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. |
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Course files (to be updated during the semester): Google forms:
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| Date | Speaker | Title | References |
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| February 3 (Background questionnaire due 2:30pm on February 4) |
Robin Zhang | Organizational meeting | |
Emily Robinson |
Communications workshop: preparing for presentations |
[Ruf19] |
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Robin Zhang |
What is Diophantine approximation |
[Bak75]§1 [Bur00]§1 [Sch80]§1 |
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| February 5 | All students | 3-minute introductory talks (favorite definition / example / theorem) | |
| February 10 | Ana Illanes Martinez De La Vega & Alicia Lin | What is a real number | [HW71]§4.1-4.3 [Rud76]§1 [Sch14]§1.1-1.3 [Sut15]§1.1-1.3 |
Cheuk Hei Chu & Paul Gutkovich |
What is a Farey sequence |
[Dum22]§6.2.1 [HW71]§3.1-3.8 |
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Reina Wang & Tony Wu |
What is modular arithmetic |
[HW71]§5.2-5.5, 6.1 [IR90]§3-4, 7 [Ros11]§4-5, 9 [Smi23]§II |
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| February 12 | Fiona Lee & Julianna Lian | What is the pigeonhole principle | [Bic20] [Goe15] |
Diego Andrés Rivera Orona & Alex Yang |
What is the Euclidean algorithm |
[Ros11]§3.4 |
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Yina Wang & Zachary West |
What is equidistribution |
[KN74]§1.1 |
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| February 17 | President's Day Tuesday (no meeting) | President's Day Tuesday (no meeting) | |
| February 19 | Benjamin Li & Adelmo Morrison Orozco | What is an algebraic integer | [Mur15] [Ogg10]§1 |
Tiago Oliveira Marques & Ghaura Mahabaduge |
What is a p-adic number |
[Con06] [Gou97]§1-3 |
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Emily Robinson |
Communications workshop: effective mathematics presentations |
[Ben01]§1 |
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| February 26 | — (pair) | — | — |
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| March 3 | — (pair) | — | — |
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| March 5 | — | — | — |
Emily Robinson |
Communications reading workshop: finding sources for research papers |
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| March 12 | — | — | — |
Emily Robinson |
Communications reading workshop: genre sources for research papers |
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| March 17 | — | — | — |
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| March 19 (Paper topic proposal due 2:30pm) |
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| March 24 | Spring Break (no meeting) | Spring Break (no meeting) | |
| March 26 | Spring Break (no meeting) | Spring Break (no meeting) | |
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| April 2 | — | — | — |
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| April 7 | — | — | — |
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| April 9 (Paper first draft due 2:30pm) |
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Emily Robinson |
Communications writing workshop: guiding text |
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| April 14 | — | — | — |
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| April 16 | — | — | — |
Emily Robinson |
Communications writing workshop: writing economy |
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| April 21 | — | — | — |
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| April 23 (Paper second draft due 2:30pm) |
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| April 28 | — | — | — |
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| April 30 (Peer review reports due 2:30pm) |
All students | Peer review on papers | |
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| May 7 | — | — | — |
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| May 12 (Paper final draft due 2:30pm) |
All students | Course retrospective & celebration |
Books
Notes
Communications resources
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