MATH 461: Abstract Algebra I

Assorted class resources for your enjoyment:

Syllabus and course description
Homework assignments, by date.
Here is a stylesheet that might give you some idea as to what I look for in high-quality mathematical writing.

Day-by-day goings-on:

Monday, August 22nd. First day of class! We will spend this day developing a sense of what abstract algebra is all about, laying the groundwork for our first homework assignment.
Wednesday, August 24th. Today our goal will be to get a grip on the multiplication tables you constructed outside of class: what sort of patterns emerge in them?
Friday, August 26th. We follow our pattern-finding exercise up with one designed to bring some order to our investigations.
Monday, August 29th. We begin our analysis of the most important set in all of algebra, the integers. Follow along with Handout 1 treating the Division Algorithm.
Wednesday, August 31st. More consequences of the Division Algorithm; see the handout from Monday. We may start talking about Euclid's Algorithm, too!
Friday, September 2nd. We'll finish up talking about Euclid's Algorithm, and turn our attention to the Fundamental Theorem of Arithmetic. Sound important? It is...and cool, too!
Monday, September 5th. Labor Day: no class!
Wednesday, September 7th. Today's all about the Fundamental Theorem of Arithmetic; see the notes from last Friday.
Friday, September 9th. We finish up FTA and take a brief foray into the wonderful world of Gaussian integers and their primeness. Fun stuff!
Monday, September 12th. We begin talking about congruence arithmetic, the basis for another important family of algebric objects.
Wednesday, September 14th. We continue talking about congruences, perhaps beginning the second handout on same.
Friday, September 16th. More congruences, continuing on the second congruence-related handout (from Wednesday).
Monday, September 19th. More congruences, on that same handout! (Sorry to drag it out, but I enjoyed our free-wheeling foray on Friday!)
Wednesday, September 21st. Before going any further, we'll need to take a whirlwind tour of set theoretical basics and other tricks o' the trade you may need to remember from MATH 280.
Friday, September 23rd. After reviewing any of the set-theoretical definitions about which we still feel shaky, we'll take a sneak peek at the idea of a group, our object of study for the next several weeks.
Monday, September 26th. We work on groups, following the handout passed out on Friday. We may have a chance to start talking about the family of permutation groups, which plays a pivotal role in group theory; we'll study these groups carefully!
Wednesday, September 28th. More on permutation groups; see the previous handout.
Friday, September 30th. We should be able to wrap up the first handout on permutations, and move on to the second.
Monday, October 3rd. More permutations, with the handout linked to on Friday!
Wednesday, October 5th. More permutations...same handout! We'll decompress after we finish our "Funamdental Theorem of Permutations" decomposition, going through a bunch of more explicit examples.
Friday, October 7th. We continue with our computational foray into S_n, using the handout given on Wednesday. Also, see this handout offering a nice proof of the structure of the cyclic subgroups of a given group.
Monday, October 10th. Fall Break: no class! Enjoy the long weekend.
Wednesday, October 12th. We wrap up our decomposition of permutations into transpositions, and we may even get started on our our final handout on permutations. I'd like to take a side-trip into more general groups of symmetry first!
Friday, October 14th. Let's "off-road" a little bit, working out the groups of symmetry of some ordinary (and not-so-ordinary) objects.
Monday, October 17th. Finally...we'll get started on the last handout on permutations; see last Wednesday's entry for the link!
Wednesday, October 19th. We should finish up our discussion of permutation groups; see last Wednesday for the handout.
Friday, October 21st. Let's get a little more precise about subgroups.
Monday, October 24th. We'll finish up our intro to subgroups and start talking about cosets and Lagrange's Theorem. Oh ho ho HO!
Wednesday, October 26th. More on cosets of subgroups...see the handout from Monday!
Friday, October 28th. More cosets! We may also spend a little time talking about matrix groups, the topic of your next problem set...
Monday, October 31st. We wrap up our discussion of cosets and Lagrange's Theorem.
Wednesday, November 2nd and Friday, November 4th. No class: I'll be out of town! Please do come on Wednesday to discuss the committee problems from Problem Set 7, and feel free to use both class periods as a chance to get to work on Exam 2 together. (The exam will be posted on the homework website soon.)
Monday, November 7th. Our next handout deals with homomorphisms, their kernels, and what they have to do with subgroups.
Wednesday, November 9th. We continue with the previous handout, on homomorphisms, kernels, and normal subgroups.
Friday, November 11th. No class! You might wish to use our class time as a time to gather and work on the exam.
Monday, November 14th. We will wrap up the most recent handout, on homomorphisms, etc. See last Monday for the handout!
Wednesday, November 16th. We should get started with our next handout, on isomorphisms and the First Homomorphism Theorem!
Friday, November 18th. Let's continue talking about the First Homomorphism Theorem. See Wednesday's post for the notes.
Monday, November 21st. Finishing up FHT! See last week's notes.
Wednesday, November 23rd and Friday, November 25th. No class! Thanksgiving Break!
Monday, November 28th. We begin our final handout, concerning rings and related objects.
Wednesday, November 30th. No class! Please take time today to support your friends and classmates as they present their work in the Fall Undergraduate Research Symposium.
Friday, December 2nd. We continue our discussion of rings; see the notes from Monday.
Monday, December 5th. More on rings, including the First Homomorphism Theorem for rings!
Friday, December 9th. From 11:30 a.m. to 2:00 p.m. we have our scheduled final exam slot. Any idea what we should do with it?