Time and place: TuTh 3:30-4:50 p.m.; Library W4550
Instructor: Radu Laza
Office: Math Tower 4-121
Email:
radu.laza@stonybrook.edu
Office hours: Tue 5:00-6:15 p.m.; Thu 2:15-3:15 p.m.
TAs: Connor Lehmacher (Recitations 1 and 3) and Zhulei Pan (Recitation 2)
This course is an introduction to abstract algebra, focusing on groups, rings, homomorphisms, and related algebraic concepts. Alongside the theoretical foundations, the course has a strong applied component, with particular emphasis on public-key cryptography and error-correcting codes. Other topics and applications may include informal set theory, relations, the Chinese remainder theorem, Burnside's theorem, and computational complexity. This course is offered as both AMS 351 and MAT 312.
Prerequisite: AMS 210 or MAT 211.
Textbook: Humphreys and Prest, Numbers, Groups and Codes , 2nd edition.
| Week | Topic | Sections Covered | HW Assignments |
|---|---|---|---|
| (1) Aug 25, 27 | Euclidean algorithm and gcd | 1.1 | |
| (2) Sept 1, 3 |
Primes and unique factorization Congruence classes |
1.3 1.4 |
HW1 (due the week of Sept 7) |
| (3) Sept 8, 10 |
Solving linear congruences Euler's theorem; Public-key cryptography |
1.5 1.6 |
HW2 (due the week of Sept 14) |
| (4) Sept 15, 17 |
Permutations Sign of a permutation |
4.1 4.2 |
HW3 (due the week of Sept 21) |
| (5) Sept 22, 24 | More on permutations
Review |
Chapter 1, Sections 4.1-4.2 |
|
| (6) Sept 29, Oct 1 |
Midterm 1: Tuesday, Sept 29 (in class) Introduction to groups |
Chapter 1, Sections 4.1-4.2 4.3 |
HW4 (due the week of Oct 5) |
| (7) Oct 6, 8 |
Algebraic structures Subgroups |
4.4 5.1 |
HW5 (due the week of Oct 19) |
| (8) Oct 13, 15 |
No class Cosets and Lagrange's theorem |
— 5.2 |
HW6 (due the week of Oct 26) |
| (9) Oct 20, 22 |
Normal subgroups and quotient groups Groups and error-correcting codes |
5.3 5.4 |
HW7 (due the week of Nov 2) |
| (10) Oct 27, 29 |
Review Midterm 2: Thursday, Oct 29 (in class) |
Sections 4.3-4.4, Chapter 5 Sections 4.3-4.4, Chapter 5 |
|
| (11) Nov 3, 5 | Polynomials | 6.1, 6.2 | HW8 (due the week of Nov 9) |
| (12) Nov 10, 12 | Irreducible polynomials and factorization | 6.3 | HW9 (due the week of Nov 16) |
| (13) Nov 17, 19 | Polynomial congruence classes | 6.4 | |
| (14) Nov 24, 26 |
Cyclic codes No class - Thanksgiving |
6.5 — |
HW10 (due the week of Nov 30) |
| (15) Dec 1, 3 |
Review Final Exam: Thursday, Dec 3 (in class) |
Discussion of sample final Cumulative |