Math 221: Commutative algebra
E-mail: tayou@math.harvard.edu ,
Office: Science Center 238.
E-mail: yjiang@math.harvard.edu ,
Office: Science Center 426i.
Syllabus:
This course is an introduction to modern commutative algebra. We will cover primary decompositions in Noetherian rings, localization, integral extensions, Nullstellensatz, Noether normalization, and dimension theory. Other topics may include Zariski topology, completion, regularity, flatness, smoothness, and Dedekind rings.
Recommended books:
The first part of the class will follow the book of Atiyah-Macdonald, "Commutative algebra". We will also use the book of David Eisenbud, "Commutative algebra with a view towards algebraic geometry". A more advanced reading for this class, which we will occasionally refer to, is Hideyuki Matsumura's book, "Commutative algebra".
Prerequisites:
Math 122-123 (Algebra I-II) or equivalent.
Grading:
Weekly homework will count for at least 80% of the final grade. No late homework will be accepted (except under special circumstances) and the lowest score will be dropped. Collaborative work on homework is accepted but you must write your own solution as well as the names of the collaborators. There will be a final project, which together with participation will count for 20% of the grade.
Schedule:
- Meeting times: Tuesday-Thursday 09:00 AM-10:15 AM.
- Room: Science center 221.
- First meeting: Thursday, September 2, 2021.
- Office hours: Wednesday 1-2:30 PM Science Center 238.