Syllabus

Course

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Math 6150: Commutative Algebra, Fall 2020

Syllabus

COVID-19:
This course will be taught remotely and synchronously. The Department of Mathematics has arranged that some of the remote courses are listed as hybrid in order to get a classroom assigned to the course. Having a classroom free at the time of the lecture will give students a quiet place on campus to participate in the class, if desired. The room assigned to our class is STAD 112, but the class will be held remotely and synchronously.

I intend to record the lecture and post the recordings. This will allow students to participate asynchronously, if desired, or to review the lecture afterwards. No student is obligated to reveal his/her face/background during these recordings.

If a student discloses to me that they have tested positive for COVID-19 or are having symptoms of COVID-19 or have had close contact with someone who has tested positive for COVID-19, then I am required to submit that information to the Medical Services Public Health Office of CU for contact tracing.

Course description:
Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals and Noetherian rings.

Prerequisites:
MATH 6140. Instructor consent required for undergraduates.

Text:
Introduction to commutative algebra. Addison-Wesley Publishing Co. 1969. by M. F. Atiyah and I. G. MacDonald.

The CU library has 3 hard copies of the 1969 printing. I have requested electronic access for students. (Warning: Amazon sells a 1994 reprinting for way-too-much, and 25 percent of Amazon reviewers complain about the quality of this printing. I haven't seen this version myself.)

Other books I will consult during the semester:

Commutative algebra with a view toward algebraic geometry. David Eisenbud. Graduate Texts in Mathematics, 150. Springer. 1995.

Commutative ring theory. Hideyuki Matsumura. Cambridge studies in Advanced Mathematics. (My copy is the ninth printing from 2006, but I think it is the same from 1989 onwards.)

Homework:
If you are enrolled for credit I will ask you to solve some problems. You will be asked to work on the problems in small groups of 2-3. Different groups will be assigned different problems, and groups will change with each assignment. You will typically have a week for your group to solve its assigned problem(s) and submit the solution(s). (This deadline is not strict. but I'll check in with you if I don't get solutions within a couple days of the due date.)

HW should be submitted electronically in some form of TeX. A LaTeX HW template (which you are not obligated to use) may be found here (.tex), (.pdf). If you are solving Problem M of HW assignment N, please submit the solution as a PDF file called "calgNpM.pdf" (which abbreviates "commutative algebra, assignment N, problem M"). At the top of the first page of the solution please include the names of all group members and the assignment number. After receiving your solution I will correspond with you about improvements and corrections, if I can think of any. This step in the process should take at most one week. You are not obligated to take any of my advice, but if one of my comments involves a correction, then you should correct that part in some way. For example, if I say "Here is a shorter way to do it", you don't have to change anything unless you want to. If I say "The first displayed equation is wrong. Here is how to fix it …", then you should fix the error, not necessarily along the lines of my suggestion. If you believe that one of my criticisms is incorrect, then you do not have to change your work, but you do have to explain why the criticism is incorrect.

New assignments will be posted regularly starting the second week. Solutions to old assignments will be posted when they are in final form. You should read your classmates' solutions.