Catalog of MAA Publications 2011 Annual : Page 5NEW Counterexamples in Calculus Sergiy Klymchuk ■ Classroom Resource Materials Calculus Deconstructed . Textbook Supplement A Second Course in First-Year Calculus Zbigniew H. Nitecki ■ MAA Textbooks A thorough and mathematically rigorous ex-position of single-variable calculus for readers with some previous exposure to calculus tech-niques but not to methods of proof, this book is appropriate for a beginning honors calculus course assuming high school calculus or a “bridge course” using basic analysis to moti-vate and illustrate mathematical rigor. It can serve as a combination text-book and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in the context of a co-herent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive histori-cal notes explore the arguments of the originators of the subject. No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum , induction, con-trapositives, etc.) are introduced by example along the way. Between the text and the exercises, proofs are available for all the basic results of calcu-lus for functions of one real variable. As a robust repertoire of examples is essen-tial for students to learn the practice of mathematics, so a mental library of coun-terexamples is critical for students to grasp the logic of mathematics. Counterexamples are tools that reveal incorrect beliefs. Without such tools, learners’ natural mis-conceptions gradually harden into convic-tions that seriously impede further learning. This slim volume brings the power of counterexamples to bear on one of the largest and most important courses in the mathematics curriculum. —Professor Lynn Arthur Steen, St. Olaf College, Co-author of Counterexamples in Topology Counterexamples in Calculus serves as a supplementary resource to en-hance the learning experience in single-variable calculus courses. This book features carefully constructed incorrect mathematical statements that re-quire students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times, the converse of a well-known theorem is presented. In other instances crucial conditions are omit-ted or altered, or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continu-ity, Differential Calculus, and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calcu-lus. In that light, it may well be useful for high school teachers and univer-sity faculty as a teaching resource, high school and college students as a learning resource, or as a professional development resource for calculus instructors. 504 pp., 2009 List: $74.95 ISBN: 978-0-88385-756-4 MAA Member: $59.95 Hardbound Catalog Code: CDE/YD11 Instructors adopting Calculus Deconstructed for classroom use may request a copy of the Solutions Manual. See the inside cover of this catalog to learn about our examination copy policy, or call 1-800-331-1622 for more details. Solutions Manual for Calculus Deconstructed: A Second Course in First-Year Calculus Contains solutions for all of the problems contained in the textbook. 112 pp., 2010 List: $39.95 ISBN: 978-0-88385-765-6 MAA Member: $31.95 Paperbound Catalog Code: CXC/YD11 325 pp., 2010 ISBN: 978-0-88385-758-8 List price: $15.00 (Available only to instructors. Order on your department letterhead.) Free with adoption orders of 20 or more copies of the textbook. The Calculus Collection A Resource for AP * and Beyond Caren L. Diefenderfer & Roger B. Nelsen, Editors ■ Classroom Resource Materials The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a two-or four-year college or uni-versity. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine . The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and com-puters into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interest-ing and timeless explorations of the mathematics encountered in a first course in calculus. The MAA has twice previously issued a calculus reader, collecting articles on calculus from its journals: Selected Papers in Calculus , published in 1969 and reprinted as Part I of A Century of Calculus , and Part II, published in 1992. In a sense, The Calculus Collection is the third volume in that series, but differ-ent in that it is a collection chosen for its usefulness to those who teach first-year calculus in high schools as well as colleges and universities. 527 pp., 2010 List: $74.95 ISBN: 978-0-88385-761-8 MAA Member: $59.95 Hardbound Catalog Code: CCE/YD11 * AP is a registered trademark of the College Board, which was not involved in the production of the volume. 5 5 To Order : Call 1.800.331.1622 or Online at www.maa.org Publication List |
