Prof. Wickerhauser's Math 450 class

Math 450
Topics in Applied Mathematics:
Mathematics for Multimedia

Spring, 2023

Professor Wickerhauser

NEWS

Solutione to HW 6 are now available.
Final Exam is now available.
intmod2poly.txt Functions to manipulate integer-sized mod-2 polynomials.
gilbertcode.m Gilbert's algorithm for error-correcting codes.

QUICK LINKS

CRC-32 polynomial: x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1
Finite Fields manual "gf_manual.pdf"
Practice Midterm (from 2014).
Example Midterm (from 2017).
Example Midterm (from 2019).
Example Final (from 2010).
Example Final (from 2014).
Example Final (from 2017).
Example Final (from 2019).
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 algorithm and the proofs omitted in lecture.
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 Linux/Unix computer, it already has a C compiler installed. If you have a MacOS X computer, you should install the XCode development environment.

EXAMPLE PROGRAMS

crypt.m, Octave/Matlab function to perform modular exponentiation for RSA encryption and decryption.
Example Octave commands for Chapter 1 and Chapter 4.
Example Macsyma commands for Chapter 1.
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.
d4.m Daubechies' filters of length 4
pcqfilter.m periodic filtering function
ipcqfilter.m periodic adjoint filtering function
gilbertcode.m Gilbert's algorithm for error-correcting codes.
intmod2poly.txt Functions to manipulate integer-sized mod-2 polynomials. Copy and paste these into your Octave command window.

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 the permission of the instructor.

Time. Classes meet Mondays, Wednesdays and Fridays, 3:00 pm to 4:00 pm, in Cupples I Hall room 115.

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 Sunday, February 5 (Solutions)
HW #2, due Sunday, February 19 (Solutions)
HW #3, due Sunday, March 5 (Solutions)
HW #4, due Sunday, April 2 (Solutions)
HW #5, due Sunday, April 16 (Solutions)
HW #6, due Sunday, April 30 (Solutions)

Solutions are due by 11:00pm 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 GradeScope, including the printed results of any programs.

	HW #1, due Sunday, February 5 (Solutions) HW #2, due Sunday, February 19 (Solutions) HW #3, due Sunday, March 5 (Solutions) HW #4, due Sunday, April 2 (Solutions) HW #5, due Sunday, April 16 (Solutions) HW #6, due Sunday, April 30 (Solutions)

Tests. There will be one midterm examination on Wednesday, March 8th, 2023, in class. The cumulative take-home final examination, which will emphasize material in the latter part of the course, is due by 11:00pm on Friday, May 5th, 2023, on GradeScope.

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:	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.

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

Math 450 Topics in Applied Mathematics: Mathematics for Multimedia