MATH 420 Fall 2009 Section 1

This webpage contains information specific to section 1. This page is updated frequently; please peek in every couple days or so, and at least once a week.

The documents contained herein are all pdf files and require Adobe Acrobat (or something similar) to view them. Go back to the math department's course information page here for more information on how to obtain (for free!) Adobe Acrobat.

Basic Information

• Instructor: Jeff Thunder
• Office: WH 348
• Phone: 753-6712
• e-mail: jthunder@math.niu.edu
• Office Hours: Monday, Wednesday, Friday, 9:00-10:00 a.m. or by appointment.

The textbook for the course is Abstract Algebra with a Concrete Introduction by Beachy and Blair, second 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."

Course Objectives

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.

Grading Scale

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

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).

Exams

The midterm exam will be during class on Friday, October 16. The final exam is from noon to 1:50 p.m. on Monday, December 7. Here is what to expect. You can look at a couple of previous midterms. The final will be similar. You can view a previous final exam as a study guide.

Homework Assignments

• Week #1 (due 8/28): Exercises 4, 6, 7, 9 and 17 from section 1.1. I've written up some remarks/partial solutions for you to peruse.
• Week #2 (due 9/4): Exercises 3, 8 and 18 from section 1.2 and the two exercises here.
• Week #3 (due 9/11): Exercises 1, 7 and 18 from section 1.3.
• Week #4 (due 9/21): Exercises 1, 3, 7, 13, 14, and 27 from section 1.4.
• Week #5 (due 10/2): Exercises 5, 8, 9a,b,d and 14 from section 2.1.
• Week #6 (due 10/9): Exercises 2, 3, 5, 11a,b and 12a,b from section 2.2.
• Week #7 (due 10/16): Exercises 1b,d and f, 4b and d, 6, 13 and 15 from section 2.3. Here are some solutions.
• Week #8 (due 10/23): Exercises 2b,d and f, 8, 11, 12 and 15 from section 3.1.
• Week #9 (due 10/30): 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 a few solutions.
• Week #10 (due 11/6): Exercises 17, 21 and 24 from section 3.2, and exercises 4 and 8 from section 3.3. Here are some solutions.
• Week #11 (due 11/13): Exercises 2, 4, 11, 16 and 17 from section 3.4.
• Week #12 (due 11/20): Exercises 2, 11, 13 and 20 from section 3.5. Also, find all of the primitive roots modulo 41.
• Week #13 (due 12/4): Exercises 7, 13, 15, 17 and 21 from section 3.6.

Daily Log

• Monday, August 24: axioms for integers, little results
• Wednesday, August 26: the Euclidean algorithm
• Friday, August 28: Ideals and Theorem 1.1.4, the Greatest Common Divisor and Ideals, Polynomials, Little Results for Polynomials
• Monday, August 31: An ``absolute value" for Polynomials, the Division Algorithm for Polynomials, Ideals, Theorem 1.1.4, and GCDs for Polynomials
• Wednesday, September 2: Euclid's Lemma and Primes, Everything Interesting Factors, Everything Interesting Factors Uniquely
• Friday, September 4: Amazing Computations!, Last Digits and Divisibility
• Wednesday, September 9: Congruences and the Euclidean Algorithm (again)
• Friday, September 11: Some Addition and Multiplication Tables
• Monday, September 14: Small, Simple Number Systems, "Little Results" for Integers mod n
• Wednesday, September 16: A Closer Look at Integers Modulo a Prime, Euler's Theorem
• Friday, September 25: Another way to prove Wilson's Theorem, A clever (and useful) application of congruences,
• Monday, September 28: Mathematical Relations
• Wednesday, September 30: Functions as a "Number System?"
• Wednesday, October 7: Yes, I said Functions as a "Number System!", Cycles
• Friday, October 9: More about Cycles
• Monday, October 12: Even More about Cycles and Permutations
• Monday, October 19: Groups I
• Wednesday, October 21: Groups II
• Friday, October 23: Groups III, Cyclic Subgroups
• Monday, October 26: A look back at Euler's Theorem
• Monday, November 2: Some Groups of Order 4, Direct Products
• Wednesday, November 4: Groups of Order 6
• Friday, November 6: Some groups are the same, And some are not
• Monday, November 9: Multiplication tables for two groups of order 8, Group isomorphisms, part I
• Wednesday, November 11: Group isomorphisms, part II
• Friday, November 13: More about cyclic groups
• Monday, November 16: More about the exponent of a group, Roots of unity
• Wednesday, November 18: Primitive roots
• Monday, November 30: Dihedral Groups
• Wednesday, December 2: Homomorphisms

Numbers, Sets and Axioms

• The Axioms of Set Theory
• The Natural Numbers
• The Integers and Rational Numbers

Homer does math!

Last update: December 1, 2009