Abstract Algebra I, Fall 2025

Course information

Course description: The fundamental topics of modern algebra including elementary number theory, groups, rings, polynomials and fields.
Credits: 3
Prerequisites: A grade of C or better in MATH 2710 or 2142Q. Recommended preparation: MATH 2144Q or 2210Q. Cannot be taken after passing MATH 3231.
Class meetings: TuTh 9:30-10:45am in Monteith 111

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 at the end of class on Thursdays and cover material from the previous week's lectures. You may either hand-write your solutions (legibly) or type them (if you choose to type your solutions, I strongly urge you to learn LaTeX; you can either install it on your computer or use Overleaf).

Homework:

Midterms

There will be two in-class midterms. Tentatively, one will be on Tuesday, September 30, and one will be on Thursday, October 30. The second midterm will primarily cover material from the previous 4–5 weeks but may include earlier material.

Textbook

We will follow Abstract Algebra: Theory and Applications by Judson. It is freely available from the linked website.

Other resources

The Book of Proof covers key background material from Math 2710, such as the language of sets, the principles of formal logic, and various techniques of proof. You may also find these video lectures helpful.

In addition, you may find these video lectures useful as a supplement to this course.

Assessment

Grades in this class will be based on the following:

Late work

You are responsible for any material that you miss. Any work that is due on a day that you are absent is still due and will be considered late if turned in at a later time. Late work will not be accepted or graded unless you contact me about it in advance.

If you need to reschedule a midterm, you must contact me before the exam, as soon as possible. Late requests will not be granted except under extenuating circumstances. If you have a conflict with the final exam, you must contact the Dean of Students Office; I am not permitted to reschedule final exams without their approval.

If you have an ongoing situation (such as a medical or family emergency) that results in missing a significant amount of class time or coursework, please get in touch with me as soon as possible so that special arrangements can be made. You can also contact the Dean of Students Office to request support.

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/}.

I encourage you to collaborate with your classmates, but work you hand in must be your own. Do not use LLMs (such as ChatGPT, Gemini, or Claude) to do your homework. You will not learn the course material without grappling with it yourself.

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.

Schedule

The following schedule is tentative and subject to change.
Week of Topic(s) Due date(s)
8/25 Administrivia
Introduction to groups
9/1 Cyclic groups 9/4: Homework 1
9/8 Permutation groups 9/11: Homework 2
9/15 Lagrange's theorem 9/18: Homework 3
9/22 Fermat and Euler's theorems 9/25: Homework 4
9/29 9/30: Midterm 1 10/2: No lecture
10/6 Isomorphisms 10/7 (Tuesday!): Homework 5
10/13 Normal subgroups 10/16: Homework 6
10/20 Homomorphisms 10/23: Homework 7
10/27 Matrix groups 10/30: Midterm 2
11/3 Finite abelian groups 11/4 (Tuesday!): Homework 8
11/10 Group actions 11/13: Homework 9
11/17 Sylow's theorems 11/20: Homework 10
11/24 Thanksgiving recess
12/1 Review 12/4: Homework 11
12/8 Finals