
Mathematical World 2003; 136 pp; softcover Volume: 19 ISBN10: 0821832824 ISBN13: 9780821832820 List Price: US$32 Member Price: US$25.60 Order Code: MAWRLD/19 This item is also sold as part of the following set: MAWRLDGSET  This book will bring the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, readerfriendly style. Included are exercises and many figures illustrating the main concepts. The first chapter presents the geometry and topology of surfaces. Among other topics, the authors discuss the PoincaréHopf theorem on critical points of vector fields on surfaces and the GaussBonnet theorem on the relation between curvature and topology (the Euler characteristic). The second chapter addresses various aspects of the concept of dimension, including the Peano curve and the Poincaré approach. Also addressed is the structure of threedimensional manifolds. In particular, it is proved that the threedimensional sphere is the union of two doughnuts. This is the first of three volumes originating from a series of lectures given by the authors at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and undergraduate mathematics courses in the sciences and liberal arts. The second volume is available as Volume 20 in the AMS series, Mathematical World. A third volume is forthcoming. Readership Advanced highschool students and undergraduates in mathematics. Reviews "With A Mathematical Gift, I, there is no reason why every undergraduate student should not be exposed to some topology ... accessible to even high school students ... beautiful illustrations and straightforward explanations of sophisticated ideas. Real world and concrete scenarios are used ... elegant explanations ... exercises ... are friendly and nonthreatening ... the perfect choice for anyone who conducts summer workshops for high school students ... an ideal supplement for graduate students studying topology for the first time ... also excellent for undergraduate independent studies ... I enjoyed reading this book ... fun to look at ... instructive and motivating ... impressed ... wowed by the detail and clarity presented by the authors. Readers of A Mathematical Gift, I will want to read A Mathematical Gift, II."  MAA Online Table of Contents



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