18.785 - Number Theory I

Lecturer: Andrew Sutherland

Office: 2-341B

Email: drew@math.mit.edu

Time and Place: MW 12:30-2:00, 2-132

Office Hours: M 2:00-3:00 (in-person), T 2:30-3:30 (virtual)

Grader: Gefei Dang


This is the first semester of a graduate course in number theory; see the syllabus for details. The lecture notes from 2019 can be found here and on OCW. We will follow a similar path, but there will be some minor changes.

Format: Lectures are in-person (2-132). Office hours are in-person (2-341B) on Mondays but online on Tuesdays.

Corequisite: 18.705 (Commutative Algebra).


09-15-21    Problem 3 on Problem Set 1 has been updated to include the assumption that the given prime ideal of OK does not contain the integer 2d (this is implied by the previous assumption it does not divide (2d), since OK is a Dedekind domain, but we haven't proved OK is a Dedekind domain yet, this will happen next week). I won't penalize anyone who assumes OK is a Dedekind domain for the purpose of solving this problem.

09-15-21    Problem Set 2 has been posted and is due by Sep 23 (by midnight). Submit solutions via Gradescope.

09-15-21    The notes for Lecture 3 have been posted.

09-14-21    Tuesday office hours will take place 2:30-3:30 (note the time change!) over Zoom. The Zoom link is available on Canvas.

09-13-21    There was a question in office hours about the signs in problem 4(e). The signs are correct as written; note that the product is over all a in A with 0<|a|<|b|.

09-13-21    The notes for Lecture 2 have been posted.

09-08-21    The notes for Lecture 1 have been posted. Those who want a quick intro/refresher to commutative algebra might find Milne's primer useful (in addition to the book Commutative ring theory I mentioned in class).

09-08-21    Problem Set 1 has been posted and is due by Sep 16 (by midnight). Submit solutions via Gradescope.

08-30-21    18.785 is now listed on pset partners.