%20Clark&type=R
  Readership:

  Undergraduate students interested in geometry and secondary education.

  Reviews:

  An interesting and singular approach of the Euclidean geometry is contained in this book … [The] book covers all the topics listed in the common core state standards for high school synthetic geometry … [T]he didactical approach of the large collection of problems, solutions and geometrical constructions is very important to consider it as a good textbook for teaching and learning synthetic geometry.

  -- Mauro Garcia Pupo, Zentralblatt MATH

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• 

  Knots, Molecules, and the Universe: An Introduction to Topology

  Online: Sale price: $41.40

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  Product Code: MBK/96

  Published in 2016
  Knots, Molecules, and the Universe: An Introduction to Topology
  Base Product Code Keyword List: mbk; MBK; mbk/96; MBK/96; mbk-96; MBK-96
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  Title (HTML): Knots, Molecules, and the Universe: An Introduction to Topology
  Author(s) (Product display): Erica Flapan
  Affiliation(s) (HTML): Pomona College, Claremont, CA
  Abstract:

  This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook.
  
  The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material.
  
  The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.

  Publication Month and Year: 2015-12-22
  Copyright Year: 2016
  Page Count: 386
  Cover Type: Hardcover
  Print ISBN-13: 978-1-4704-2535-7
  Online ISBN 13: 978-1-4704-2819-8
  Online ISSN:
  Primary MSC: 57; 92; 94
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2819-8&pisbn=978-1-4704-2535-7&epc=MBK/96.E&ppc=MBK/96&title=Knots%2C%20Molecules%2C%20and%20the%20Universe%3A%20An%20Introduction%20to%20Topology&author=Erica%20Flapan&type=R
  Readership:

  Undergraduate students and instructors interested in elementary topology.

  Reviews:

  [T]his is a wonderful introduction to geometry and topology and their applications to the sciences. The book contains a unique collection of topics that might entice young readers to continue their academic careers by learning more about the world of mathematics.

  -- Claus Ernst, Zentralblatt MATH

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• 

  How to Teach Mathematics: Third Edition

  Online: Sale price: $21.00

  Print: Sale price: $21.00

  Product Code: MBK/89

  Published in 2015
  How to Teach Mathematics: Third Edition
  Base Product Code Keyword List: mbk; MBK; mbk/89; MBK/89; mbk-89; MBK-89
  Print Product Code: MBK/89
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  Title (HTML): How to Teach Mathematics: Third Edition
  Author(s) (Product display): Steven G. Krantz
  Affiliation(s) (HTML): Washington University, St. Louis, MO
  Abstract:

  This third edition is a lively and provocative tract on how to teach mathematics in today's new world of online learning tools and innovative teaching devices. The author guides the reader through the joys and pitfalls of interacting with modern undergraduates—telling you very explicitly what to do and what not to do. This third edition has been streamlined from the second edition, but still includes the nuts and bolts of good teaching, discussing material related to new developments in teaching methodology and technique, as well as adding an entire new chapter on online teaching methods.

  Publication Month and Year: 2015-10-01
  Copyright Year: 2015
  Page Count: 146
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-2552-4
  Online ISBN 13: 978-1-4704-2673-6
  Online ISSN:
  Primary MSC: 97
  Textbook?: true
  Applied Math?: false
  MAA Book?: false
  Home Page?: false
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  Apparel or Gift: false
  SXG Subject: ME
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/mbk-89
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2673-6&pisbn=978-1-4704-2552-4&epc=MBK/89.E&ppc=MBK/89&title=How%20to%20Teach%20Mathematics%3A%20Third%20Edition&author=Steven%20G.%20Krantz&type=R
  Readership:

  Graduate students and researchers interested in improving their teaching of college mathematics.

  Reviews:

  'How to Teach Mathematics' is an excellent resource for anyone who teaches post-secondary mathematics. While the author, Steven G. Krantz, is a self-proclaimed traditionalist and much of the book is focused on lecturing, even the most ardent active learning proponent will find useful nuggets...The book is also a useful read for those who conduct research in undergraduate mathematics education because it provides insights and perspectives from a reflective mathematician...I feel comfortable recommending the book to anyone interested in mathematics teaching, especially at the undergraduate level...I think this book could play a helpful role in the ongoing conversations between mathematicians and mathematics educators regarding undergraduate mathematics instruction.

  -- Sean Larsen, International Journal of Research in Undergraduate Mathematics Education

  The author guides the reader through the joys and pitfalls of interacting with modern undergraduates --- telling you very explicitly what to do and what not to do.

  -- Zentralblatt MATH

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• 

  Sage for Undergraduates

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  Product Code: MBK/87

  Published in 2015
  Sage for Undergraduates
  Base Product Code Keyword List: mbk; MBK; mbk/87; MBK/87; mbk-87; MBK-87
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  Title (HTML): Sage for Undergraduates
  Author(s) (Product display): Gregory V. Bard
  Affiliation(s) (HTML): University of Wisconsin–Stout, Menomonie, WI
  Abstract:

  Professor Bard has provided a valuable service by carefully explaining everything an undergraduate student of mathematics, or a teacher of these topics, needs to get started with Sage quickly and easily. It will also be useful for any student or teacher of another STEM discipline. There is an excellent mix of the most frequently used commands, along with warnings about common pitfalls or caveats. I highly recommend it for anyone new to Sage, or who desires an overview of the system's impressive capabilities.

  —Robert A. Beezer, University of Puget Sound

  This book is a sort of “Missing Manual” that explains how Sage can be used in a range of standard mathematics courses, instead of targeting specialists like much existing Sage documentation. The depth of content is very impressive, and describes—in a single coherent narrative—how to successfully use Sage for a wide swath of undergraduate applied topics.

  —William Stein, University of Washington, Seattle
  
  As the open-source and free competitor to expensive software like Maple™, Mathematica®, Magma, and MATLAB®, Sage offers anyone with access to a web browser the ability to use cutting-edge mathematical software and display his or her results for others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students toward the end of Calculus II (single-variable integral calculus) or higher-level course work such as Multivariate Calculus, Differential Equations, Linear Algebra, or Math Modeling.
  
  The book assumes no background in computer science, but the reader who finishes the book will have learned about half of a first semester Computer Science I course, including large parts of the Python programming language. The audience of the book is not only math majors, but also physics, engineering, finance, statistics, chemistry, and computer science majors.

  Publication Month and Year: 2015-02-16
  Copyright Year: 2015
  Page Count: 352
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-1111-4
  Online ISBN 13: 978-1-4704-2042-0
  Primary MSC: 15; 34; 65; 90; 97
  Secondary MSC: 11; 12; 28; 40; 68
  Textbook?: true
  Applied Math?: true
  MAA Book?: false
  Electronic Media?: false
  Apparel or Gift: false
  SXG Subject: GI; NT; AN; AP
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/mbk-87
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2042-0&pisbn=978-1-4704-1111-4&epc=MBK/87.E&ppc=MBK/87&title=Sage%20for%20Undergraduates&author=Gregory%20V.%20Bard&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2042-0&pisbn=978-1-4704-1111-4&epc=MBK/87.E&ppc=MBK/87&title=Sage%20for%20Undergraduates&author=Gregory%20V.%20Bard&type=R
  Readership:

  Undergraduate students, graduate students, and research mathematicians interested in using Sage in (teaching) math modeling, engineering, physics, multivariate calculus, differential equations, matrix algebra, and linear algebra.

  Reviews:

  Gregory Bard's 'Sage for Undergraduates' is sitting on the desktop of all of my computers. I've been interested in using Sage for sometime now, but have not successfully overcome my unfamiliarity with the syntax. Thanks to Bard's reference, I am now using Sage daily for my classes, research projects, and interaction with my students. If it were not for Bard's reference, I would not have found Sage so useful. Each day, I am more familiar with Sage and more confident that I can use it for computing and visualization. I intend to recommend that my students use it and have already referred my complex analysis class to it. I have also used it to demonstrate geometric concepts to my 11-year-old grandchildren.

  -- Jim Morrow, University of Washington, Seattle

  This excellent Sage book itself is 'open' in both the spirit and letter senses: Its realizations include an online, web-based version; color and black-and-white, downloadable PDF versions; and ancillary material, including two excellent Sage-informed algebra texts (linear [5], abstract [6]), running the gamut of Sage applications and examples. ...The book's content is well written, well organized, and keeps the reader (more accurately and fortuitously, user) constantly attentive and engaged. ...This jewel of a book-cum-infrastructure is not just 'for undergraduates,' but will be of great benefit to all.

  -- George Hacken, Computing Reviews

  Click here to watch UC Berkeley Professor Kenneth Ribet review Sage.

  -- Professor Kenneth Ribet, UC Berkeley

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• 

  An Introduction to Stochastic Differential Equations

  Online: Sale price: $20.40

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  Product Code: MBK/82

  Published in 2013
  An Introduction to Stochastic Differential Equations
  Base Product Code Keyword List: mbk; MBK; mbk/82; MBK/82; mbk-82; MBK-82
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  Title (HTML): An Introduction to Stochastic Differential Equations
  Author(s) (Product display): Lawrence C. Evans
  Affiliation(s) (HTML): University of California, Berkeley, Berkeley, CA
  Abstract:

  These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic.

  —Srinivasa Varadhan, New York University

  This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability.

  —George Papanicolaou, Stanford University

  This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically.

  —Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch
  
  This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive “white noise” and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Itô stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing.
  
  This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

  Publication Month and Year: 2013-12-13
  Copyright Year: 2013
  Page Count: 151
  Cover Type: Softcover
  Print ISBN-13: 978-1-4704-1054-4
  Online ISBN 13: 978-1-4704-1612-6
  Primary MSC: 65; 60
  Textbook?: true
  Applied Math?: true
  MAA Book?: false
  Electronic Media?: false
  Apparel or Gift: false
  SXG Subject: DE; PR; AP
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/mbk-82
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1612-6&pisbn=978-1-4704-1054-4&epc=MBK/82.E&ppc=MBK/82&title=An%20Introduction%20to%20Stochastic%20Differential%20Equations&author=Lawrence%20C.%20Evans&type=R
  Readership:

  Undergraduate and graduate students interested in probability theory and stochastic differential equations.

  Reviews:

  ... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evans' always clear explanations, it is fun too.

  -- MAA Reviews

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• 

  Computational Topology: An Introduction

  Online: Sale price: $37.20

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  Product Code: MBK/69

  Published in 2010
  Computational Topology: An Introduction
  Base Product Code Keyword List: mbk; MBK; mbk/69; MBK/69; mbk-69; MBK-69
  Print Product Code: MBK/69
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  Title (HTML): Computational Topology: An Introduction
  Author(s) (Product display): Herbert Edelsbrunner; John L. Harer
  Affiliation(s) (HTML): Duke University, Durham, NC and Geomagic, Research Triangle Park, NC; Duke University, Durham, NC
  Abstract:

  Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering.
  
  The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

  Publication Month and Year: 2009-12-08
  Copyright Year: 2010
  Page Count: 241
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4925-5
  Online ISBN 13: 978-1-4704-1208-1
  Primary MSC: 00; 52; 55; 57; 68
  Textbook?: true
  Applied Math?: true
  MAA Book?: false
  Electronic Media?: false
  Apparel or Gift: false
  SXG Subject: GT; AP
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/mbk-69
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1208-1&pisbn=978-0-8218-4925-5&epc=MBK/69.E&ppc=MBK/69&title=Computational%20Topology%3A%20An%20Introduction&author=Herbert%20Edelsbrunner%3B%20John%20L.%20Harer&type=R
  Readership:

  Graduate students and research mathematicians interested in topology, algorithms, and applications to science and engineering.

  Reviews:

  This book is a very welcome, untraditional, thorough and well-organized introduction to a young and quickly developing discipline on the crossroads between mathematics, computer science, and engineering.

  -- DMV Newsletter

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• 

  Game Theory, Alive

  Online: Sale price: $45.00

  Print: Sale price: $45.00

  Product Code: MBK/101

  Published in 2017
  Game Theory, Alive
  Base Product Code Keyword List: mbk; MBK; mbk/101; MBK/101; mbk-101; MBK-101
  Print Product Code: MBK/101
  Online Product Code: MBK/101.E
  Title (HTML): Game Theory, Alive
  Author(s) (Product display): Anna R. Karlin; Yuval Peres
  Affiliation(s) (HTML): University of Washington, Seattle, WA; Microsoft Research, Redmond, WA
  Abstract:

  We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities.
  
  This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments.
  
  The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

  Publication Month and Year: 2017-04-27
  Copyright Year: 2017
  Page Count: 372
  Cover Type: Hardcover
  Print ISBN-13: 978-1-4704-1982-0
  Online ISBN 13: 978-1-4704-3667-4
  Online ISSN:
  Primary MSC: 91
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  SXG Subject: DM; AP
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/mbk-101
  Online Price 1 Label: List
  Online Price 1: 75.00
  Print Price 1 Label: List
  Print Price 1: 75.00
  Online Price 2 Label: AMS Member
  Online Price 2: 60.00
  Print Price 2 Label: AMS Member
  Print Price 2: 60.00
  Online Price 3 Label: MAA Member
  Online Price 3: 67.50
  Print Price 3 Label: MAA Member
  Print Price 3: 67.50
  Dual Price 1 Label: List
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  Dual Price 2 Label: AMS Member
  Dual Price 2: 75
  Online Sale Terms: Sale price: $45.00
  Print Sale Terms: Sale price: $45.00
  Print Add to Cart URL: /some/url/at/AMS/MBK-101
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3667-4&pisbn=978-1-4704-1982-0&epc=MBK/101.E&ppc=MBK/101&title=Game%20Theory%2C%20Alive&author=Anna%20R.%20Karlin%3B%20Yuval%20Peres&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3667-4&pisbn=978-1-4704-1982-0&epc=MBK/101.E&ppc=MBK/101&title=Game%20Theory%2C%20Alive&author=Anna%20R.%20Karlin%3B%20Yuval%20Peres&type=R
  Readership:

  Undergraduate and graduate students and professors interested in game theory and decision making.

  Reviews:

  This is an attractive candidate as a text for a mathematically rigorous course in game theory at the upper undergraduate or elementary graduate level. It offers an appealing and versatile selection of topics (including some modern ones), clear and well-motivated exposition, a good selection of examples, and a nicely-chosen selection of exercises (some but not all of which have solutions in the back of the book). People who teach, or simply have an interest in game theory, will certainly find this book worth a look.

  -- Mark Hunacek, MAA Reviews

  Game theory's influence is felt in a wide range of disciplines, and the authors deliver masterfully on the challenge of presenting both the breadth and coherence of its underlying world-view. The book achieves a remarkable synthesis, introducing the reader to the blend of economic insight, mathematical elegance, scientific impact, and counter-intuitive punch that characterizes game theory as a field.

  -- Jon Kleinberg, Cornell University, 2006 Nevanlinna Prize winner

  A game theory textbook by people who love … games! It covers many classic as well as recent topics of game theory. Its rigorous treatment, interspersed with illuminating examples, makes it a challenging pleasure to read.

  -- Sergiu Hart, The Hebrew University of Jerusalem

  This beautifully written book introduces the reader to the rich and flourishing subject of game theory. From an exhaustive account of basics of the classical theory to a wide range of modern themes—including auctions, matching markets, sequential decision making—the book presents a great variety of topics in a rigorous yet entertaining manner. The authors guide the reader through the intricacies of game theory with an exquisite mathematical elegance. For anyone interested in the topic, experts and beginners alike, this book is a must.

  -- Gábor Lugosi, Pompeu Fabra University, Barcelona, Spain

  It is great to have a comprehensive game theory textbook including so many modern topics.

  -- Éva Tardos, Cornell University

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• 

  The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots

  Online: Sale price: $20.40

  Print: Sale price: $20.40

  Product Code: KNOT

  Published in 2004
  The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
  Base Product Code Keyword List: knot; KNOT
  Print Product Code: KNOT
  Online Product Code: KNOT.E
  Title (HTML): The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
  Author(s) (Product display): Colin C. Adams
  Affiliation(s) (HTML): Williams College, Williamstown, MA
  Abstract:

  Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research.
  
  The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics.
  
  This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book.
  
  Colin Adams received the Mathematical Association of America (MAA) Award for Distinguished Teaching and has been an MAA Polya Lecturer and a Sigma Xi Distinguished Lecturer.
  
  Other key books of interest available from the AMS are Knots and Links and The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes.

  Publication Month and Year: 2004-08-11
  Copyright Year: 2004
  Page Count: 307
  Cover Type: Softcover
  Print ISBN-13: 978-0-8218-3678-1
  Online ISBN 13: 978-1-4704-2490-9
  Online ISSN:
  Primary MSC: 57
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  SXG Subject: GT
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/knot
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  Online Price 2 Label: AMS Member
  Online Price 2: 27.20
  Print Price 2 Label: AMS Member
  Print Price 2: 27.20
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  Online Price 3: 30.60
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  Dual Price 2: 34
  Online Sale Terms: Sale price: $20.40
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2490-9&pisbn=978-0-8218-3678-1&epc=KNOT.E&ppc=KNOT&title=The%20Knot%20Book%3A%20An%20Elementary%20Introduction%20to%20the%20Mathematical%20Theory%20of%20Knots&author=Colin%20C.%20Adams&type=R
  Readership:

  Undergraduates, graduate students, and research mathematicians interested in topology and knot theory.

  Reviews:

  From reviews of the first edition:

  Amazingly understandable … After reading it twice, I still pick it up and scan it … this book belongs in every mathematical library.

  -- Charles Ashbacher, Book Reviews Editor, Journal of Recreational Mathematics

  Throughout the book there are lots of exercises of various degrees of difficulty. Many 'unsolved questions' provide opportunity for further research. I liked reading this book. ... well written, enjoyable to read, and very accessible.

  -- Zentralblatt MATH

  I thought the book was very well suited for an undergraduate knot theory/ topology course. The exposition was very clear.

  -- Jennifer Taback, Bowdoin College

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• 

  An Introduction to Measure Theory

  Online: Sale price: $33.60

  Print: Sale price: $33.60

  Product Code: GSM/126

  Published in 2011
  An Introduction to Measure Theory
  Base Product Code Keyword List: gsm; GSM; gsm/126; GSM/126; gsm-126; GSM-126
  Print Product Code: GSM/126
  Online Product Code: GSM/126.E
  Title (HTML): An Introduction to Measure Theory
  Author(s) (Product display): Terence Tao
  Affiliation(s) (HTML): University of California, Los Angeles, Los Angeles, CA
  Abstract:

  This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis.
  
  There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text.
  
  As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

  Book Series Name: Graduate Studies in Mathematics
  Volume: 126
  Publication Month and Year: 2011-09-14
  Copyright Year: 2011
  Page Count: 206
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-6919-2
  Online ISBN 13: 978-1-4704-1187-9
  Print ISSN: 1065-7339
  Online ISSN: 1065-7339
  Primary MSC: 28
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  SXG Subject: AN
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/gsm-126
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1187-9&pisbn=978-0-8218-6919-2&epc=GSM/126.E&ppc=GSM/126&title=An%20Introduction%20to%20Measure%20Theory&author=Terence%20Tao&type=R
  Readership:

  Graduate students interested in analysis, in particular, measure theory.

  Reviews:

  The entire book is not just an introduction to measure theory as the title says but a lively dialogue on mathematics with a focus on measure theory.

  -- Mahendra Nadkarni, Mathematical Reviews

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• 

  Algebra: Chapter 0

  Online: Sale price: $53.40

  Print: Sale price: $53.40

  Product Code: GSM/104

  Published in 2009
  Algebra: Chapter 0
  Base Product Code Keyword List: gsm; GSM; gsm/104; GSM/104; gsm-104; GSM-104
  Print Product Code: GSM/104
  Online Product Code: GSM/104.E
  Title (HTML): Algebra: Chapter 0
  Author(s) (Product display): Paolo Aluffi
  Affiliation(s) (HTML): Florida State University, Tallahassee, FL
  Abstract:

  Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

  Book Series Name: Graduate Studies in Mathematics
  Volume: 104
  Publication Month and Year: 2009-07-15
  Copyright Year: 2009
  Page Count: 713
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4781-7
  Online ISBN 13: 978-1-4704-1168-8
  Print ISSN: 1065-7339
  Online ISSN: 1065-7339
  Primary MSC: 00
  Secondary MSC: 12; 13; 15; 18; 20
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  SXG Subject: AA
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/gsm-104
  Online Price 1 Label: List
  Online Price 1: 89.00
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1168-8&pisbn=978-0-8218-4781-7&epc=GSM/104.E&ppc=GSM/104&title=Algebra%3A%20Chapter%200&author=Paolo%20Aluffi&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1168-8&pisbn=978-0-8218-4781-7&epc=GSM/104.E&ppc=GSM/104&title=Algebra%3A%20Chapter%200&author=Paolo%20Aluffi&type=R
  Readership:

  Undergraduate and graduate students interested in algebra.

  Reviews:

  An obvious question: why another graduate algebra book? Aren't there all but too many already? Is there anything genuinely novel to be done when it comes to educating fledgling graduate students in this subject, given such an already well-populated and high-quality field? Well, the answer is yes. And the title of the book under review, Algebra: Chapter 0, is already a clue to what the author, Paolo Aluffi, is up to. In a perhaps Bourbakian sense, the prevailing motivation and objective is to present the subject at hand in a manner that pays proper due to relatively new foundations, making for a rather different orientation and flavor for what ensues. ...His treatment of these preliminaries is thorough as well as eminently accessible: Aluffi writes well, clearly and engagingly. This characterizes all of Algebra: Chapter 0, actually, and makes it easy to recommend the book enthusiastically even aside from the fact that I am a big fan of category theory to begin with.

  -- MAA Online

  This self-contained introduction is suitable for a first sequence at the beginning graduate or upper undergraduate level. A distinguishing feature of the book is the early introduction of categories, used as a unifying theme.

  -- SciTech Book News

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• 

  Advanced Calculus: Second Edition

  Online: Sale price: $52.20

  Print: Sale price: $52.20

  Product Code: AMSTEXT/5

  Published in 2006
  Advanced Calculus: Second Edition
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/5; AMSTEXT/5; amstext-5; AMSTEXT-5
  Print Product Code: AMSTEXT/5
  Online Product Code: AMSTEXT/5.E
  Title (HTML): Advanced Calculus: Second Edition
  Author(s) (Product display): Patrick M. Fitzpatrick
  Affiliation(s) (HTML): University of Maryland, College Park, MD
  Abstract:

  Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables.
  
  Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material.
  
  Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis.
  
  An instructor's manual for this title is available electronically. Please send email to textbooks@ams.org for more information.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 5
  Publication Month and Year: 2009-01-13
  Copyright Year: 2006
  Page Count: 590
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4791-6
  Online ISBN 13: 978-1-4704-1118-3
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 26
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  SXG Subject: AN
  Online Price 1 Label: List
  Online Price 1: 87.00
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  Print Add to Cart URL: /some/url/at/AMS/AMSTEXT-5
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1118-3&pisbn=978-0-8218-4791-6&epc=AMSTEXT/5.E&ppc=AMSTEXT/5&title=Advanced%20Calculus%3A%20Second%20Edition&author=Patrick%20M.%20Fitzpatrick&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1118-3&pisbn=978-0-8218-4791-6&epc=AMSTEXT/5.E&ppc=AMSTEXT/5&title=Advanced%20Calculus%3A%20Second%20Edition&author=Patrick%20M.%20Fitzpatrick&type=R
  Readership:

  Undergraduate students interested in teaching and learning undergraduate analysis.

  Reviews:

  This is a well-written and well-structured book with clearly explained proofs and a good supply of exercises, some of them are quite challenging. It is this reviewer's opinion that the volume should be an excellent and useful tool for undergraduate students.

  -- Teodora-Liliana Radulescu, Zentralblatt MATH

  CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=978-0-8218-4791-6&WT.mc.id=American%20Mathematical%20Society
• 

  Fourier Analysis and Its Applications

  Online: Sale price: $45.60

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  Product Code: AMSTEXT/4

  Published in 1992
  Fourier Analysis and Its Applications
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/4; AMSTEXT/4; amstext-4; AMSTEXT-4
  Print Product Code: AMSTEXT/4
  Online Product Code: AMSTEXT/4.E
  Title (HTML): Fourier Analysis and Its Applications
  Author(s) (Product display): Gerald B. Folland
  Affiliation(s) (HTML): University of Washington, Seattle, WA
  Abstract:

  This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 4
  Publication Month and Year: 2009-01-13
  Copyright Year: 1992
  Page Count: 433
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4790-9
  Online ISBN 13: 978-1-4704-1117-6
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 42
  Secondary MSC: 00; 33; 34; 44; 46
  Textbook?: true
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  MAA Book?: false
  Home Page?: false
  Featured?: false
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  Online Price 1 Label: List
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1117-6&pisbn=978-0-8218-4790-9&epc=AMSTEXT/4.E&ppc=AMSTEXT/4&title=Fourier%20Analysis%20and%20Its%20Applications&author=Gerald%20B.%20Folland&type=R
  Readership:

  Undergraduate and graduate students interested in studying the Fourier transform.

  Reviews:

  The book is a detailed and very readable treatise on the theory and practice of series expansions and transforms. The primary audience consists of advanced undergraduates in mathematics, physics, and engineering, but the book is also a useful reference for more advanced workers . . . The strength of the book comes from its careful presentation of theory followed by detailed applications, with good illustrations, and finally a generous collection of exercises (with answers). The prose is smooth and gives understandable discussions of technical difficulties . . . This text can surely be recommended for use in a one or two semester course, or as a reference for graduate students or other persons who want to see what sort of problems Fourier analysis was invented to solve.

  -- C. F. Dunkl, Zentralblatt MATH

  With the same mastery as in his Real analysis, the author now offers us this excellent textbook on Fourier analysis: Fourier series, orthogonal systems, Bessel functions, Fourier and Laplace transforms, which are all very powerful mathematical tools in many a scientific domain. Without being exhaustive and without falling into a profusion of boring details, it nevertheless gives a panorama of these topics that is as complete as the framework of the book allows. Thus this text, which is designed for courses at the advanced undergraduate level and beyond, will also serve as a useful reference book.

  -- Mathematical Reviews

  CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=978-0-8218-4790-9&WT.mc.id=American%20Mathematical%20Society
• 

  A Discrete Transition to Advanced Mathematics

  Online: Sale price: $45.60

  Print: Sale price: $45.60

  Product Code: AMSTEXT/3

  Published in 2004
  A Discrete Transition to Advanced Mathematics
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/3; AMSTEXT/3; amstext-3; AMSTEXT-3
  Print Product Code: AMSTEXT/3
  Online Product Code: AMSTEXT/3.E
  Title (HTML): A Discrete Transition to Advanced Mathematics
  Author(s) (Product display): Bettina Richmond; Thomas Richmond
  Affiliation(s) (HTML): Western Kentucky University, Bowling Green, KY; Western Kentucky University, Bowling Green, KY
  Abstract:

  As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last three chapters address topics such as continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio, and may be used for independent reading assignments. The treatment of sequences may be used to introduce epsilon-delta proofs. The selection of topics provides flexibility for the instructor in a course designed to spark the interest of students through exciting material while preparing them for subsequent proof-based courses.
  
  The book includes a large number of problems of varying difficulty. A student manual with solutions to selected problems is available electronically: www.ams.org/bookstore/pspdf/amstext-3-solutions.pdf.
  
  An instructor's manual for this title is available electronically. Please send email to textbooks@ams.org for more information.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 3
  Publication Month and Year: 2009-02-18
  Copyright Year: 2004
  Page Count: 424
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4789-3
  Online ISBN 13: 978-1-4704-1116-9
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 00
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  Dual Price 2: 76
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1116-9&pisbn=978-0-8218-4789-3&epc=AMSTEXT/3.E&ppc=AMSTEXT/3&title=A%20Discrete%20Transition%20to%20Advanced%20Mathematics&author=Bettina%20Richmond%3B%20Thomas%20Richmond&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1116-9&pisbn=978-0-8218-4789-3&epc=AMSTEXT/3.E&ppc=AMSTEXT/3&title=A%20Discrete%20Transition%20to%20Advanced%20Mathematics&author=Bettina%20Richmond%3B%20Thomas%20Richmond&type=R
  Readership:

  Undergraduate students interested in becoming mathematicians.

  Reviews:

  This nice text is a welcome addition to existing literature on discrete mathematics, mathematical reasoning and proofs, and similar topics.

  -- Zentralblatt MATH

  CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=978-0-8218-4789-3&WT.mc.id=American%20Mathematical%20Society
• 

  The Tools of Mathematical Reasoning

  Online: Sale price: $41.40

  Print: Sale price: $41.40

  Product Code: AMSTEXT/26

  Published in 2016
  The Tools of Mathematical Reasoning
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/26; AMSTEXT/26; amstext-26; AMSTEXT-26
  Print Product Code: AMSTEXT/26
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  Title (HTML): The Tools of Mathematical Reasoning
  Author(s) (Product display): Tamara J. Lakins
  Affiliation(s) (HTML): Allegheny College, Meadville, PA
  Abstract:

  This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 26
  Publication Month and Year: 2016-09-08
  Copyright Year: 2016
  Page Count: 217
  Cover Type: Hardcover
  Print ISBN-13: 978-1-4704-2899-0
  Online ISBN 13: 978-1-4704-3496-0
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 00
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  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/amstext-26
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  Online Sale Terms: Sale price: $41.40
  Print Sale Terms: Sale price: $41.40
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3496-0&pisbn=978-1-4704-2899-0&epc=AMSTEXT/26.E&ppc=AMSTEXT/26&title=The%20Tools%20of%20Mathematical%20Reasoning&author=Tamara%20J.%20Lakins&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3496-0&pisbn=978-1-4704-2899-0&epc=AMSTEXT/26.E&ppc=AMSTEXT/26&title=The%20Tools%20of%20Mathematical%20Reasoning&author=Tamara%20J.%20Lakins&type=R
  Readership:

  Undergraduate students interested in advancing beyond computation-oriented mathematics courses to proof-based courses.

  Reviews:

  Lakins' book is a nice, solid exposition of the tools students need as they transition to abstract mathematical thinking.

  -- Michele Intermont, MAA Reviews

  Cover Image URL: ~~FreeAttachments/amstext-26-cov.jpg
  CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=978-1-4704-2899-0&WT.mc.id=American%20Mathematical%20Society
• 

  Partial Differential Equations: Second Edition

  Online: Sale price: $55.80

  Print: Sale price: $55.80

  Product Code: GSM/19.R

  Published in 2010
  Partial Differential Equations: Second Edition
  Base Product Code Keyword List: gsm/19; GSM/19; gsm; GSM; gsm/19.r; GSM/19.R; gsm-19.r; GSM-19.R; gsm-19; GSM-19; gsm-19-r; GSM-19-R
  Print Product Code: GSM/19.R
  Online Product Code: GSM/19.R.E
  Title (HTML): Partial Differential Equations: Second Edition
  Author(s) (Product display): Lawrence C. Evans
  Affiliation(s) (HTML): University of California, Berkeley, Berkeley, CA
  Abstract:

  This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including

  • a new chapter on nonlinear wave equations,
  • more than 80 new exercises,
  • several new sections,
  • a significantly expanded bibliography.

  About the First Edition:

  I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. … Evans' book is evidence of his mastering of the field and the clarity of presentation.

  —Luis Caffarelli, University of Texas

  It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations … Every graduate student in analysis should read it.

  —David Jerison, MIT

  I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's … I am very happy with the preparation it provides my students.

  —Carlos Kenig, University of Chicago

  Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge … An outstanding reference for many aspects of the field.

  —Rafe Mazzeo, Stanford University

  Book Series Name: Graduate Studies in Mathematics
  Volume: 19
  Publication Month and Year: 2010-03-02
  Copyright Year: 2010
  Page Count: 749
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4974-3
  Online ISBN 13: 978-1-4704-1144-2
  Print ISSN: 1065-7339
  Online ISSN: 1065-7339
  Primary MSC: 35
  Secondary MSC: 49; 47
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  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/gsm-19-r
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1144-2&pisbn=978-0-8218-4974-3&epc=GSM/19.R.E&ppc=GSM/19.R&title=Partial%20Differential%20Equations%3A%20Second%20Edition&author=Lawrence%20C.%20Evans&type=R
  Readership:

  Graduate students and research mathematicians interested in partial differential equations.

  Reviews:

  This second edition of the textbook addresses even more of the current research directions on PDEs and Professor Evans should be praised for taking the time and effort to make an already successful and wonderful book even better. Needless to say, I recommend this book, with unreserved enthusiasm, to anyone with an interest on the study of PDEs.

  -- Mathematical Reviews

  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

  Related Products:
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• 

  Analysis: Second Edition

  Online: Sale price: $28.80

  Print: Sale price: $28.80

  Product Code: GSM/14.R

  Published in 2001
  Analysis: Second Edition
  Base Product Code Keyword List: gsm/14; GSM/14; gsm; GSM; gsm/14.r; GSM/14.R; gsm-14.r; GSM-14.R; gsm-14; GSM-14; gsm-14-r; GSM-14-R
  Print Product Code: GSM/14.R
  Online Product Code: GSM/14.R.E
  Title (HTML): Analysis: Second Edition
  Author(s) (Product display): Elliott H. Lieb; Michael Loss
  Affiliation(s) (HTML): Princeton University, Princeton, NJ; Georgia Institute of Technology, Atlanta, GA
  Abstract:

  Significantly revised and expanded, this new Second Edition provides readers at all levels—from beginning students to practicing analysts—with the basic concepts and standard tools necessary to solve problems of analysis, and how to apply these concepts to research in a variety of areas.
  
  Authors Elliott Lieb and Michael Loss take you quickly from basic topics to methods that work successfully in mathematics and its applications. While omitting many usual typical textbook topics, Analysis includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to an advanced level of understanding with a minimum of fuss, and, at the same time, doing so in a rigorous and pedagogical way. Many topics that are useful and important, but usually left to advanced monographs, are presented in Analysis, and these give the beginner a sense that the subject is alive and growing.
  
  This new Second Edition incorporates numerous changes since the publication of the original 1997 edition and includes:
  
  Features:

  • a new chapter on eigenvalues that covers the min-max principle, semi-classical approximation, coherent states, Lieb-Thirring inequalities, and more
  • extensive additions to chapters covering Sobolev Inequalities, including the Nash and Log Sobolev inequalities
  • new material on Measure and Integration
  • many new exercises
  • and much more …

  
  
  The Second Edition continues its no-nonsense approach to the topic that has made it one of the best selling books on the subject. It is an authoritative, straightforward volume that readers—from the graduate student, to the professional mathematician, to the physicist or engineer using analytical methods—will find useful both as a reference and as a guide to real problem solving.
  
  About the authors: Elliott Lieb is Professor of Mathematics and Physics at Princeton University and is a member of the US, Austrian, and Danish Academies of Science. He is also the recipient of several prizes including the 1988 AMS/SIAM Birkhoff Prize. Michael Loss is Professor of Mathematics at the Georgia Institute of Technology.

  Book Series Name: Graduate Studies in Mathematics
  Volume: 14
  Publication Month and Year: 2001-03-21
  Copyright Year: 2001
  Page Count: 348
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-2783-3
  Online ISBN 13: 978-1-4704-1143-5
  Print ISSN: 1065-7339
  Online ISSN: 1065-7339
  Primary MSC: 28; 42; 46; 49
  Secondary MSC: 26; 31; 81
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  SXG Subject: AN
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/gsm-14-r
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1143-5&pisbn=978-0-8218-2783-3&epc=GSM/14.R.E&ppc=GSM/14.R&title=Analysis%3A%20Second%20Edition&author=Elliott%20H.%20Lieb%3B%20Michael%20Loss&type=R
  Readership:

  Introductory-level graduate students in mathematics; research mathematicians, natural scientists, and engineers interested in learning some of the important tools of modern analysis.

  Reviews:

  This is an excellent textbook on analysis and it has several unique features: Proofs of heat kernel estimates, the Nash inequality and the logarithmic Sobolev inequality are topics that are seldom treated on the level of a textbook. Best constants in several inequalities, such as Young's inequality and the logarithmic Sobolev inequality, are also included. A thorough treatment of rearrangement inequalities and competing symmetries appears in book form for the first time. There is an extensive treatment of potential theory and its applications to quantum mechanics, which, again, is unique at this level. Uniform convexity of \(L^p\) space is treated very carefully. The presentation of this important subject is highly unusual for a textbook. All the proofs provide deep insights into the theorems. This book sets a new standard for a graduate textbook in analysis.

  -- Shing-Tung Yau

  Begins with a down-to-earth intro … aims at a wide range of essential applications … The book should work equally well in a one-, or in a two-semester course … great for students to have … This choice of book is also especially agreeable to grad students in physics who need to read up on the tools of analysis.

  -- Palle Jorgensen

  Praise for the previous edition …

  I find the selection of the material covered in the book very attractive and I recommend the book to anybody who wants to learn about classical as well as modern mathematical analysis.

  -- European Mathematical Society Newsletter

  The essentials of modern analysis … are presented in a rigorous and pedagogical way … readers … are guided to a level where they can read the current literature with understanding … treatment of the subject is as direct as possible.

  -- Zentralblatt MATH

  Lieb and Loss offer a practical presentation of real and functional analysis at the beginning graduate level … could be used as a two-semester introduction to graduate analysis … not all of the topics covered are typical. The authors introduce the subject with a thorough presentation … [an] informative exposition.

  -- CHOICE

  This is definitely a beautiful book … useful reference even for specialists since the authors present basic tools in a very rigorous way … they show clever methods how to calculate, equally useful for beginners as well as advanced specialists … well known exercises.

  -- Mathematica Bohemica

  Interesting textbook ... brings the reader quickly to a level where a wide range of topics can be appreciated ... well-written textbook ... can be read by anyone with a good knowledge of calculus ... useful for graduate students in mathematics and physics.

  -- ZAMM–Journal of Applied Mathematics and Mechanics

  I liked the book very much. The topics chosen were suited toward concepts that I wanted students to master.

  -- Gary Sampson, Auburn University

  In the area of analysis / real analysis / functional analysis there are a very large number of books at all levels, many of them very well known: the one under review is an unusual addition to the list. The book by Lieb and Loss assumes little on the part of the reader beyond a good college calculus course and, as such, begins with the basics of Lebesgue integral and yet is able to go deep into quite a few topics usually treated in advanced or more specialised texts. This unorthodox development makes it possible for a reader to reach, in the space of less than three hundred pages, completely rigorous mathematical treatment of several interesting physical problems. The authors have exercised remarkable discipline in their choice of topics to reach such depths quickly, yet they have not made it a linear development with the sole aim of showing these applications.

  To sum up, this is an excellent book and the present inexpensive edition is recommended for the libraries of all interested in analysis.

  -- Resonance: Journal of Science Edition

  CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=978-0-8218-2783-3&WT.mc.id=American%20Mathematical%20Society
• 

  Differential Topology

  Online: Sale price: $25.20

  Print: Sale price: $25.20

  Product Code: CHEL/370.H

  Published in 1974
  Differential Topology
  Base Product Code Keyword List: chel/370; CHEL/370; chel; CHEL; chel/370.h; CHEL/370.H; chel-370.h; CHEL-370.H; chel-370; CHEL-370; chel-370-h; CHEL-370-H
  Print Product Code: CHEL/370.H
  Online Product Code: CHEL/370.H.E
  Title (HTML): Differential Topology
  Author(s) (Product display): Victor Guillemin; Alan Pollack
  Affiliation(s) (HTML): Massachusetts Institute of Technology, Cambridge, MA;
  Imprint Blurb: AMS Chelsea Publishing: An Imprint of the American Mathematical Society
  Abstract:

  Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within.
  
  The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea—transversality—the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré–Hopf index theorem, and Stokes theorem.
  
  The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance.
  
  The book is suitable for either an introductory graduate course or an advanced undergraduate course.

  Book Series Name: AMS Chelsea Publishing
  Volume: 370
  Publication Month and Year: 2010-08-17
  Copyright Year: 1974
  Page Count: 222
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-5193-7
  Online ISBN 13: 978-1-4704-1135-0
  Primary MSC: 53; 57; 58
  Textbook?: true
  Applied Math?: false
  MAA Book?: false
  Electronic Media?: false
  Apparel or Gift: false
  SXG Subject: GT
  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/chel-370
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  Online Price 1: 42.00
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  Dual Price 2: 43.05
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  Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1135-0&pisbn=978-0-8218-5193-7&epc=CHEL/370.H.E&ppc=CHEL/370.H&title=Differential%20Topology&author=Victor%20Guillemin%3B%20Alan%20Pollack&type=DE
  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1135-0&pisbn=978-0-8218-5193-7&epc=CHEL/370.H.E&ppc=CHEL/370.H&title=Differential%20Topology&author=Victor%20Guillemin%3B%20Alan%20Pollack&type=R
  Readership:

  Undergraduate and graduate students interested in differential topology

  Cover Image URL: ~~FreeAttachments/chel-370-h-cov.jpg
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• 

  Spaces: An Introduction to Real Analysis

  Online: Sale price: $53.40

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  Product Code: AMSTEXT/29

  Published in 2017
  Spaces: An Introduction to Real Analysis
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/29; AMSTEXT/29; amstext-29; AMSTEXT-29
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  Title (HTML): Spaces: An Introduction to Real Analysis
  Author(s) (Product display): Tom L. Lindstrøm
  Affiliation(s) (HTML): University of Oslo, Oslo, Norway
  Abstract:

  Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis.
  
  The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 29
  Publication Month and Year: 2017-11-28
  Copyright Year: 2017
  Page Count: 369
  Cover Type: Hardcover
  Print ISBN-13: 978-1-4704-4062-6
  Online ISBN 13: 978-1-4704-4311-5
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 26; 28; 42; 46; 54
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4311-5&pisbn=978-1-4704-4062-6&epc=AMSTEXT/29.E&ppc=AMSTEXT/29&title=Spaces%3A%20An%20Introduction%20to%20Real%20Analysis&author=Tom%20L.%20Lindstr%F8m&type=R
  Readership:

  Undergraduate and graduate students interested in real analysis.

  Reviews:

  [T]he presentation is done in a way to make the book eminently readable by undergraduate students...I think that reading 'Spaces' or taking a course based on the text would serve very well as a bridge between undergraduate level and modern graduate level mathematics.

  -- Jason M. Graham, MAA Reviews

  Cover Image URL: ~~FreeAttachments/amstext-29-cov.jpg
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• 

  Algebra in Action: A Course in Groups, Rings, and Fields

  Online: Sale price: $69.00

  Print: Sale price: $69.00

  Product Code: AMSTEXT/27

  Published in 2017
  Algebra in Action: A Course in Groups, Rings, and Fields
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/27; AMSTEXT/27; amstext-27; AMSTEXT-27
  Print Product Code: AMSTEXT/27
  Online Product Code: AMSTEXT/27.E
  Title (HTML): Algebra in Action: A Course in Groups, Rings, and Fields
  Author(s) (Product display): Shahriar Shahriari
  Affiliation(s) (HTML): Pomona College, Claremont, CA
  Abstract:

  This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 27
  Publication Month and Year: 2017-08-16
  Copyright Year: 2017
  Page Count: 675
  Cover Type: Hardcover
  Print ISBN-13: 978-1-4704-2849-5
  Online ISBN 13: 978-1-4704-3661-2
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 00
  Secondary MSC: 20; 13; 12
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  Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/amstext-27
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-3661-2&pisbn=978-1-4704-2849-5&epc=AMSTEXT/27.E&ppc=AMSTEXT/27&title=Algebra%20in%20Action%3A%20A%20Course%20in%20Groups%2C%20Rings%2C%20and%20Fields&author=Shahriar%20Shahriari&type=R
  Readership:

  Undergraduate students interested in abstract algebra.

  Reviews:

  The structure of the text "Algebra in Action" lets students see what groups really do right from the very beginning. In the very first chapter, the author introduces a rich selection of examples, the dihedral groups, the symmetric group, the integers modulo n, and matrix groups, that students can see 'in action' before the presentation of the formal definitions of groups and group actions in chapter 2 where the theoretical foundations are introduced. Students return to these examples again and again as the formal theory unfolds, seeing how the theory lets them study all groups at once...It is one of the few texts at the undergraduate level that supports the incorporation of group actions at an early stage in the course.

  -- Jessica Sidman, Mount Holyoke College

  Shahriar Shahriari has written an exquisite text that will become, and deserves to be, widely used for introducing generations of students to abstract algebra.The presentation is engaging, modern, and sufficiently detailed, making the book ideal for self-study..."Algebra in Action" is a gem and, no doubt, it is the work of a master teacher whose passion and respect for the subject is apparent everywhere in the book. I highly recommend it to students and professors alike!

  -- Ehssan Khanmohammadi

  It is rigorous, well-written, ample in terms of problems and solutions provided, and sufficiently advanced for its target audience.

  -- Jason M. Graham, MAA Reviews

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• 

  Numerical Analysis: Mathematics of Scientific Computing, Third Edition

  Online: Sale price: $56.40

  Print: Sale price: $56.40

  Product Code: AMSTEXT/2

  Published in 2002
  Numerical Analysis: Mathematics of Scientific Computing, Third Edition
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/2; AMSTEXT/2; amstext-2; AMSTEXT-2
  Print Product Code: AMSTEXT/2
  Online Product Code: AMSTEXT/2.E
  Title (HTML): Numerical Analysis: Mathematics of Scientific Computing, Third Edition
  Author(s) (Product display): David Kincaid; Ward Cheney
  Affiliation(s) (HTML): University of Texas at Austin, Austin, TX; University of Texas at Austin, Austin, TX
  Abstract:

  This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs.
  
  In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages.
  
  This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.
  
  An instructor's manual for this title is available electronically. Please send email to textbooks@ams.org for more information.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 2
  Publication Month and Year: 2009-01-13
  Copyright Year: 2002
  Page Count: 788
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4788-6
  Online ISBN 13: 978-1-4704-1115-2
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 65
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1115-2&pisbn=978-0-8218-4788-6&epc=AMSTEXT/2.E&ppc=AMSTEXT/2&title=Numerical%20Analysis%3A%20Mathematics%20of%20Scientific%20Computing%2C%20Third%20Edition&author=David%20Kincaid%3B%20Ward%20Cheney&type=R
  Readership:

  Undergraduate and graduate students interested in applied mathematics and scientific computing.

  Reviews:

  This text offers a thorough and elegant presentation of basic topics in numerical analysis. ... the text is skillfully written, by authors who are among the best in the field. Throughout, the presentation shows the unique insights that each brings to the subject. In all, it is an enjoyable text to use.

  -- Bulletin of Mathematics Books and Computer Science

  CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=978-0-8218-4788-6&WT.mc.id=American%20Mathematical%20Society
• 

  Introduction to Analysis: Fifth Edition

  Online: Sale price: $39.60

  Print: Sale price: $39.60

  Product Code: AMSTEXT/1

  Published in 1998
  Introduction to Analysis: Fifth Edition
  Base Product Code Keyword List: amstext; AMSTEXT; amstext/1; AMSTEXT/1; amstext-1; AMSTEXT-1
  Print Product Code: AMSTEXT/1
  Online Product Code: AMSTEXT/1.E
  Title (HTML): Introduction to Analysis: Fifth Edition
  Author(s) (Product display): Edward D. Gaughan
  Affiliation(s) (HTML): New Mexico State University, Las Cruces, NM
  Abstract:

  Introduction to Analysis is designed to bridge the gap between the intuitive calculus usually offered at the undergraduate level and the sophisticated analysis courses the student encounters at the graduate level. In this book the student is given the vocabulary and facts necessary for further study in analysis. The course for which it is designed is usually offered at the junior level, and it is assumed that the student has little or no previous experience with proofs in analysis. A considerable amount of time is spent motivating the theorems and proofs and developing the reader's intuition. Of course, that intuition must be tempered with the realization that rigorous proofs are required for theorems. The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section. Also, at the end of each section, one finds several Projects. The purpose of a Project is to give the reader a substantial mathematical problem and the necessary guidance to solve that problem. A Project is distinguished from an exercise in that the solution of a Project is a multi-step process requiring assistance for the beginner student.
  
  An instructor's manual for this title is available electronically. Please send email to textbooks@ams.org for more information.

  Book Series Name: Pure and Applied Undergraduate Texts
  Volume: 1
  Publication Month and Year: 2009-01-13
  Copyright Year: 1998
  Page Count: 240
  Cover Type: Hardcover
  Print ISBN-13: 978-0-8218-4787-9
  Online ISBN 13: 978-1-4704-1114-5
  Print ISSN: 1943-9334
  Online ISSN: 1943-9334
  Primary MSC: 26
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  Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1114-5&pisbn=978-0-8218-4787-9&epc=AMSTEXT/1.E&ppc=AMSTEXT/1&title=Introduction%20to%20Analysis%3A%20Fifth%20Edition&author=Edward%20D.%20Gaughan&type=R
  Readership:

  Undergraduate students interested in learning analysis.

  CCC Permissions Link: https://www.copyright.com/openurl.do?isbn=978-0-8218-4787-9&WT.mc.id=American%20Mathematical%20Society