Math 450
Topics in Applied Mathematics
Mathematics for Multimedia

Prof. M. Victor Wickerhauser

NEWS

QUICK LINKS

  • Kalman filtering notes: kalman.pdf
  • Kalman filtering m-files: kalmanf.m, runkf.m, taylor3.m
  • Here is Chapter 1 from the next revision of our textbook, which contains a description of the RSA slgorithm and the proofs omitted in lecture.
  • Download old free MatLab (for Windows or Linux PCs) via this link.
  • Download Octave (for Windows or MacOS X or Linux on PCs) via this link.
  • Download MinGW (for Windows PCs) via this link. If you have a MacOS or Linux/Unix computer, it already has a C compiler installed.

EXAMPLE PROGRAMS

  • Download convergence.m, daub4.m, daub6.m, graph.m, hatfn.m, bspline.m, coif6.m, MatLab m-files for generating MRA scaling functions from a few filters, by the fixed-point iteration method.
  • Download simplex.txt, MatLab commands for drawing and rotating a 3-simplex in 3-space.
  • Download gcd.c, an example program for computing the greatest common divisor by Euclid's algorithm.

Introduction

Welcome to the mathematics of multimedia signal processing! In the past few decades, important theories from mathematics have migrated into digital communication, image and signal processing, and multimedia visualisation and data analysis. Understanding these theories confers greater ability to solve practical problems.

Syllabus

Topics. This course will lead through a list of example problems in multimedia communication, develop the mathematical principles useful for their solution, and implement some solutions using theoretical results discussed in class.

Prerequisites. Math 449 (or Math 404 or Math 405), or the permission of the instructor.

Time. Classes meet Mondays, Wednesdays and Fridays, 3:00 pm to 4:00 pm, in Cupples I, room 113.

Text. The lectures will follow the book Mathematics for Multimedia by M. V. Wickerhauser, ISBN 978-0-8176-4879-4 (2009).
A recommended reference book is Adapted Wavelet Analysis from Theory to Software by M. V. Wickerhauser, ISBN 1-56881-041-5 (1994).

Homework assignments:
Solutions are due at the end of class on the due date. Late homework will not be accepted. The homework will sometimes require writing a working computer program, which will be judged for correctness and clarity. Homework should be submitted on paper, including the printed results of any programs. However, you will occasionally be requested to provide the machine-readable program source via email to victor@math, so find out now how to use your campus email account. (Note: from outside Washington University's campus network, append the domain .wustl.edu to this address)

Tests. There will be one midterm examination on Friday, March 9th, 2012, in class. The cumulative take-home final examination, which will emphasize material in the latter part of the course, is due by 4:00 pm on Friday, May 4th, 2012, in Cupples I, room 100, or you may hand it to me at any earlier time. Classroom time will be set aside on Thursday May 3rd, 2012, from 6:00 PM until 8:00 PM, for students' convenience.

Grading. One grade will be assigned for homework, one for the midterm examination, and one for the final examination. These three will contribute as follows to the course grade: HW 40%, Midterm 30%, Final 30%. Letter grades, computed from the course score, will be at least the following:

Course score at least:90%80%70%60%
Letter grade at least:ABCD

Students taking the Cr/NCr or P/F options will need a grade of D or better to pass.

Office Hours. See the instructor in Cupples I, room 105a, on Wednesdays from 4-5 pm, or by appointment.

Questions? Return to M. Victor Wickerhauser's home page for contact information.