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Discusses the theory of trigonometric and elliptic functions. This book includes subjects such as power series expansions, addition and multiple-angle formulas, and arithmetic-geometric means. It describes various aspects of the Poncelet Closure Theorem.

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). This book describes the notio

This book will bring the beauty and fun of learning mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures that illustrate the main concepts. The first chapter presents the geometry and topology of surfaces. Among other topics, the authors discuss the Poincare-Hopf theorem on critical points of vector fields on surfaces and the Gauss-Bonnet theorem on the relation between curvature and topology (the Euler characteristics). The second chapter addresses various aspects of the concept of dimension, including the...

Addresses the interplay between topology, functions, geometry, and algebra. This title offers serious mathematics in a reader-friendly style. It includes exercises and many figures illustrating the main concepts. It is suitable for advanced high-school stu