Al Boggess. Office in Miln 217. office hours will be announced at a later date. E-mail address is boggess@math.tamu.edu - - - URL address is http://www.math.tamu.edu/~boggess/
Fourier Series and Wavelets are important mathematical building blocks for signal analysis and many other areas in science and engineering. Fourier Series is the study of how a function (or signal) can be decomposed into a sum of sine and cosine waves of various frequencies. Wavelets are similar to sines and cosines in that they look like waves of various frequencies. However, they are different in that wavelets can be isolated by the user (unlike sine and cosine waves which keep repeating forever). This localization feature of wavelets allows the user to filter or modify certain parts of the signal without affecting other parts.
This course will present an overview of Fourier and Wavelet Analysis along with some applications. The goal of this course is to present the general ideas behind the construction of Fourier Series and Wavelets. The technical jargon of signal analysis and other fields of applications will be minimized. No prior knowledge of Fourier Series or Wavelets will be assumed. Keep in mind, this is a senior level mathematics course. As such, you will be expected to learn mathematical theory as well as gain computing skills using fourier analysis and wavelets. The prerequisites are a three semester calculus sequence and linear algebra (Math 304, 311 or 323). Some computer programming experience would be very helpful (especially with Matlab).
The required text for this course is A First Course in Wavelets and Fourier Analysis, 2nd Edition, by Boggess & Narcowich
Other (optional) references include:
Grades will be determined by problem sets, one midterm exam (just before spring break) a written project and a final exam. The grade weights are as follows.
Problem Sets Midterm Project Final Exam
30% 20% 20% 30%
The midterm and final exam will be in-class exams and you will be required to do your own work without help from others or the ability to consult with any references or notes. Homework will be submitted and graded through eLearning (Login with your NetID and password). You may consult with each other on homework problem sets, BUT only submit work which is in your own words AND be sure to cite any sources of help (either texts or people). The project will be due at the end of the semester. You may work in small groups (at most 3) but again a clear statement must be made that specifies the contributions of each member of the group. Academic plagarism on out of class work or dishonesty during the exams will not be tolerated and will be dealt with through the Honors Council.
Make-ups and late work will be allowed with a University authorized excuse in writing (see University Regulations).
All handouts and web documents for this course are protected by copyright. One copy may be made (our downloaded) for personal use. Multiple copies require permission of the instructor.
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