Catalog Description: Topics in algebra: groups, informal set theory, relations, homomorphisms. Applications: error correcting codes, BurnsideÕs theorem, computational complexity, Chinese remainder theorem. This course is offered as both AMS 351 and MAT 312.
Prerequisite: AMS 210 or MAT 211
3 credits
Textbook: Numbers, Groups, and Codes, by J. Humphreys and M. Prest, Second Edition, Cambridge University Press
THIS COURSE IS STAFFED AND CONTROLLED BY THE MATHEMATICS DEPARTMENT. ANY QUESTIONS ABOUT THIS COURSE SHOULD BE ADDRESS TO THE UNDERGRADUATE MATHEMATICS OFFICE.
Fall 2009 Section
92987 LEC 01 TUTH 11:20-12:40PM Loc: Math P131 Inst: Lowell Jones AMS 351 Webpage
93813 REC R01 TU 12:50-02:10PM Loc: Old Chem 144Inst: Julia Viro
93814 REC R02 W 11:45-12:40PM Loc: Old Chem 144 Inst: Julia Viro
Spring 2010 Sections
52500 LEC 01 MWF 11:45-12:40PM Loc: TBA Inst: Lowell Jones
53536 REC R01 TU 03:50-04:45PM Loc: TBA Inst: TBA
1. Group codes and error correction (Chap. 1) – 5 class hours
2. Elements of Group Theory, including subgroups and permutation groups (Chap. 2)– 8 class hours
3. Informal Set Theory: definitions, Russell’s Paradox, Cardinality, Schroder-Bernstein Theorem (supplementary notes) – 5 class hours
4. Relations, Lagrange's Theorem and Burnside’s Theorem (Chap. 3) – 6 class hours
5. Complexity of Adding and Sorting (first half of Chap 6) – 5 class hours
6. Chinese Remainder Theorem and Homomorphisms (rest of Chap 6) – 7 class hours
7. Examinations – 6 class hours