# Math 3330: Abstract Algebra, Fall 2017

## Basic Info

Office: 601 PGH Instructor: Dr. Mark Tomforde

### Assignments

Homework #10, Due Wednesday, November 29
Chapter 10, p.219, Problems 10, 48, 59
Chapter 11, p.234, Problems 4, 6, 9, 10, 12, 22

Homework #9, Due Monday, November 20
Chapter 9, p.202, Problems 6, 7, 8, 9, 11, 13, 14, 15, 35, 39

Reading Assignment #9, to be done prior to class on Friday, November 17
Chapter 10, Section "The First Isomorphism Theorem"
Chapter 8, Section "Definition and Examples"
Chapter 8, Section "Properties of External Direct Products"
Chapter 8, Section "The Group of Units Modulo n as an External Direct Product"
Chapter 11, Section "The Fundamental Theorem"
Chapter 11, Section "The Isomorphism Classes of Abelian Groups"
Chapter 11, Section "Proof of the Fundamental Theorem"

Homework #8, Due Wednesday, November 15
Chapter 7, p.156, Problems 1, 7, 8, 9, 11, 17, 22, 24, 30, 33

Reading Assignment #8, to be done prior to class on Monday, November 13
Chapter 7, Section "Properties of Cosets"
Chapter 7, Section "Lagrange’s Theorem and Consequences"
Chapter 7, Section "An Application of Cosets to Permutation Groups"
Chapter 9, Section "Normal Subgroups"
Chapter 9, Section "Factor Groups"
Chapter 9, Section "Applications of Factor Groups"
Chapter 9, Section "Internal Direct Products"

Homework #7, Due Wednesday, October 25
Chapter 6, p.138, Problems 2, 4, 8, 12, 14, 16, 18, 20, 22, 24
(Note: You have two weeks to work on these problems.)

Homework #6, Due Wednesday, October 11
Chapter 5, p.118, Problems 2(a)(b), 6, 7, 8, 11(a)(b)(c)(d)(e), 15, 23; (Scoring: #2 is 3 points total, #11 is 2.5 points total, #15 is 0.5 points, and the rest are 1 point each)

Reading Assignment #6, to be done prior to class on Monday, October 9
Chapter 6, Section "Motivation"
Chapter 6, Section "Definition and Examples"
Chapter 6, Section "Cayley’s Theorem"
Chapter 6, Section "Properties of Isomorphisms"
Chapter 6, Section "Automorphisms"
Also read p.208-210, including Theorem 10.1 and its proof.

Homework #5, Due Wednesday, October 4

Reading Assignment #5, to be done prior to class on Wednesday, October 4
Reread any sections in Chapter 1-4 you feel that you could use review on as you go over your returned Exam #1. Also, as we discuss permutations in class, reread any sections of Chapter 5 you need to review.

Exam #1 is Wednesday, September 27.

Homework #4, Due Wednesday, September 27
Chapter 4, p.87 (1 point each), Problems 10, 12, 21, 26, 27, 28, 31, 32, 33, 36

Reading Assignment #4, to be done prior to class on Monday, September 25
Chapter 5, Section "Definition and Notation"
Chapter 5, Section "Cycle Notation"
Chapter 5, Section "Properties of Permutations"

Homework #3, Due Wednesday, September 20
Chapter 3, p.68 (1 point each), Problems 8, 12, 18, 22, 32, 36, 50, 52, 68, 77

Reading Assignment #3, to be done prior to class on Monday, September 18
Chapter 4, Section "Properties of Cyclic Groups"
Chapter 4, Section "Classification of Subgroups of Cyclic Groups"

Homework #2, Due Wednesday, September 13
Please turn in the following problems. Be sure to follow the Homework Rules in the Syllabus, since you will lose points for each infraction. Also keep in mind that homework is late once I start lecturing on September 13, and late homework will not be accepted.
Chapter 2, p.54 (1 point each), Problems 4, 5, 12, 13, 15, 22, 25, 28, 32, 33

Reading Assignment #2, to be done prior to class on Monday, September 11
Chapter 3, Section "Terminology and Notation"
Chapter 3, Section "Subgroup Tests"
Chapter 3, Section "Examples of Subgroups"

Reading Assignment #1, to be done prior to class on Wednesday, August 23
Chapter 1, Section "Symmetries of a Square"
Chapter 1, Section "The Dihedral Groups"
Chapter 2, Section "Definition and Examples of Groups"
Chapter 2, Section "Elementary Properties of Groups"
Chapter 2, Section "Historical Note"

Also, the material in Chapter 0: Preliminaries should be familiar to you from your Transitions to Advanced Mathematics course. You should skim p.3-40 of the book, and read in detail any sections dealing with topics you don't feel comfortable with or believe you would benefit from review on.

Homework #1, Due Wednesday, August 23
Please complete and turn in this information sheet.

### Dates of Exams

Exam 1: Wednesday, September 27 in class. (Note: Date changed due to hurricane Harvey.)
Exam 2: Friday, October 27 in class.
Final: Friday, December 8, 11AM--2PM in our usual classroom.