AMS 351, Applied Algebra

Catalog Description: Topics in algebra: groups, informal set theory, relations, homomorphisms. Applications: error correcting codes, Burnside's theorem, computational complexity, Chinese remainder theorem. This course is offered as both AMS 351 and MAT 312.

Prerequisite: AMS 210 or MAT 211

Advisory prerequisite:  MAT 200 or CSE 150 or CSE 250 or equivalent

3 credits

Fall 2023 Course Materials:
"Numbers, Groups and Codes" (paperback) by J.F. Humphreys and M.Y. Prest, 2nd edition, Cambridge University Press (May 24, 2004), ISBN 978-0521540506

THIS COURSE IS STAFFED AND CONTROLLED BY THE MATHEMATICS DEPARTMENT. ANY QUESTIONS ABOUT THIS COURSE SHOULD BE ADDRESS TO THE UNDERGRADUATE MATHEMATICS OFFICE.

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