### MAT 312/AMS 351 Syllabus Applied Algebra

Fall 2016

The schedule for topics covered in lecture is as follows. You must do the assigned reading prior to lecture. This will make the lectures more effective for you.

• Tuesday, August 30
Section 1.1 The division algorithm and greatest common divisors.

• Thursday, September 1
Section 1.2 Mathematical induction.
In-class Diagnostic Quiz.

• Tuesday, September 6
LABOR DAY. NO CLASS.

• Thursday, September 8
Section 1.3 Primes and the Unique Factorization Theorem.
Problem Set 1 due in lecture.

• Tuesday, September 13
Section 1.4 Congruence classes.

• Thursday, September 15
Section 1.5 Solving linear congruences.
Problem Set 2 due in lecture.

• Tuesday, September 20
Section 1.6 Euler's Theorem and public key codes.

• Thursday, September 22
Section 1.6 Euler's Theorem and public key codes.
Problem Set 3 due in lecture.

• Tuesday, September 27
REVIEW FOR MIDTERM 1

• Thursday, September 29
MIDTERM 1

• Tuesday, October 4
Section 4.1 Permutations.

• Thursday, October 6
Section 4.3 Definition and examples of groups.
Problem Set 4 due in lecture.

• Tuesday, October 11
Section 4.3 Definition and examples of groups.

• Thursday, October 13
Section 4.2 The order and sign of a permutation.
Problem Set 5 due in lecture.

• Tuesday, October 18
Section 5.1 Preliminaries on group theory.

• Thursday, October 20
Section 5.2 Cosets and Lagrange's Theorem.
Problem Set 6 due in lecture.

• Tuesday, October 25
REVIEW FOR MIDTERM 2

• Thursday, October 27
MIDTERM 2

• Tuesday, November 1
Section 5.3 Groups of small order.

• Thursday, November 3
Section 5.4 Error-detecting and error-correcting codes.
Problem Set 7 due in lecture.

• Tuesday, November 8
Binary Codes.

• Thursday, November 10
Section 6.1 Introduction to polynomials.
Problem Set 8 due in lecture.

• Tuesday, November 15
Section 6.2 The division algorithm for polynomials.

• Thursday, November 17
REVIEW FOR MIDTERM 3
Problem Set 9 due in lecture.

• Tuesday, November 22
MIDTERM 3

• Thursday, November 24
THANKSGIVING. NO CLASS.

• Tuesday, November 29
Section 6.3 Factorisation.

• Thursday, December 1
Section 6.4 Polynomial congruence classes.
Problem Set 10 due in lecture.

• Tuesday, December 6
Section 6.5 Cyclic codes.

• Thursday, December 8
FINAL REVIEW
Problem Set 11 due in lecture.

Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr