Wavelet theory is on the boundary between mathematics and engineering, making it ideal 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. Intended to be as elementary an introduction to wavelet theory as possible, the text does not claim to be a thorough or authoritative reference on wavelet theory.

This text was originally written for a "Capstone" course at Michigan State University. Basic wavelet theory seems to be a perfect topic for such a course. It is on the boundary between mathematics and engineering. 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.

This introduction to wavelets thoroughly covers the basics of the theory Shows non-trivial mathematics leading to natural and important applications, such as video compression and numerical solution of differential equations Includes an interesting prologue which explains the use of wavelet compression in storing the FBIs fingerprint files Requires only a basic linear algebra background along with a bit of analysis Wavelets are a hot area of modern mathematical research Request lecturer material: sn.pub/lecturer-material

Inhalt
Prologue: Compression of the FBI Fingerprint Files.- Background: Complex Numbers and Linear Algebra.- The Discrete Fourier Transform.- Wavelets on ZN.- Wavelets on Z.- Wavelets on R.- Wavelets and Differential Equations.