<p>This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly 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 Bolyai-Gerwien theorem about scissors-congruent 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.</p>

A Mathematical Gift, III (Mathematical World)

Science & Math

Koji Shiga

Toshikazu Sunada

Mathematics

American Mathematical Society

<p>This three-volume set addresses the interplay between topology, functions, geometry, and algebra. Bringing the beauty and fun of mathematics to the classroom, the authors offer serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. It is suitable for advanced high-school students, graduate students, and researchers.</p>

A Mathematical Gift: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World)

Shigeyuki Morita

Kenji Ueno

Amer Mathematical Society

Paradox of the new edition Banach-Tarski (Iwanami Library of Science) (2009) ISBN: 4000295659 [Japanese Import]

ToÌ„kyoÌ„ : Iwanamishoten, 2009

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Books by Toshikazu Sunada