MAT 312/AMS351: Applied Algebra
Spring 2014

## Syllabus

Below is the tentative syllabus for MAT 312/AM 351. It is subject to change.

Homeworks for very week shoudl be handed to your recitation instructor during the recitation next week (e.g., homework for week 1 shoudl be handed during recitation in week 2). It will be graded and returned to you the following week.

 Week Sections covered Homework Jan 27 - 31 1.1 1, 2, 3, 4, 5, 6, 7 Feb 3 - 7 1.2, 1.3 1.2: # 1, 2, 3, 6, 9, 12 1.3: # 1, 2,7, 8, 9 Feb 10 - 14 1.4, 1.5 1.4: 2, 3, 5, 6, 7 and extra problem (see below) 1.5: 1, 2, 3, 5 Feb 17 - 21 1.6 1,2,5,7,12 Feb 24 - 28 review; midterm 1 Mar 3 - 7 4.1, 4.3 HW for Lecture 1 4.3: 1,2,3,4, 6, 7 4.1: 1, 2 HW for Lecture 2 4.1: 1, 2, 4 4.2: 1, 2, 4, 7, 10 Mar 10 - 14 4.1, 4.2 HW for Lecture 1 4.1: 3, 4 4.2: 1, 3, 4, 7, 9, 10 HW for Lecture 2 4.3 1, 2, 3, 4, 7, 8, 9 Mar 17 - 21 Sping break Mar 24 - 28 5.1 5.1: 1, 2, 3, 5, 7, 8, 9 Mar 31 - Apr 4 5.2, 5.3 5.2: 1, 2, 3, 5 5.3: 1, 3, 4, 7 Apr 7 - 11 5.4; notes on binary codes Exercises 1, 2, 3, in the Notes Apr 14 - 18 Review; midterm 2 Apr 21 - 25 6.1,6.2, 6.3 6.1: 2, 3 6.2: 1, 2 (i)--(iii), 3 6.3: 2, 4 (not the Z3 part). Apr 28 - May 2 6.3, 6.4 6.3: 3, 4 (the Z3 part), 6, and extra problem (see below). May 5 - 9 6.5; review for final

Extra problem for 1.4:
Let A,B,C be integers such that A3+B3+C3 is a multiple of 7. Prove that then the product ABC is a multiple of 7.

Extra problem for 6.3:
For each pair of polynomials in Exercise 6.2 #3, find their least common multiple.