Approximation Theory From Taylor Polynomials to Wavelets [Paperback]

This concisely written book gives an elementary introduction to a classical area of mathematics  approximation theory  in a way that naturally leads to the modern field of wavelets.  The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.  Featuring classical, illustrative examples and constructions, exercises, and a discussion of the role of wavelets to areas such as digital signal processing and data compression, the book is one of the few to describe wavelets in words rather than mathematical symbols.

This book gives an elementary introduction to a classical area of mathemat? ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the idea of ap? proximating complicated expressions with simpler expressions, and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their second year of uni? versity. Often, teachers do not have adequate elementary material to give to students as motivation and encouragement for their further studies. The present book will be of use in this context because the exposition demon? strates the dynamic nature of mathematics and how classical disciplines influence many areas of modern mathematics and applications. The book may lead readers toward more advanced literature, such as the other pub? lications in the Applied and Numerical Harmonic Analysis series (ANHA), by introducing ideas presented in several of those books in an elementary context. The focus here is on ideas rather than on technical detl³|