Abstract Linear Algebra, Fall 2026

Course information

Course description: Vector spaces and linear transformations over fields.
Credits: 3
Prerequisites: MATH 2210Q or 2144Q; a grade of C or better in MATH 2142Q or 2710.
Class meetings: TuTh 3:30-4:45pm in Monteith 320

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, February 24, and one will be on Tuesday, March 31. The second midterm will primarily cover material from the previous 4–5 weeks but may include earlier material.

Textbook

We will follow Linear Algebra Done Right by Sheldon Axler. You can buy it at the campus bookstore, and it is freely available at the author's website. We will also refer to Linear Algebra Done Wrong by Sergei Treil, available here, for some supplementary material.

Handouts

Other resources

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)
1/19 Vector spaces; LADR 1A-B
1/26 Finite-dimensional vector spaces; LADR 1C-2B
2/2 Finite-dimensional vector spaces; LADR 2B-C
2/9 Linear maps; LADR 3A-B
2/16 Linear maps; LADR 3C-D
2/23 Polynomials; LADR 4 Midterm 1
3/2 Invariant subspaces and eigenvalues; LADR 5A-B
3/9 Invariant subspaces and eigenvalues; LADR 5C-D
3/16 Determinants: LADW 3
3/23 Spring recess
3/30 Inner product spaces; LADR 6A Midterm 2
4/6 Inner product spaces; LADR 6A-B
4/13 Operations on inner product spaces; LADR 7
4/20 Generalized eigenspaces; LADR 8
4/27 TBD/Revew
5/4 Finals