Classes

Math 4500

Office:       Ross Hall 321

e-mail:       bshader at uwyo dot edu

Phone:      766-6826

Hours:       M 2-3, , W 3:00-4:00, Th 11-12 or by appointment

Homework               25%

2 Midterm Exams    25% each

1 Final Exam           25%

Homework sets will be given about once each week and a half.  Your will be given one week to 10 days to complete each homework set.  No late homework will be accepted.  Your homework solutions should be mathematically correct and written in full mathematical sentences.  The homework will be a mix between computation, application of the theory taught in class, real-world applications, and concepts.  Feel free to ask me specific questions (i.e. ones that show that you've already thought about the problem and just need some help getting unstuck) about the homework. It is okay to broadly discuss homework problems with other students in the class.  However, the main ideas of a solution and the final work should be your own.

There is no required textbook for this course.  Homework and exams will be based on the lectures.

A good reference book for the course is: Applied Linear Algebra by P. Olver and C. Shakiban

(Prentice Hall,  2006,  ISBN 0-13-147382-4).

Matrix theory is one of the fundamental areas of mathematics.  It is used in virtually every area of advanced mathematics, and over the past century has been an important tool in various applications.  Accordingly, the goals of the course are two-fold:

The goals of the course are to develop

1.  a thorough conceptual understanding of, and proficient computational skills for matrix theory, and

2.  an understanding of how matrix theory is used in a variety of applications.

Topics to be covered include: linear transformations, spectra of matrices, similarity, Jordan Canonical Form, inner products, unitary and normal matrices, the Singular Value Decomposition, and the Perron-Frobenius theory of nonnegative matrices.   Some applications that we will (hopefully) encounter are: the Discrete Fourier Transform, the Fast Fourier Transform, basic signal processing, population modeling, data compression, face recognition, least squares and database searches.

A positive attitude toward learning and a willingness to work are required.  Ask questions, come to

office hours, carefully go over your notes (several times), and enjoy learning something new!