MATH 511A: Algebra (Fall 2017)

Essential course information is contained in the syllabus.

Instructor

Jack Hall
lectures: Tuesday and Thursday, 12:30-1:45pm in MATH 501
office hours: Monday 3-4pm and Wednesday 4-5pm in ENR2 S349
email: firstnamelastname at math dot arizona dot edu

Teaching Assistant

Anthony Kling
problem sessions: Tuesday, 5-6pm in ENR2 S375
email: amlastname at math dot arizona dot edu

Texts

The following texts I have found to be useful references.
James Milne's notes on group theory.
Atiyah-Macdonald's book on commutative algebra.
Lang's Algebra.
Grove's Algebra.

Homework

Homework 1: due 8/31/2017 pdf, tex, solutions
Homework 2: due 9/7/2017 pdf, tex
Homework 3: due 9/14/2017 handed out in class
Homework 4: due 9/21/2017 handed out in class
Homework 5: due 10/12/2017 handed out in class
Homework 6: due 10/19/2017 handed out in class
Homework 7: due 10/26/2017 handed out in class
Homework 8: due 11/2/2017 handed out in class
Homework 9: due 11/21/2017 handed out in class
Homework 10: due 12/5/2017 handed out in class

Topics covered

8/22/2017: Definitions and examples of groups and subgroups.
8/24/2017: Dihedral groups, group homomorphisms, cosets, and Lagrange's Theorem.
8/29/2017: Normal subgroups and quotients.
8/31/2017: Free groups, presentations, and Coxeter groups.
9/5/2017: The Symmetric group as a Coxeter group; group actions, orbits, and stabilizers.
9/7/2017: Class equation, Cauchy's Theorem, applications.
9/12/2017: Sylow I and II.
9/14/2017: Automorphisms of groups.
9/19/2017: Semidirect products and group classification.
9/21/2017: More classifications and solvable groups.
9/26/2017: Simplicity of the alternating group (guest lecture by Anthony Kling).
9/28/2017: Midterm 1.
10/3/2017: Definitions, ideals, quotients.
10/5/2017: Fields, division rings, prime and maximal ideals.
10/10/2017: Units, localizations.
10/12/2017: Localizations and their ideals.
10/17/2017: Modules, Nakayama's Lemma.
10/19/2017: Finitely presented modules, noetherian modules and rings.
10/24/2017: Hilbert Basis Theorem, Tensor products, integral extensions.
10/26/2017: Going up, Artin-Tate.
10/31/2017: Nullstellsatz, Zariski's Lemma, UFDs, PIDs
11/9/2017: Midterm 2.
11/14/2017: Structure of finitely generated modules over PIDs
11/16/2017: Structure of finitely generated modules over PIDs, continued
11/21/2017: Rational and Jordan forms
11/28/2017: Semisimple modules
11/30/2017: Semisimple rings
12/5/2017: Review
12/8/2017: Final