## Math 450 Topics in Applied Mathematics Mathematics for Multimedia Winter-Spring, 2017

### NEWS

• Example Midterm (from 2014).
• 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 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

• simplex.txt: draw and rotate a 3-simplex in 3-space.
• convergence.m, daub4.m, daub6.m, graph.m, hatfn.m, bspline.m, coif6.m: generate MRA scaling functions from a few filters by the fixed-point iteration method.
• gcd.c: compute the greatest common divisor by Euclid's algorithm.
• rcf.m, an example program for computing the iterated-sine rising cutoff functions of Equations 3.12 and 3.13.
• fray.m, splice.m, apply the fraying and splicing operators of Equation 3.20.

### 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 Eads Hall room 103.

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:
 HW #1, due Friday, February 3 (Solutions) HW #2, due Friday, February 17 (Solutions) HW #3, due Friday, March 3 (Solutions) HW #4, due Friday, March 31 (Solutions) HW #5, due Friday, April 14 (Solutions) HW #6, due Friday, April 28 (Solutions)
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, so find out now how to use your campus email account.

Tests. There will be one midterm examination on Wednesday, March 8th, 2017, in class. The cumulative take-home final examinationhw, which will emphasize material in the latter part of the course, is due by 12:00 noon on Friday, May 5th, 2017, in my office, Cupples I, room 105a, or you may hand it to me at any earlier time.

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: Letter grade at least: 90% 80% 70% 60% A B C D

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 Mondays and Wednesdays after class from 4:00 pm to 5:00 pm, or by appointment.