Abstract Algebra 1 [2019t]

. Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Checklist The checklist

(pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).

We'll start using the notation of the commutator of two elements in class. We are heading towards Burnside's lemma, an application of Orb-Stabilizer.
Our TicTacToe-ish Home-B was pictorial, and now has solns.

It wouldn't surprise me if you are curious about Enumerating TTT-automorphisms for 4x4, and the reasoning involved.

While we're on this topic, I'm looking for suggestions on clever names for some of the 4x4 TTT-automorphism pictures.

The nifty Class-B now has all solns. Please go over it in detail.

Available are illustrative solns to some HW problems from Gallian.
Our thought-provoking Home-A has complete solns. (Slightly updated, Tuesday, 01Oct2019.)
The Wikipedia page on permutations is useful, as is Lagrange's thm that the order of a subgp divides the order of the enclosing group.
My old notes on permutations use different convensions from what Gallian and we are using this semester, but I want to refer to it in class today.
The thrilling Class-A now has complete solns.
In one convenient location: All 6 Alg quizzes so far (pdf), [Friday, 01Nov2019]
In this quizzes link, please have read the binomial/multinomial conventions on page 2, together with Operations on Sets.
Slightly expanding Ring Notes, please read Group Notes (pdf). [Wedn., 13Nov2019] See also Burnside's lemma and its application to Counting necklaces.
In order to facilitate for students posting solns to our Archive, in addition to Gallian, we will use Abstract Algebra: Theory and Applications by Thomas Judson (2016 Edition), an online text made publicly available by its author. Students will be posting solns both from their edition of Gallian, as well as Judson text, as well as any interesting algebra problems students create.
Here is the first posting assignment for the weekend of Sept. 7,8.
Our Algebra syllabus/calendar. [11Sep2019]
Does Zero = One? (pdf). Here are some ~~proofs~~ poofs about which you can post to our Archive.
Nostalgic?, see the 2008g, 2005t, 2003g page.
[Old] Have read and throughly understood Set-builder notation (up through “Equivalent predicates...”).
[Old] Have learned the Math-Greek alphabet (pdf). which we will use in class frequently.
[Old] You looked at this Practice-prereq (pdf) to see what you might want to review.

As the semester progresses, you will also need to print-out a few pages of handouts that I have prepared for you.

We will cover some material that is not in our text; in particular, applications of group-theory for solving certain games and puzzles.

Computer&Projector	Time	Memory/Telepathy	Blackboard	E-Probs
Joey F.	Tess D.	Kat B.	Tyler M.	Abigail

Individual Algebra Project [IAP]

There will be a (possibly optional) Algebra Project, to be done individually. It will be due, slid u n d e r my office door (Little Hall 402, Northeast corner) , by 2PM, Thursday, 05Dec2019 The project must be carefully typed and carefully proofread.

At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist (pdf, 3pages) to earn full credit.

Author:	Joseph A. Gallian	ISBN:	9781305657960
Year:	2017	Publisher:	Houghton Mifflin

(abstract) Algebra 1

Algebra on The Web

Individual Algebra Project [IAP]