Math 4023 - Applied algebra - Spring 2006

These are old pages for past course, here for reference only.

Course text book:

Modern algebra and discrete structures, by Robert Lax.

Topics covered in this course:

(from the course descriptions web page) Finite algebraic structures relevant to computers: groups, graphs, groups and computer design, group codes, semigroups, finite-state machines.

Topics I will emphasize:

Cryptography, error correcting codes

Handouts and links

Homework

Numbers refer to text book questions.
Questions Date set Date due
1 Write a program to list subsets of a set Jan 18 Jan 23 (Monday week 2)
2 1.2, 1.3, 1.4, 1.5, 1.8, 1.9, 1.12, 1.15, 1.16, 1.17 Jan 18 Jan 30 (Monday week 3)
3 Write a program to find the GCD g of two integers a,b, and also to find u, v with au + bv =g. Jan 23 Feb 6 (Monday week 4)
4 Mostly induction and number theory Feb 3 Feb 13 (Monday week 5)
5 Write a program to produce multiplication and powers mod N tables. Feb 8 Feb 20 (Monday week 6)
6 Chapter IV, 2.1, 2.2, 2.4, 2.5, 2.9, 5.4, 5.5, 5.7, plus question about making your own RSA encryption system. (see handout) Feb 20 March 6 (Monday week 8)
7 Send encrypted messages (by March 13), and dycrypt messages (by March 14) sent to you by other students. March 6 March 13/14 (Monday/Tuesday week 9)
8 pg164: 4.6, 4.9; pg60-61: 1.2, 1.4, 1.5, 1.7; pg66-67: 2.1, 2.2, 2.7, 2.11 March 7 March 20 (Monday week 10)
9 Fill in sheet on symmetries of a tetrahedron March 10 March 17 (Friday week 10)
10 Write a program to list all possible groups of order n=3 and 4 by listing possible multiplication tables, given by n by n arrays, satisfying group axioms, as described in class. March 13 April 3 (Monday week 12)
11 pg 43, 3.1, pg 79, 4.1, 4.2, 4.3, 4.4, 4.9. March 27 April 7 (Friday week 11)
12 5 questions from handout plus pg 213 1.1, 1.2, 1.3, 1.4, 1.5 April 17 April 24 (Monday week 15)
13 pg 223, 2.2, 2.4, 2.6, 2.8, pg 234 3.2, 3.5, 3.6, 3.7 April 19 May 1 (Monday week 16)
14 pg 242: 4.2, 4.3, 4.7, pg 249: 5.3, 5.5, 5,8, pg 262: 6.2, 6.6. May 1 May 13

Helena Verrill
Last modified: Fri Jan 12 17:35:02 CST 2007