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

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

Problem Sets

• Homework 11
• Homework 10
• Homework 9 (fixed)
• Homework 8
• Homework 7
• Homework 6
• Homework 5 (fixed)
• Homework 4
• Homework 3 (fixed)
• Homework 2 (fixed)
• Homework 1 (fixed)

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
• 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