MAT 312/ AMS 351 (Applied Algebra) - Fall 2022

Time and Place : TuTh 11:30-12:50; Earth&Space 131

Instructor : Radu Laza

Office : Math Tower 4-120
Email : radu.laza@stonybrook.edu

Office Hours: Th 1:30-3 (and by appointment)

TAs : Austin Konkel (R01) / Jared Krandel (R02, R03)

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

HW9 (due Nov 22)
HW10 (due Dec 1)
Final Exam 2020 (use it as sample for the final)

Announcements

Welcome! This is the official source for homework assignments, schedule updates, and other announcements. Please check it frequently (once a week or so) for up-to-date info.
The HW assignments are collected in class on the due date. No late HW, no exception. There will be an extra make-up HW (HW10*) replacing the lowest scoring HW (or a missing HW).
The dates of the exams are fixed (see schedule below). The midterms will take place in class during the class time. The final exam is scheduled by the university (details on location to follow). There will be no make-up exam (except exceptional individual circumstances, with documentation); please plan accordingly.
The first midterm will take place in class on Thursday, Sept 22. The material covered is Chapter 1 and Sections 4.1, 4.2 (permutations). A sample exam can be found here .
The second midterm will take place in class on Thursday, Nov 3. The material covered is Chapter 4 and 5 (excluding 4.4 and 5.4). HW7 can be used as a sample for the exam.

Grading

2 Midterms (20% each), 1 Final (40%), 10 HW assignments (20% in total) [The lowest score or a missing Hw are dropped from the HW score computation.]
No late HWs, and no make-up exams.
A small number of extra points (for class participation, attendance, and quizzes) will be awarded during the regular classes and recitations.

Schedule

Week	Topic	Sections Covered	HW Assignments
(1) Aug 23, 25	Euclid's Algorithm & gcd Unique Factorization Theorem	1.1 1.3
(2) Aug 30, Sept 1	Modular arithmetic	1.4, 1.5	HW1 (due Sept 6)
(3) Sept 6, 8	Euler's Theorem Public key cryptography	1.6	HW2 (due Sept 13)
(4) Sept 13, 15	Permutations	4.1, 4.2	HW3 (due Sept 20)
(5) Sept 20, 22	Review Midterm 1: Thursday, Sept 22 (in class)	Arithmetic (Ch. 1) and Permutations (4.1, 4.2)
(6) Sept 27, 29	Intro to Groups	4.3	HW4 (due Oct 4)
(7) Oct 4, 6	Group Theory	5.1, 5.2	HW5 (due Oct 20)
(8) Oct 13	Groups of small order	5.3
(9) Oct 18, 20	Groups of small order Groups and codes	5.3 5.4	HW6 (due Nov 1)
(10)Oct 25, 27	Groups and codes Other algebraic structures	5.4 4.4	HW7 (due Nov 3)
(11) Nov 1, 3	Review Midterm 2: Thursday, Nov 3 (in class)	Ch 4 and Ch 5
(12) Nov 8, 10	Polynomials Division and Factorization of polynomials	6.1 6.2	HW8 (due Nov 15)
(13) Nov 15, 17	Factorization of polynomials Polynomial congruence classes	6.3 6.4	HW9 (due Nov 22)
(14) Nov 22	Cyclic Codes	6.5	HW10 (due Dec 1)
(14) Nov 29, Dec 1	Review	Chapters 1, 4, 5, 6
Dec 14 (11:15-1:45)	Final Exam	Chapters 1, 4, 5, 6