MAT 534: Algebra I (Fall 2018)


About the course

Abstract algebra is the study of algebraic structures such as groups, rings, fields, or vector spaces. In the course, we will study groups, rings and modules, and basic linear algebra. You can find a more detailed list of topics on this page.


The textbook for the course is “Abstract Algebra” (3rd edition) by David S. Dummit and Richard M. Foote. Please see the official syllabus for additional information about the course, including university-wide policies.


The final exam for the course will be on December 20. We are also going to have two midterms (in class) and weekly homework assignments. Your grade will be determined based on the final exam (35%), the two midterms (20% each), and your homework (25%). The general policy is no make-up exams and no late homework, but there will be an extra homework assignment at the end of the semester to make up for any missed assignments.

Time and location

We meet on Tuesday and Thursday, 10:00–11:20 am, in room ESS 183 (in the Earth & Space Sciences building).

Office hours

My office hours are on Tuesday afternoon from 1:00pm–4:00pm.


Please read the corresponding sections before or after class.

Week Chapters Topics
1 I.1 and I.2 Groups, subgroups, examples
2 I.3 and some of I.4 Factor groups, isomorphism theorems, group actions
3 I.4 and some of I.5 Sylow theorems, applications, direct products, symmetric groups
4 Some of I.5 Automorphisms, An is simple, solvable groups
5 Some of I.6 Finitely generated abelian groups, Midterm 1
6 Appendix II Category theory
7 Some of II.7 Rings, ideals, examples
8 II.7 Integral domains, maximal/prime ideals, fractions fields
9 II.8 PIDs, unique factorization, UFDs
10 Some of II.9 Gauss lemma, Noetherian rings, Hilbert basis theorem
11 Some of II.10 Modules, submodules, examples
12 Modules over PIDs
13 Modules over PIDs, torsion modules, vector spaces
14 Modules over PIDs, linear transformations, Jordan canonical form
15 Multilinear algebra, determinant, inner products, normal operators

Homework assignments

There will be a written homework assignment almost every week. Please write up your solutions nicely, staple all the pages together, and hand them in during the following week, at the beginning of Thursday's class. Some of the problems will be graded ; the grader is Qianyu Chen. We are also going to discuss some of the problems in class on the following Tuesday; you are expected to participate in the discussion and, from time to time, volunteer to present a solution in front of class.

Week Assignment
1 Problem Set 1 (due Thursday, September 6)
2 Problem Set 2 (due Thursday, September 13)
3 Problem Set 3 (due Thursday, September 20)
4 Problem Set 4 (due Thursday, September 27)
6 Problem Set 5 (due Thursday, October 11)
8 Problem Set 6 (due Thursday, October 25)
9 Problem Set 7 (due Thursday, November 1)
10 Problem Set 8 (due Thursday, November 8)
12 Problem Set 9 (due Tuesday, November 20)
14 Problem Set 10 (due Thursday, December 6)
15 Problem Set 11 (due Thursday, December 20)