MAT 312/ AMS 351 (Applied Algebra) - Fall 2017

Time and Place : TuTh 11:30-12:50; Mathematics P131

Instructor : Radu Laza

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

Office Hours: Thr 1:30-2:30, Thr 4-6

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

Schedule
Sample Final
Solutions to sample
HW 10 (due December 7)
The Sample Final can be used as a make-up HW (due December 5)

Announcements

Welcome!
The first midterm will take place in class on Tuesday, Sept 26. It will cover all Chapter 1 of the textbook ("Number Theory"). To prepare for the exam, please review HW1-3, and the sample midterm .
The second midterm will take place in class on Tuesday, Nov 7. It will focus on groups (All of Chapter 4, and 5.1-5.3). See the sample questions for Midterm 2 (this is longer than the actual exam). Solutions to the sample exam.
The final exam will cover the material from Midterm 1, Midterm 2, and the Chapter 6 on polynomials. Some sample questions are available here.

Grading

There will be 2 midterms and a final. We will have approximately 10 homework assignments.
The exams count for 75% of the final grade. The division is roughly: 35% for the final and 20% for each midterm. The remaining 25% will be for the homework assignments.
No late HWs, and no make-up exams. (There will an extra make-up HW in case you missed one HW assignment).

Schedule

Week	Topic	Sections Covered	HW Assigments
(1) Aug 29, 31	Division Algorithm & gcd ------------------------------------------ Induction	1.1 ------------------------------------------ 1.2
(2) Sept 7	Primes and Unique Factorization	1.3	HW1 (due Sept 14)
(3) Sept 12, 14	Congruence classes ------------------------------------------ Solving linear congruences	1.4 ------------------------------------------ 1.5	HW2 (due Sept 21)
(4) Sept 19, 21	Euler's Theorem ------------------------------------------ Review (Chapter 1)	1.6	HW3 (due Sept 28)
(5) Sept 26, 28	Midterm 1: Tuesday, Sept 26 (in class) ------------------------------------------ Permutations (1)	Chapter 1 (Number theory) ------------------------------------------ 4.1
(6) Oct 3, 5	Permutations (2) ------------------------------------------ Intro to Groups	4.2 4.3	HW4 (due Oct 12)
(7) Oct 10, 12	Algebraic Structures	4.4	HW5 (due Oct 19)
(8) Oct 17, 19	Groups and Codes	5.1 5.2	HW6 (due Oct 26)
(9) Oct 24, 26	Groups	5.2 5.3	HW7
(10) Oct 31, Nov 2	Groups Review	Ch. 5
(11) Nov 7, 9	Midterm 2: Tuesday, Nov 7 (in class) ------------------------------------------ Group and Codes	Ch. 4, 5.1--5.3 ----------------------------- 5.4	HW8 (due Nov 16)
(12) Nov 14, 16	Polynomials	5.4 6.1, 6.2
(13) Nov 21	Factorization	6.3	HW9 (due Nov 28)
(14) Nov 28, 30	Polynomial congruence classes Cyclic Codes	6.4 6.5	HW10 (due Dec 7) HW11* (due Dec 5)
(15) Dec 5, 7	Review