# A Mathematical Gift, II: The interplay between topology, functions, geometry, and algebra

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*Kenji Ueno; Koji Shiga; Shigeyuki Morita*

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 trigonometric and elliptic
functions. It includes subjects such as power series expansions,
addition and multiple-angle formulas, and arithmetic-geometric means. The second
chapter discusses various aspects of the Poncelet Closure Theorem. This
discussion illustrates to the reader the idea of algebraic geometry as a method
of studying geometric properties of figures using algebra as a tool.

This is the second volume 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 for undergraduate mathematics
courses in the sciences and liberal arts. The first volume is available
as Volume 19 in the AMS
series, Mathematical World.

#### Readership

Advanced high-school students and undergraduates in mathematics.