This webpage contains information specific to section 2. This page is updated frequently; please peek in every couple days or so, and at least once a week.

**Instructor**: Jeff Thunder**Office**: WH 362**Phone**: 753-6761**e-mail**: jthunder@niu.edu**Office Hours**: Monday 11-12 and Wednesday, Friday 2:00-2:50 p.m. or by appointment.

The textbook for the course is *Abstract Algebra*
by Beachy and Blair, third edition. We will cover
the first three chapters, with some deletia.
The prerequisite for this course is MATH 240. We will use matrices in
some important examples, but the main reason for the requirement
is to attempt to guarantee a certain level of "mathematical maturity."

The student is expected to acquire an understanding of the elementary theory of groups, together with the necessary number theoretic prerequisites. There will be some discussion of the computational aspects of these topics, but the main thrust of the course will be theoretical. The student will be expected not only to follow the proofs presented in class and in the text, but also to learn to construct new proofs. Proofs must be logically correct and care must be taken to write precisely and in grammatically correct English.

Grades for section 2 will be based on homework, a midterm exam and the final exam. The weights for these are 40%, 20% and 40%, respectively.

Homework will be collected once a week on Friday. It will be turned in at the beginning of class. You are free to work with other students on the homework; in fact, this is encouraged. Sloppy and/or illegible work will be returned back with no credit! Your homework is something of which you should be proud (notice how I didn't end with a preposition there). Expect to spend lots of time on it. The specific assignment for each week will be available on this webpage that Monday (see below).

The midterm exam will be during class on Friday, October 14. The final exam is from 4:00 to 5:50 p.m. on Monday, December 5. Here is what to expect, and a previous midterm.

The final will be similar. You can view a previous final exam as a study guide.

- Week #1 (due 8/26): Exercises 4, 6, 7, 9 and 17 from section 1.1. Here are some solutions.
- Week #2 (originally due 9/2, moved to 9/7): Exercises 3, 8, 10, 11, 13 and 18 from section 1.2.
- Week #4 (due 9/16): Exercises 1, 7, 8, 10 and 18 from section 1.3.
- Week #5 (due 9/23): Exercises 1, 3, 7, 13, 14, and 27 from section 1.4.
- Week #6 (due 9/30): Exercises 5, 8, 9a,b,d and 14 from section 2.1.
- Week #7 (due 10/7): Exercises 2, 3, 5, 11a,b and 12a,b from section 2.2.
- Week #8 (due 10/14): Exercises 1b,d and f, 4b and d, 6, 13 and 15 from section 2.3. Here are some solutions.
- Week #9 (due 10/21): Exercises 2b,d and f, 8, 11, 12 and 15 from section 3.1.
- Week #10 (due 10/28): Exercises 20 and 22 from section 3.1, and exercises 1b and d, 4, 8 and 11 from section 3.2. I've typed up some solutions to a couple of them.
- Week #11 (due 11/4): Exercises 17, 21 and 24 from section 3.2, and exercises 4 and 8 from section 3.3. Here are some solutions.
- Week #12 (due 11/11): Exercises 2, 4, 11, 16 and 17 from section 3.4.
- Week #13 (due 11/18): Exercises 2, 11, 13 and 20 from section 3.5. Also, find all of the primitive roots modulo 41.
- Week #14 (due 11/30):
**Note due date change!**Exercises 7, 13, 15, 17 and 21 from section 3.6.

- Monday, August 22: axioms for integers, little results
- Wednesday, August 24: the Euclidean algorithm
- Monday, August 29: Ideals and Theorem 1.1.4, the Greatest Common Divisor and Ideals, Polynomials, Little Results for Polynomials
- Wednesday, August 31: An "absolute value" for Polynomials, the Division Algorithm for Polynomials, Ideals, Theorem 1.1.4, and GCDs for Polynomials
- Wednesday, September 7: Euclid's Lemma and Primes, Everything Interesting Factors, Everything Interesting Factors Uniquely
- Friday, September 9: Amazing Computations!, Last Digits and Divisibility
- Wednesday, September 14: Congruences and the Euclidean Algorithm (again)
- Friday, September 16: Some Addition and Multiplication Tables, Small, Simple Number Systems,
- Monday, September 19: "Little Results" for Integers mod n, A Closer Look at Integers Modulo a Prime
- Wednesday, September 21: Euler's Theorem
- Friday, September 23: Polynomials (Again!) and Wilson's Theorem A clever (and useful) application of congruences
- Monday, September 26: Mathematical Relations
- Wednesday, September 28: Functions as a "Number System?"
- Wednesday, October 5: Yes, Functions as a "Number System!"
- Friday, October 7: Cycles and More about Cycles
- Monday, October 10: Even More about Cycles and Permutations
- Wednesday, October 19: Groups I, Groups II
- Friday, October 21: Groups III, Cyclic Subgroups
- Monday, October 24: A look back at Euler's Theorem
- Monday, October 31: Some Groups of Order 4, Direct Products
- Wednesday, November 2: Groups of Order 6, Some groups are the same
- Friday, November 4: Groups of Order 8
- Monday, November 7: Group isomorphisms, part I
- Wednesday, November 9: Group isomorphisms, part II
- Friday, November 11: More about cyclic groups
- Monday, April 14: More about the exponent of a group, Roots of unity
- Wednesday, November 16: Primitive roots
- Monday, November 21: Dihedral Groups
- Monday, November 25: Homomorphisms

Last update: November 30, 2016