The final exam will take place on December 8, 2022 from 9:00 AM - 11:30 AM in LC 315 (the usual classroom). No notes, calculators, or other aids are permitted.

The final exam is cumulative. You are expected to know all of the material from the midterms as well as the new material on rings. In particular, you should be familiar with the following material from Dummit and Foote:

• §7.1-7.6
• §8.1-8.3
• §9.1-9.5

As in the midterms, the primary goal of formal exams is “practice” for the qualifying exam, so the questions will have a similar flavor as qualifying exam questions. If you are comfortable with most of the problems from the relevant sections of Dummit and Foote, then you should be well prepared.

The tenth assignment is now available and is due on Thursday, December 1.

The ninth assignment is now available and is due on Thursday, November 17.

The eighth assignment is now available and is due on Thursday, November 10.

The seventh assignment is now available and is due on Thursday, November 3.

Midterm 2 will take place in class on October 27, 2022. No notes, calculators, or other aids are permitted.

Material from linear algebra may appear, but the focus is on group theory. You should be familiar with the following material from Dummit and Foote:

• §0.1-0.3
• §1.1-1.7
• §2.1-2.7
• §3.1-3.5
• §4.1-4.5
• §5.1-5.5

Notice that §4.6 is not included. It is important to know that \(A_n\) is simple for \(n \ge 5\), but not as important to be intimately familiar with the proof.

Despite not being “on” the exam, I strongly recommend you read §6.2. Here the various theorems you have learned are used to study finite groups of “medium” order. The exercises in this chaper are exactly the type of problems that show up on qualifying exams (albeit the exam problems will typically not be quite as challenging). If you can master this chapter, you will be overprepared for the midterm.

As in the first midterm, the primary goal of formal exams is “practice” for the qualifying exam, so the questions will have a similar flavor as qualifying exam questions. If you are comfortable with most of the problems from the relevant sections of Dummit and Foote, then you should be well prepared.

The sixth assignment is now available and is due on Thursday, October 20.

The fifth assignment is now available and is due on Thursday, October 6.

The fourth assignment is now available and is due on Thursday, September 29.

Midterm 1 will take place in class on September 22, 2022. No notes, calculators, or other aids are permitted.

The material covered is as follows. For linear algebra:

• vector spaces, linear independence, bases, subspaces, direct sum, direct product
• linear transformations, representations as matrices, change of bases
• dual spaces, dual bases
• endomorphism algebras, similarity, determinants, minimal and characteristic polynomials
• eigenvectors, eigenvalues, diagonalization, Jordan canonical forms

For group theory, be familiar with the material from §0.1-0.3, §1.1-1.7, §2.1-2.5, §3.1 of Dummit and Foote.

Notice that bilinear forms and inner product spaces will not be on the exam. Additionally, we will revisit the Jordan canonical form when we discuss modules for PIDs; currently they are a bit of a “black box” so I will not ask deep theoretical questions about the JCF. (We may revisit bilinear forms and inner product spaces in 702 from the perspective of multilinear algebra in 702 if time permits.)

The primary goal of formal exams is “practice” for the qualifying exam, so the questions will have a similar flavor as qualifying exam questions. If you are comfortable with most of the problems from the relevant sections of Dummit and Foote, then you should be well prepared.

This week only (September 12-16) my office hours will be Tuesday 12:00-3:00, while Wednesday’s office hours will be canceled. As usual, my students from graduate classes are welcome to simply drop by my office at any time (although no guarantees I won’t be busy). I can also make appointments if the scheduled hours don’t work for some reason.

The third assignment is now available and is due on Thursday, September 15.

The second assignment is now available and is due on Thursday, September 8.

The first assignment is now available and is due on Friday, September 2.

This website will be the main source of information for the course outside of lecture. Announcements for the course will be posted on the website here. You can also find the course syllabus, lecture schedule, and additional resources. As the course progresses, you can check your grades on Blackboard

Unfortunately, LeConte college is still closed due to delays in renovation.  This means that we will be meeting online until the building is ready.  We will be meeting virtually via Microsoft Teams until then. Please send the instructor an email if you did not receive a link.