MTH 331/431 Abstract Algebra I (Fall 2017):


Schedule:

Week of
Class Topics Remarks, Materials, Assignments

8/28 Introduction. Preliminaries (Ch.1). Integers (Ch.2).

9/4 Continued: Preliminaries (Ch.1). Integers (Ch.2). No class on 9/4
Homework 1 due 9/8:
All students: Ch. 1, Sect. 1.3 "Exercises" (online text),
exer. 7, 9, 18(b), 19, 20(b), 21, 22(c), 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.)
Homework 1 Solutions

9/11 Continued: Integers (Ch.2). Groups (Ch.3) (Baby) Homework 2 due 9/15:
All students: Ch. 2, Sect. 2.3 "Exercises" (online text),
exer. 2, 5, 15(d), 18.
Graduate (MTH 431) students: in addition, do exer. 23.
(MTH 331 students are welcome to do this problem for extra credit.)
Everyone: extra credit problem is exer. 12.
Homework 2 Solutions

9/18 Groups (Ch.3).

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

Exam I solutions: MTH 331 version and MTH 431 version
Homework 3 due 9/25:
All students: Section 2.3 "Exercises": exer. 28, 31,
Section 3.4 "Exercises": exer. 1 (b,d), 2 (d), 7, 8, 13, 24.
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.)
Homework 3 Solutions

9/25 Subgroups (Ch. 3). Cyclic Groups (Ch. 4).

10/2 Cyclic Groups (Ch. 4). Permutation Groups (Ch. 5).
Homework 4 due 10/6:
All students: Section 3.4 Exercises 16, 26, 33, 43, 47, 48
Section 4.4 Exercises 1(b) and 2(b).
Graduate (MTH 431) students: in addition, do exer. 34 and 39 in Section 3.4.
(MTH 331 students are welcome to do these problems for extra credit.)
Extra problem for all: 45 in Section 3.4.
Homework 4 Solutions

10/9 Permutation Groups (Ch. 5).

Fall Recess 10/12-10/15
Homework 5 due 10/18:
All students: Section 4.4 Exercises 3(h and k), 4 (d), 6, 23 (a and c), 31.
Section 5.3 Exercises 2 (g and j), 3 (d), 4, 6, 23.
Graduate (MTH 431) students:
in addition, do exer. 11 and 26 in Section 4.4 and exer. 34 in Section 5.3.
(MTH 331 students are welcome to do these problems for extra credit.)
Extra problems for all: 13 and 27 in Section 5.3. Homework 5 Solutions

10/16 Cosets and Lagrange's Theorem (Ch. 6).

Study for Exam II (10/20): study guide

Exam II solutions: MTH 331 version and MTH 431 version

10/23 Cosets and Lagrange's Theorem (Ch. 6).
Isomorphisms (Ch. 9).
Homework 6 due 10/30:
All students: Section 6.4 Exercises 1, 3, 4, 5 (b and f), 8,
11 (prove only that statements (a) and (d) are equivalent), 17.
Graduate (MTH 431) students: in addition, do Exercises 18, 19.
(MTH 331 students are welcome to do these problems for extra credit.)
Extra problem for all: Exercise 13.
Homework 6 Solutions

10/30 Normal Subgroups and Factor Groups (Ch. 10). Homework 7 due 11/8:
All students: Section 9.3 Exercises 2, 3, 7, 8,
9 (do not need to proof that G is a group, prove isomorphism only), 16 (b and d), 34, 46, 50.
Graduate (MTH 431) students: in addition, do Exercises 25 and 41.
(MTH 331 students are welcome to do these problems for extra credit.)
Extra problem for all: Exercise 24.
Homework 7 Solutions

11/6 Homomorphisms (Ch. 11) Homework 8 is due 11/15:
All students: Section 10.3 Exercises 1 (a,b,c,e), 5, 6, 8, 9.
Graduate (MTH 431) students: in addition, do Exercises 11 and 12.
(MTH 331 students are welcome to do these problems for extra credit.)
Extra problem for all: Exercise 13 (a,c).
Homework 8 Solutions

11/13 Finite Abelian Groups (Ch. 13).

Study for Exam III (11/17): study guide


11/20 Rings (Ch. 16).
Thanksgiving Recess 11/22-11/26
(Tuesday follows Thursday schedule)
Homework 9

11/27 Rings (Ch. 16). Polynomial Rings (Ch. 17). Homework 10

12/4 Polynomial Rings (Ch. 17). Fields (Ch. 21). Homework 11

12/11 Final Exam and Graduate Student Presentations
(Monday follows Friday schedule)
Homework 12 (optional)