Topics in Diophantine Approximation

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:

  • Algebraic geometry
  • Algebraic number theory
  • Analytic number theory
  • Complex analysis
  • p-adic analysis
  • Dynamical systems
  • Game theory

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):
Google forms (to be updated):

The seminar meets in Room 2-151 from 2:30pm—4:00pm (ET) on Tuesdays and Thursdays.


To contact me, please email me or message me in the course Slack.
To contact our communications instructor, TBD, you can email them at TBD.


Course schedule

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