MATH 522
WAVELETS
Office: LeConte College 313 D Office Hours: TTh 10:4511:45 am (or by appointment) 


Final Exam (updated Tuesday 12/09/03 at 7:30 pm) The best way to prepare is to go over the previous tests. Primary topics are:

Background
The subject of "Wavelets" was motivated by early orthonormal
representations developed by Haar and Stromberg and inspired the
development of a general theory by Yves Meyer in the mid 1980's.
The fundamental mathematical discovery by Ingrid Daubechies of
compactly supported, smooth wavelets in 1988 has let to an explosion
of mathematical and scientific discoveries. The mathematics of
wavelets has had a profound effect upon applied mathematics, image
and signal processing, statistical data processing, feature
identification, visualization & computer animations, and multiscale
data representations. Over the last decade, the mathematical aspects
of the subject have been clarified and reduced to a form now suitable
for undergraduate instruction.
Course Syllabus
The course will develop the basic principles and methods of Fourier
transforms, wavelets, and multiresolution analysis. Application of
the concepts will be to differential equations, data compression,
signal and image processing. Numerical experiments will be used to
illustrate the primary principles of multiscale decomposition,
approximation, and reconstruction. Computational algorithms developed
in lectures will be implemented in a high level programming language
such as Matlab and/or Maple.
Prerequisites
(
Math 544 or Math 526), or consent of department.
Required Text
A First Course in Wavelets with Fourier Analysis, by A.
Boggess and F.J. Narcowich, Prentice Hall, Upper Saddle River, NJ,
2001. [ISBN: 0130228095]
Course Grading
Two tests (25%) each, Homework (20%), and Final Exam (30%). Homework will be
collected on a regular basis. Graduate Students will be required to write a term paper
(counting 25% of the Final Exam) on wavelet applications in the
student's subject area, as well as additional test and homework problems.
Attendance: Classroom attendance is both expected and required according to the official university 10% rule.
Important Course Dates:

Homework Assignments
Click here for an uptodate list of Homework
Assignments and other course materials.


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and last updated Mar 2003. This page ©20022003, The Board of Trustees of the University of South Carolina. URL: http://www.math.sc.edu/~sharpley/math522 