Math 501 Course Webpage

Algebraic Structures I

Fall 2023, Duke University

General information | Course description | Lecture notes | Assignments | Homework schedule | Grading | Links | Fine print

General information

Lectures: Tuesday and Thursday, 13:25 – 14:40, Physics Building 119

Text: Abstract Algebra, by David S. Dummit and Richard M. Foote (third edition)

Secondary texts:

Contact information for the Instructor

Name: Professor Ezra Miller
Address: Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320
Office: Physics 209
Phone: (919) 660-2846
Course webpage: you're already looking at it... but it's
Sakai site: available to registered students via Duke NetID
Office hours: Tuesday 14:40 – 16:00 & Wednessday 14:00 – 15:10, in Physics 209

Course description

Course content:

Groups encapsulate the notion of symmetry. They constitute the simplest way to compose a single type of invertible operation, such as addition of numbers, multiplication of matrices with nonzero determinant, rotations of spheres, rigid motions of polygons and polyhedra, or permutations of sets of objects. The study of groups in this course includes decompositions, enumerations, quotients, and actions.

Rings combine two operations: addition and multiplication. In familiar situations, particularly the integers and univariate polynomials, interactions between the two operations lead to fundamental theorems concerning factorization into primes. What results is a main goal of the course: a single structure theorem that classifies all finite abelian groups and also produces Jordan canonical forms of linear transformations.

Prerequisites: Math 501 is a demanding course. Students are expected to have a firm grasp of linear algebra before beginning the course. In addition, it is expected that every student begin the course comfortable and proficient at writing rigorous mathematical arguments (proofs).

Lecture notes

All lectures in one PDF file

The lecture notes can and often are updated or corrected. If you think you have found an error, check that you have the latest version before sending a correction.


Check here two weeks before each homework is due, or one week before each exam is due, for the specifics of the assignments. If an assignment hasn't been posted, and you think it should have been, please do email me. Sometimes I encounter problems (such as, for example, the department's servers going down) while posting assignments; other times, I might simply have neglected to copy the assignment into the appropriate directory or to set the permissions properly. (I do try to check these things, of course, but sometimes web pages act differently for users inside and outside the Math department.)

Assignment Due Date Problems Reading
Homework #1 Sat.    9 September in PDF or LaTeX §1.1–1.6, §2.1, §2.3
Homework #2 Thu. 21 September in PDF or LaTeX §2.2, §2.4, §3.1–3.3, §5.1
Midterm 1 Thu. 28 September in PDF or LaTeX §1.7, §4.1, §3.5
Homework #3 Sat.  14 October in PDF or LaTeX §4.2–4.6, §5.3–5.5, §6.3
Homework #4 Sat.    4 November in PDF or LaTeX §7.1–7.4, §7.6
Midterm 2 Sat.  11 November in PDF or LaTeX §8.1–8.3, §7.5
Homework #5 Thu. 30 November in PDF or LaTeX §9.1–9.2, §10.1–10.3, §10.5, §12.1, §15.4
Cumulative problems Thu.   7 December, 23:59 in PDF or LaTeX

Grading scheme

Final course grades: Participation in class discussion and office hours can substantially enhance your homework score.


University academic links Departmental links

The fine print

I will do my best to keep this web page for Math 501 current, but this web page is not intended to be a substitute for attendance. Students are held responsible for all announcements and all course content delivered in class.
Many thanks are due to Jeremy Martin and Vic Reiner, who provided templates for this webpage many years ago.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Duke University.
Thu Dec 7 04:49:17 EST 2023

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