Math 594: Algebra II

Professor: David E Speyer

Winter 2022

Gauss's construction of the regular heptadecagon

Course meets: Tuesday and Thursday, 10-11:30 AM, 4088 East Hall.

Office hours: 2844 East Hall, Tuesdays 2-5 PM, Thursdays 12-3 PM. At the moment I am planning to have all office hours open to all my courses; if this is a problem, we'll adjust. If you'd like to meet on Zoom, send an e-mail and I'll be glad to log on.

Professor: David E Speyer, 2844 East Hall,

Course homepage:

Level: Graduate students and advanced undergraduates.

Prerequisites: Prior exposure to the definitions of groups, rings, modules and fields, at the level of 593 or a similar course. Abstract linear algebra over an arbitrary field.

Structure of class: This class will be taught in an IBL style, meaning that a large portion of the class time will be spent solving problems that develop the theory we are studying. Students are expected to attend class and participate in solving problems, as the class will not work otherwise. Some portion of your grade will be allocated for participation in class work.

Climate: Each of you deserves to learn in an environment where you feel safe and respected.

I want our classroom, the collaborations between my students outside class, and our department as a whole, to be an environment where students feel able to share their ideas, including those which are imperfectly formed, and where we will respectfully help each other develop our understanding. I want to provide a space where questions are very welcome, especially on basic points.

Please ask all questions you have; remember that every question you have is likely a question that many share. Please share your insights and suggestions, partial or complete. Please treat your peers questions, comments and ideas with respect.

Homework: I will assign weekly problem sets, due on Tuesday nights at midnight (through Gradescope).

QR practice: Most students in this class are preparing to take the QR exam in algebra. This course will cover the vast bulk of the material from the Algebra 1 syllabus (and more).

Each week, I will assign a timed quiz on Gradescope consisting of two QR questions, on topics related to the current class material, to be done within a one hour period. See below for quiz policies.

Grading: A numerical score will be computed as follows: These numerical scores will be converted into letter grades

Weekly assignments

The intermediate fields of a dihedral extension

Homework PoliciesYou are welcome to work together with your classmates provided (1) you list all people and sources who aided you, or whom you aided and (2) you write-up the solutions independently, in your own language. If you seek help from mathematicians/math students outside the course, you should be seeking general advice, not specific solutions, and must disclose this help. I am, of course, glad to provide help!

I do not intend for you to need to consult other sources, printed or online. If you do consult such, you should be looking for better/other expositions of the material, not solutions to specific problems. Math problems are often called "exercises"; note that you cannot get stronger by watching someone else exercise!

You MAY NOT post homework problems to internet fora seeking solutions. Although I know of cases where such fora are valuable, and I participate in some, I feel that they have a major tendency to be too explicit in their help. You may post questions asking for clarifications and alternate perspectives on concepts and results we have covered.

Quiz policies Just as on the QR exams, please schedule a single uninterrupted time period to take this quiz and please complete the quiz without aid of any other resources, including written notes, internet references or other people.

I hope and believe that this practice will be useful beyond the QR exam. I think that the ability to solve problems which take 5-20 minutes is what unlocks the ability to solve problems that take months or years. I should say that this is something where different mathematicians experience varies wildly: I have found my ability to prove and disprove minor claims quickly has been extremely helpful in letting me explore difficult areas without getting lost; other mathematicians whom I greatly respect disagree. I hope that giving you some practice in this skill will be at least of some help.

I also encourage students to attempt other past QR exams. I am glad to discuss problems on these exams with you.

Problem Sets

Problem sets will generally be due at midnight (or, more precisely, 11:59 PM) between Tuesday and Wednesday.

The first practice QR quiz will be due January 25.

Class schedule and worksheets

These worksheets are written by David E Speyer and released under a Creative Commons By-NC-SA 4.0 International License. Here are all the worksheets in a single file.

Below are the worksheets which we have used so far, and the worksheets which I anticipate using in the next few days. Feel free to look ahead at future worksheets before class. I do not promise to follow this schedule, but it is my best estimate.