Abstract Algebra I, Fall 2026

Group theory, ring theory and modules, and universal mapping properties.

Course information

Credits: 3
Class meetings: MW 9:30-10:45am in ITE336

Instructor information

Professor: Rebecca Bellovin
E-mail: r dot m dot bellovin at the usual UConn domain
Office: Monteith 229
Office hours: TBA

Homework

Homework will generally be due every other week on Wednesdays and cover material from the previous two weeks' lectures. It should be prepared used LaTeX, which you can either install on your own computer, or use via the website Overleaf.

Textbook

We will use Dummit and Foote, Abstract Algebra, 3rd edition, for group theory and ring theory, and Axler's Linear Algebra Done Right, 4th edition, for linear algebra.

Assessment

Grades in this class will be based on the following:

Schedule

The following schedule is tentative and subject to change.
Week of Topic(s) Due date(s)
8/31 Groups, homomorphisms, quotients
Major examples
9/7 Isomorphism theorems
9/14 Group actions, orbits, stabilizers 9/16: Homework 1
9/21 Cauchy's theorem, Sylow theorems 9/21: No lecture
9/28 Semidirect products 9/30: Homework 2
10/5 Rings and ideals
10/12 Quotient rings
Isomorphism theorems		 10/14: Homework 3
10/19 Euclidean domains, PIDs, UFDs 10/19: Midterm
10/26 Euclidean domains, PIDs, UFDs (cont'd)
11/2 Localization
Rings of fractions		 11/2: Homework 4
11/9 Vector spaces
Linear maps
11/16 Dual spaces 11/16: Homework 5
11/23 Thanksgiving recess
11/30 br>Eigenvectors and eigenvalues
12/7 12/7: Homeowrk 6 Determinant and trace

University policies

Academic integrity

Please respect your work and the work of others. Cheating will be taken seriously. Examples of things that will be addressed include, but are not limited to, communicating with anyone not explicitly allowed during any quiz or exam, representing another person's work as your own (this includes copying or paraphrasing a solution from a friend, solution manual, tutor, or website), or bringing unauthorized materials to any quiz or exam. Consequences may include, but are not limited to, a score of zero on the assignment, quiz, or exam, or a grade of F in the course. To read UConn's full policy on Academic Integrity, visit \url{https://policy.uconn.edu/2023/07/11/academic-scholarly-and-professional-integrity-and-misconduct-aspim-policy-on/}.

Students with disabilities

The University of Connecticut is committed to protecting the rights of individuals with disabilities and assuring that the learning environment is accessible. If you anticipate or experience physical or academic barriers based on disability or pregnancy, please let me know immediately so that we can discuss options. Students who require accommodations should contact the Center for Students with Disabilities, Wilbur Cross Building Room 204, (860) 486-2020 or http://csd.uconn.edu.