Math 593: Algebra I

Professor: David E Speyer

Fall 2019


The Euclidean algorithm (The Elements, Book VII)

Course meets: Monday, Wednesday and Friday, 2:00-3:00 PM, 4088 East Hall

Office hours Monday and Wednesday 9:30-11:30 AM, Thursday 2:00-4:00 PM, 2844 East Hall. I am also glad to make appointments to meet at other times. At the moment, I am making all my office hours open to both my classes (593 and 665); if this causes a problem, I may restructure.

Professor: David E Speyer, 2844 East Hall, speyer@umich.edu

Course homepage: http://www.math.lsa.umich.edu/~speyer/593

Level: Graduate students and advanced undergraduates.

Prerequisites: Prior exposure to the definitions of groups, rings, modules and fields. 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. I am indebted to Stephen DeBacker for writing problem sheets to make this possible when he taught the class in Fall 2018; I have extensively modified these problem sheets for the upcoming term. 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.

Homework: I will assign weekly problem sets, due on Fridays. These problem sets will be more substantive than a typical graduate course, but they will not be the longest ones ever assigned in Math 593.

Exams: I plan to give two in class exams, in mid-October and one in December. The problems on the exams will be very close to problems from the class worksheets and homework; the goal is to make sure that you are familiar with these problems and how to solve them on your own.

Grading: I will apportion the grade for this course as 50% problem sets and 20% from each of the two exams, with the remaining 10% for class participation. I will drop the two lowest problem set grades. The number thus obtained will be converted to a letter grade by a fairly generous curve.

Extensions: I will not provide homework extensions, but please do note that I will drop the lowest two homework grades.

Accomodations for a disability: If you think you need an accommodation for a disability, please let me know as soon as possible. In particular, a Verified Individualized Services and Accommodations (VISA) form must be provided to me at least two weeks prior to the need for an accommodation. The Services for Students with Disabilities (SSD) Office (G664 Haven Hall) issues VISA forms.

QR Exam: Many of the students in this course are preparing for the QR exam. This course covers the material from the Fall term of the QR syllabus (and more). Several problems from past QR exams will appear on problem sets; my current drafts have at least one every week. That said, this is not a QR study course, and I would encourage students preparing for the QR exam to take additional past QR exams on your own. I am glad to discuss questions about those exams, in office hours or elsewhere.

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.

Problem Sets

These problem sets are based in part on earlier problem sets by Stephen DeBacker, (c) 2018 UM Math department, under a Creative Commons By-NC-SA 4.0 International License. I release these under the same license.

Homework Policy: You are welcome to consult your class notes and textbook.

You 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.

Homework formatting: In order to make our grading process efficient, please write on only one side of the page and place your problems in order. If your solution to a problem is lengthy (more than 2/3 of a page say), please don't write solutions to other problems on that page.

Also, please mark the homework with your UMID number rather than your name.

Class worksheets

These worksheets are based in part on earlier problem sets by Stephen DeBacker, (c) 2018 UM Math department, under a Creative Commons By-NC-SA 4.0 International License. I release these under the same license.

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. Especially in the early days of class, I expect that I will have to make a lot of revisions, so don't count on me following the announced schedule.