
Supplementary Material 
Mathematical World 2005; 129 pp; softcover Volume: 23 ISBN10: 0821832840 ISBN13: 9780821832844 List Price: US$32 Member Price: US$25.60 Order Code: MAWRLD/23 This item is also sold as part of the following set: MAWRLDGSET  This book brings 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 talks about the theory of manifolds. It includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form). The second chapter discusses the notion of the area of a figure on the plane and the volume of a solid body in space. It includes the proof of the BolyaiGerwien theorem about scissorscongruent polynomials and Dehn's solution of the Third Hilbert Problem. This is the third volume originating from a series of lectures given at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first and second volumes are available as Volume 19 and Volume 20 in the AMS series, Mathematical World. Readership Advanced highschool students and undergraduates in mathematics. Table of Contents



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