Math 437: Applications of Algebra (Spring 2017)

Tuesday and Thursday 10:15 - 11:30am in SAS 2102

Instructor: Cynthia Vinzant (3260 SAS, email)
Offce Hours: Tuesday 11:30am - 12:30pm, Wednesday 1:30 - 2:30pm or by appointment
Textbook: Klima-Sigmon-Stitzinger, Applications of Abstract Algebra with Maple and MATLAB, 3rd edition, Chapman & Hall/CRC, 2015
Syllabus

Grinstead and Snell, Introduction to Probability, available here. (See Chapter 11 for Markov Chains.)
Cox, Little, and O'Shea, Ideals, Varieties, and Algorithms, available here. (See Chapter 2 for the Division Algorithm and Grobner Bases.)
Hartley and Zisserman, Multiple View Geometry in Computer Vision, available here.

Homework
Here are guidelines for writing up your homework (prepared by Seth Sullivant).
Please indicate any sources you used for a given problem on the solution to that problem. For example, if you worked with another student to get the solution to a problem, please indicate who. You are welcome to work together in small groups (2-4 people), but please try the problems on your own first. You should write up your own solutions (in your own words).

Homework 1, due Thursday, January 19: KSS Ch. 3 #1, #6, #23
Homework 2, due Thursday, January 26: KSS Ch. 3 #16, #21, Ch. 1 #28
Homework 3, due Thursday, February 2: pdf tex
Homework 4, due Thursday, February 9: pdf tex
Homework 5, due Thursday, February 16: pdf tex
Homework 6, due Thursday, February 23: pdf tex
Homework 7, due Thursday, March 2: pdf tex
Homework 8, due Thursday, March 23: pdf tex
Homework 9, due Thursday, March 30: pdf tex
Homework 10, due Thursday, April 6: pdf tex
Homework 11, due Thursday, April 13: pdf tex
Homework 12, due Thursday, April 20: pdf tex

Final Project: A 3-5 page exposition of a topic related to an application of algebra (selected by the student subject to instructor approval) will be due on Tuesday, May 4 at 11am. Further details and suggested topics are posted here.

Code Examples
A [15,11]-Hamming code in MATLAB (from 1/19/2017)
The BCH code from Section 4.3 in Maple (from 2/7/2017)
RSA code example in Maple (from 2/7/2017)
An absorbing Markov chain in Mathematica (from 3/30/2017)
Applications of Gröbner bases in Mathematica (from 4/13/2017)
Nullstellensatz and Graph Colorability Mathematica (from 4/20/2017)