Virtual Instructor: Matt Kerr
Empty Office: Cupples I, Room 114 [all office hours are on Zoom]
e-mail: matkerr [at] wustl.edu
Virtual Office Hours: 8-9pm M, 2:45-3:30 W, 4-4:45 F
I. Galois Theory
II. Linear Algebraic Groups
III. Representation Theory
IV. Commutative Rings
This is the second half of a year-long course which forms the basis for the Ph.D. qualifying examination in algebra.
Prerequisites: Math 5031, or permission of the instructor.
Lectures are on Monday, Wednesday and Friday, from 2-2:45 PM, on Zoom. First class is Monday Jan. 25 and last class is Monday May 3. There is no class on Mar. 3, Mar. 22, or April 12 (study/wellness days).
Midterm Exam: due Friday Mar. 19 (take home)
Final Exam: Tuesday, May 11 The final exam is currently presumed to be a take-home exam as well, due on May 11. If the virus situation changes and we are in person, it will take place on this date from 3:30-5:30 PM.
These will be due, via PDF upload to Canvas, on Tuesdays at 5pm. Solutions will also be posted on Canvas and may include students' work. I encourage you to visit my office hours to discuss problem sets, and to form study groups to discuss the more difficult problems (though solutions must be written up independently).
This is, of course, a "proof course". Please write your solutions legibly, linearly, logically and concisely, in complete sentences with proper mathematical grammar, and cite the results you use ("by Proposition (1.2.3) in the lecture notes/Jacobson, it follows that ..."). In addition, make sure to document any ideas that come from another text, person, or online source.
Problem Set 1 (due Tuesday Feb. 2)
Problem Set 2 (due Tuesday Feb. 9)
Problem Set 3 (due Tuesday Feb. 16)
Problem Set 4 (due Tuesday Feb. 23)
No HW due week of March 1 (wellness days)
Problem Set 5 (due Tuesday Mar. 9)
Problem Set 6 (due Tuesday Mar. 16)
Problem Set 7 (due Tuesday Mar. 30)
Problem Set 8 (due Tuesday Apr. 6)
Problem Set 9 (due Wednesday Apr. 14)
Problem Set 10 (due Tuesday Apr. 20)
Problem Set 11 (due Tuesday Apr. 27)
Problem Set 12 (due Tuesday May 4)
Grader: Xiaojiang Cheng
Posted here as I write them, these will serve as our primary text, supplemented by the Jacobson book (see below).
I. Galois Theory
A. Field extensionsII. Linear algebraic groups
A. Bilinear formsIII. Representation theory
A. Semisimple modules and ringsIV. Commutative rings
A. LocalizationLink to Algebra I course notes.
Nathan Jacobson, Basic Algebra I (2nd Ed.); Dover
is the recommended textbook. We will in large part follow it and use exercises from it for the treatment of Galois theory and bilinear forms (but not for the later parts of the course).
There are many other excellent standard texts, including
D.J.H. Garling, A Course in Galois Theory; Cambridge Univ. Press,
Thomas Hungerford, Algebra; Springer-Verlag,
Serge Lang, Algebra; Springer-Verlag,
Joseph Rotman, Advanced Modern Algebra; Prentice-Hall.
Your final grade for the semester is determined as follows: HW 40%, midterm 20%, final exam 40%. I will drop the lowest two grades you receive on homework.
Homework and examination grades will be regularly updated on Canvas.
Grades are typically curved in a course like this but will never be less than the following scale:
If you are a graduate student, a letter grade of B is required to pass; if you are an undergraduate taking this class Pass/Fail, you must earn a C- to pass.
The Washington University academic integrity policies are here. All work submitted under your name is expected to be your own; please make sure to document any ideas that come from another source.