MAT 312/ AMS 351 (Applied Algebra) - Fall 2025

Time and Place : TuTh 11-12:20; Library W4550

Instructor : Radu Laza

Office : Math Tower 4-121
Email : radu.laza@stonybrook.edu

Office Hours: Tue 3:30-4:45, Thr 9:30-10:45

TA: TBA

Overview

This course covers the fundamentals of abstract algebra: groups, informal set theory, relations, polynomials, together with some applications: error correcting codes, Burnside's theorem, computational complexity, Chinese remainder theorem. This course is offered as both AMS 351 and MAT 312.

Textbook

Numbers, Groups and Codes (2nd Edition), Humphreys and Prest.

Quick Links

Tentative Schedule

Announcements

Welcome!
Further information about the course can be found on Department MAT312 site
We will use Brightspace for posting grades and making class announcements. The most up-to-date information on the schedule will be here (so please check frequently this webpage).
A tentative schedule is posted below. Minor changes are likely. The dates for the exams are fixed (see schedule below).

Grading

There will be 2 midterms and a final. Theere will be 10 homewrok assignments.
The exams count for 85% of the final grade: 25% for each midterm and 35% for the final. The remaining 15% will be for the homework assignments.

Schedule

Week	Topic	Sections Covered	HW Assigments
(1) Aug 26, 28	Division Algorithm & gcd ------------------------------------------ Induction	1.1 ------------------------------------------ 1.2
(2) Sept 2, 4	Primes and Unique Factorization	1.3	HW1 (due Sept 11)
(3) Sept 9, 11	Congruence classes ------------------------------------------ Solving linear congruences	1.4 ------------------------------------------ 1.5	HW2 (due Sept 18)
(4) Sept 16, 18	Euler's Theorem ------------------------------------------ Review	1.6 ------------------------------------------ Chapter 1	HW3 (due Sept 25)
(5) Sept 23, 25	Midterm 1: Tuesday, Sept 23 (in class) ------------------------------------------ Permutations (1)	Chapter 1 ------------------------------------------ 4.1
(6) Sept 30, Oct 2	Permutations (2) ------------------------------------------ Intro to Groups	4.2 ------------------------------------------ 4.3	HW4 (due Oct 9)
(7) Oct 7, 9	Algebraic Structures	4.4	HW5 (due Oct 16)
(8) Oct 16	Groups and Codes	5.1
(9) Oct 21, 23	Groups and Codes Groups	5.2	HW6 (due Oct 26)
(10) Oct 28, 30	Groups ------------------------------------------ Review	5.3 ------------------------------------------ Chapters 4 and 5	HW7 (due Nov 6)
(11) Nov 4, 6	Midterm 2: Tuesday, Nov 4 (in class) ------------------------------------------ Group and Codes	Ch. 4, 5.1--5.3 ------------------------------------------ 5.4	HW8 (due Nov 13)
(12) Nov 11, 13	Polynomials	6.1, 6.2	HW9 (due Nov 20)
(13) Nov 18, 20	Factorization	6.3
(14) Nov 25	Polynomial congruence classes	6.4	HW10 (due Dec 6)
(15) Dec 2, 4	Cyclic Codes ------------------------------------------ Review	6.5 ------------------------------------------ discussion of sample final
(16) Dec 11	Final Exam: Thursday, Dec 11 (scheduled by the registrar)	cumulative