Math 603, Spring 2016
- Faculty: David Harbater
harbater AT math.upenn.edu
- Telephone: (215) 898-9594; Department office: (215) 898-8178
- Office: DRL
4E2A; Department office: DRL 4W1-6.
- Office hours: After class, by appointment, and as scheduled.
Second semester graduate algebra. Prerequisite: Math 602 or the equivalent.
- modules: 5 lemma,
snake lemma, flat modules, projective modules, modules over a PID,
localization, Nakayama's Lemma, locally free modules, Ext and Tor;
- commutative rings: Noetherian rings and modules, Hilbert Basis
Theorem, Krull dimension, primary decomposition, integral extensions,
integral closure, lying over theorem, Artin rings, Dedekind domains,
discrete valuation rings, Krull's principal ideal theorem;
- field theory: degree of an extension, transcendence
degree, algebraic closures, separable extensions, splitting fields, normal
extensions, finite fields, purely inseparable
extensions, Primitive Element Theorem, perfect fields;
- Galois theory:
Galois extensions, fixed fields,
Galois groups, Fundamental Theorem of Galois Theory, Kummer's theorem,
linear independence of characters, Hilbert's Theorem 90, algebraic
independence of automorphisms, Artin-Schreier theorem, normal basis
theorem, geometric constructibility, solvability by radicals.
schedule: Mon and Fri, 1:30-3pm in DRL 4N30. There are also some classes on Wed, 1:30-3pm in DRL 4N30; details as announced.
- Textbook: Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, 1974.
- Course structure: The class meets from 1:30-3pm on Mondays and Fridays, and occasionally on Wednesdays,
from January 13 to April 27.
Wednesday classes either supplement or replace Monday/Friday classes, and the dates of the Wednesday classes
are announced in advance. Wednesday classes include January 13 (1:30), Feb. 3 (2pm), March 2 (1:30pm), March 23 (1:30pm),
April 6 (1:30), and April 27 (1:30).
There will be no class on Fri., Jan. 15; Mon., Jan. 18; Fri., Feb. 12;
Mon., March 7; Fri., March 11. The last day of the semester is Wed., April 27.
There are weekly problem sets, which are key to the course. There is one exam, which takes place in
class at the end of the semester, on Wed., April 27.
Homework assignments for Math
Sample exam. The exam was out of 75 points; the quartiles were 50.5, 56, 63.5. The quartiles on the homework
(out of 360) were 321, 326, 343.5. Individual scores are available on Canvas.