leuschke.org :: Teaching/Math 632 Spring 2009

Teaching/Math 632 Spring 2009

The course is over! Final grades have been submitted to MySlice. Thanks to everyone for a great semester, and enjoy your summer.

Basics

Instructor: Prof. Graham Leuschke
Contact: gjleusch@math.syr.edu
Time & Place: MWF 10:35—11:25, Carnegie 300
Textbook: Dummit & Foote, Abstract Algebra, 3rd ed., ISBN 0471433349
Office Hours: MW 1:30—4:00, R 10:30—12:00; by appointment; and any time my door is open (206C Carnegie)
Important documents: course syllabus Δ

The human mind has never invented a labor-saving device equal to algebra.
Josiah Willard Gibbs, 1887

Problem Sets

Links

We’re going to skip (mostly) a section on algebraic closures and algebraic closedness. They may show up on a future problem set or exam, but nothing desperately hard.
We also skipped a section on straightedge/compass constructions; we’ll come back to it if we have time. Here’s Wikipedia on straightedge and compass constructions.
How to use Zorn’s Lemma (by Fields Medalist Tim Gowers) See also Recognizing Countable Sets
the concept of a cokernel leads directly to short exact sequences (though we’re headed in another direction). from there to free resolutions is but a small step.
the word problem for groups has a pretty interesting history
a better picture of the free group on two letters
a talk I gave a few years ago about the Banach—Tarski Paradox
some history I ran across this weekend: The evolution of group theory and Algebraic geometry between Noether and Noether
Groebner bases are a generalization of gcds to multivariate polynomial rings
history of the Chinese Remainder Theorem
unique factorization played a starring role in the history of Fermat’s Last Theorem
a generalizations of unique factorization: half-factorial domains one and two
some more background on Euclidean domains etc., including the tidbit that Q[\sqrt{d}] is an ED if and only if d is one of −11, −7, −3, −2, −1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, or 73. Crazy.
a solution to Homework 2, Problem 6 Δ
a little song about the Banach-Tarski Paradox
the great finite field writeup (this is a bit early, but worthwhile anyway)
questions you could ask about polynomial and power series rings
ArXiv.org and the front
MathSciNet (subscription required, so use a campus computer)
a review of our textbook