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
for more information on how to obtain (for free!) Adobe Acrobat.
- Instructor: Jeff Thunder
- Office: WH 348
- Phone: 753-6712
- Office Hours: Monday, Wednesday, Friday, 9:00-10:00 a.m. or
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."
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 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
The final will be similar. You can view
a previous final exam as a
- 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
- 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.
- Monday, August 24:
axioms for integers,
- Wednesday, August 26:
the Euclidean algorithm
- Friday, August 28:
Ideals and Theorem 1.1.4,
the Greatest Common Divisor and Ideals,
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
- Wednesday, September 2:
Euclid's Lemma and Primes,
Everything Interesting Factors,
Everything Interesting Factors Uniquely
- Friday, September 4:
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,
- Friday, September 25:
Another way to prove Wilson's Theorem,
A clever (and useful) application of congruences,
- Monday, September 28:
- Wednesday, September 30:
Functions as a "Number System?"
- Wednesday, October 7:
Yes, I said Functions as a "Number System!",
- Friday, October 9:
More about Cycles
- Monday, October 12:
Even More about Cycles and Permutations
- Monday, October 19:
- Wednesday, October 21:
- Friday, October 23:
- Monday, October 26:
A look back at Euler's Theorem
- Monday, November 2:
Some Groups of Order 4,
- 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
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:
- Monday, November 30:
- Wednesday, December 2:
Numbers, Sets and Axioms
Homer does math!
Yes indeed, there's plenty of math humor to be found in the
look and see!
Last update: December 1, 2009