MAT 312/ AMS 351 (Applied Algebra) - Spring 2020

Time and Place : MWF 11-11:53; Heavy Engineering - Lab 201

Instructor : Radu Laza

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

Office Hours: Mon, Fri 1-2:30pm

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

HW7 (due April 24)
HW8 (due May 8)
HW9* (due May 14) (make-up HW, replaces a missing or low-scoring HW)

Announcements

(Covid-19 Update) Starting Monday (March 30), we will continue our class via Zoom. All registered participants, will receive Zoom meeting invitations from me. The content of the class remains the same, and we will follow the same schedule (both for the lectures and recitations).
The HWs will be collected by the TA via e-mail. (Please use some scanning app on your phone to produce a single Pdf file for the HW)

Grading

Due to the special circumstances, we will have only 2 exams Midterm 1 (Feb 21, in class) and a Final Exam (May 14, the exact format and further details will be communicated later).
We had 5 HW assignments before the break, and there will be 3 more assignments after the break. HW9 will be a make-up HW (to replace the lowest score HW or a missing HW).
The exams count for 75% of the final grade. The remaining 25% will be for the homework assignments and recitations.
No late HWs, and no make-up exams.

Schedule

Week	Topic	Sections Covered	HW Assigments
(1) Jan 27, 29, 31	Euclid's Algorithm & gcd Unique Factorization Theorem	1.1 1.3	HW1 (due Feb 5)
(2) Feb 3, 5, 7	Modular arithmetic	1.4, 1.5	HW2 (due Feb 12)
(3) Feb 10, 12, 14	Euler's Theorem Public key cryptography	1.6	HW3 (due Feb 19)
(4) Feb 17, 19, 21	Review Midterm 1: Friday, February 21 (in class)	Chapter 1
(5) Feb 24, 26, 28	Permutations	4.1, 4.2	HW4 (due Mar 4)
(6) Mar 2, 4, 6	Intro to Groups	4.3	HW5 (due Mar 11)
(7) Mar 9, 11, 13	Group Theory	5.1, 5.2
March 16--29	Spring Break (no classes)
(9) Mar 30, Apr 1, 3	Groups of small order	5.3	HW6 (due April 10)
(10) Apr 6, 8, 10	Groups and codes	5.4
(11) Apr 13, 15, 17	Other algebraic structures Polynomials	4.4 6.1	HW7 (due April 24)
(12) Apr 20, 22, 24	Division and Factorization of polynomials	6.2, 6.3
(13) Apr 27, 29, May 1	Polynomial congruence classes Cyclic Codes	6.4 6.5	HW8 (due May 8)
(14) May 4, 6, 8	Review	Chapters 1, 4, 5, 6	HW9* (due May 14)
May 14 (11:15-1:45)	Final Exam