18.784: Seminar in Number Theory, Spring 2026
Welcome to 18.784: Seminar in Number Theory! This course is a Communication Intensive in Mathematics (CI-M) for undergraduates at MIT. This semester, we will explore Diophantine approximation — an area of mathematics that studies how close rational numbers can be to irrational numbers. The subject has very classical origins in number theory and has intersections with a breadth of mathematical disciplines including:
Prerequisites for the course: Additional mathematical background in any of the following will be helpful but not required:
Students will learn how to communicate specific topics in Diophantine approximation through blackboard talks, a short expository term paper, and peer review. |
|
Course files (to be updated):
|
| Date | Speaker | Title | References |
|---|---|---|---|
| February 3 | Robin Zhang | Organizational meeting | |
Robin Zhang |
What is Diophantine approximation |
[Bak75]§1 [Bur00]§1 [Sch80]§1 |
|
| February 5 | All students | 3-minute introductory talks (favorite definition / example / theorem) | |
Communications workshop: preparing for presentations |
[Ruf2] |
||
| February 10 | — | — | — |
— |
— |
— |
|
| February 12 | — | — | — |
— |
— |
— |
|
| February 17 | President's Day Tuesday (no meeting) | President's Day Tuesday (no meeting) | |
| February 19 | — | — | — |
— |
— |
— |
|
| February 24 | — | — | — |
— |
— |
— |
|
| February 26 | — | — | — |
— |
— |
— |
|
| March 3 | — | — | — |
— |
— |
— |
|
| March 5 | — | — | — |
— |
— |
— |
|
| March 10 | — | — | — |
— |
— |
— |
|
| March 12 | — | — | — |
— |
— |
— |
|
| March 17 (Paper topic proposal due 2:30pm) |
— | — | — |
— |
— |
— |
|
| March 19 | — | — | — |
— |
— |
— |
|
| March 24 | Spring Break (no meeting) | Spring Break (no meeting) | |
| March 26 | Spring Break (no meeting) | Spring Break (no meeting) | |
| March 31 | — | — | — |
— |
— |
— |
|
| April 2 | — | — | — |
— |
— |
— |
|
| April 7 | — | — | — |
— |
— |
— |
|
| April 9 (Paper first draft due 2:30pm) |
— | — | — |
— |
— |
— |
|
| April 14 | — | — | — |
— |
— |
— |
|
| April 16 | — | — | — |
— |
— |
— |
|
| April 21 | — | — | — |
— |
— |
— |
|
| April 23 (Paper second draft due 2:30pm) |
— | — | — |
— |
— |
— |
|
| April 28 | — | — | — |
— |
— |
— |
|
| April 30 (Peer review reports due 2:30pm) |
— | — | — |
— |
— |
— |
|
| May 5 | — | — | — |
— |
— |
— |
|
| May 7 | — | — | — |
— |
— |
— |
|
| May 12 (Paper final draft due 2:30pm) |
All students | Course retrospective & celebration |
Books
Communications resources
|