Mathematical World 2005; 392 pp; softcover ISBN10: 0821838598 ISBN13: 9780821838594 List Price: US$83 Member Price: US$66.40 Order Code: MAWRLDGSET
 This threevolume 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, readerfriendly style. Included are exercises and many figures illustrating the main concepts. It is suitable for advanced highschool students, graduate students, and researchers. The threevolume set includes A Mathematical Gift I, II, and III. Readership Advanced highschool students and undergraduates in mathematics. Table of Contents Part I Invitation to topology (Viewing figures globally)  Introduction
 The Euler characteristic
 Vortices created by winds and the Euler characteristic
 Curvature of a surface and the Euler characteristic
The story of dimension  Introduction
 Learning to appreciate dimension
 What is dimension?
 Threedimensional figures
 Physics and dimension
Part II The legacy of trigonometric functions  Introduction
 Trigonometric functions and infinite series
 Elliptic functions
Intersection of geometry and algebra  Introduction
 The Poncelet closure theorem
 The Poncelet theorem for circles
 The Poncelet theorem in the world of complex numbers
 Proof of the Poncelet theorem using plane geometry
 Conclusion
Part III  The story of the birth of manifolds
 The prelude to the birth of manifolds
 The birth of manifolds
 The story of area and volume from everyday notions to mathematical concepts
 Transition from the notion of "size" to the concept of "area"
 Scissorscongruent polygons
 Scissorscongruent polyhedra
