An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics)

Frazier, Michael W.

ISBN 10: 0387986391 / ISBN 13: 9780387986395

Published by Springer, 1999

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Bibliographic Details

• Title: An Introduction to Wavelets Through Linear Algebra (Undergraduate Texts in Mathematics)
• Publisher: Springer
• Publication Date: 1999
• Language: English
• ISBN 10: 0387986391
• ISBN 13: 9780387986395
• Binding: Hardcover
• Condition: new

About this title

Synopsis

Mathematics majors at Michigan State University take a “Capstone” course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basicwavelettheoryisanaturaltopicforsuchacourse. Byname, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are suf?ciently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity. These are introduced in the ?rst two sections of chapter 1. In the remainder of chapter 1 we review linear algebra. Students should be familiar with the basic de?nitions in sections 1. 3 and 1. 4. From our viewpoint, linear transformations are the primary object of study; v Preface vi a matrix arises as a realization of a linear transformation. Many students may have been exposed to the material on change of basis in section 1. 4, but may bene?t from seeing it again. In section 1.

Synopsis

This text was originally written for a "Capstone" course at Michigan State University. A Capstone course is intended for undergraduate mathematics majors, as one of the final courses taken in their undergraduate curriculum. Its purpose is to bring together different topics covered in the undergraduate curriculum and introduce students to current developments in mathematics and their applications. Basic wavelet theory seems to be a perfect topic for such a course. As a subject, it dates back only to 1985. Since then there has been an explosion of wavelet research, both pure and applied. Wavelet theory is on the boundary between mathematics and engineering.In particular it is a good topic for demonstrating to students that mathematics research is thriving in the modern day: Students can see non-trivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. This text is intended to be as elementary an introduction to wavelet theory as possible.

It is not intended as a thorough or authoritative reference on wavelet theory.