MTH 331/431 Abstract Algebra I (Fall 2019):


Schedule:

Week of
Class Topics Remarks, Materials, Assignments

8/25 Introduction.
Preliminaries. (Ch. 1)
Introduction notes
Sets and Equivalence Relations

9/1 No class on 9/2
(Labor Day)

Integers. (Ch. 2)
Induction and Well-Ordering Principle
Division Algorith, Euclidean Algorithm, Prime Numbers

Homework 1 due 9/6:
All students: Ch. 1, §1.3 "Exercises" (online text),
exer. 7, 9, 18(b,c), 19, 20(b), 21, 22(c,e), 25(d).
Graduate (MTH 431) students: in addition, do exer. 26 and 29.
(MTH 331 students are welcome to do these problems for extra credit.)
Latex template for homework: here.

Homework 1 Solutions

9/8 Groups. (Ch. 3) Integer Equivalence Classes and Symmetries

Homework 2 due 9/13:
All students: Ch. 2, §2.3 "Exercises" (online text),
exer. 2, 5, 12, 15(d, f), 18.
Graduate (MTH 431) students: in addition, do exer. 17(c) and 23.
(MTH 331 students are welcome to do these problems for extra credit.)
Latex template for homework: here.

Homework 2 Solutions

9/15 Continue on Groups.
Subgroups. (Ch. 3)
Groups: Definitions and Examples

Summary of Some Groups Examples

Homework 3 due 9/20:
All students: Ch.2, §2.3, exer. 28, 31;
Ch. 3, §3.4, exer. 1 (b,d), 2 (c,d), 6, 7, 8, 14.
Graduate (MTH 431) students: in addition, do exer. 10 and 15 in Section 3.4.
(MTH 331 students are welcome to do these problems for extra credit.)
Latex template for homework: here.

Homework 3 Solutions

9/22 Exam I on 9/23 (Monday) Study for Exam I (9/23): study guide

Homework 4 due 9/27:
All students: Ch. 3, §3.4, exer. 16, 26, 33, 39, 43, 48.
Graduate (MTH 431) students: in addition, do exer. 34 and 47.
(MTH 331 students are welcome to do these problems for extra credit.)
NOTE: Extra problem for all: 45.
Latex template for homework: here.