# Directed Reading Program

## General information

The Directed Reading Program (DRP) pairs undergraduate students with graduate students/junior faculty to undertake independent study projects. It is intended to help motivated students explore topics in more depth than possible in a classroom setting.

Each project is for the duration of one academic semester, which is roughly thirteen weeks. Undergraduates can apply for DRP positions in the beginning of each term and those who are selected will be paired with mentors according to their mathematical interests and availability.

The projects are based around the self-paced reading of a particular book or article with substantial guidance from the mentor, with the specific topic arrived upon by discussion of common interests between the mentor and the mentee.

The program is organized by: Udit Mavinkurve and Sergio Zapata Ceballos, with support of Chris Kapulkin and Apurva Nakade.

## What's expected of a student?

A student is expected to:

- meet with their supervisor for 1 hour each week;
- work on the project for an agreed upon number of hours between these meetings (including: reading, problem solving, presentation preparation);
- give a final presentation towards the end of the term.

Students will not receive course credits for their projects, which on the bright side means: no exams, no grades.

## Benefits for a student

- Study an interesting topic without the stress of a usual course.
- Pursue a topic outside of the undergraduate curriculum.
- Develop independent study and oral communication skills.
- Connect with a graduate mentor and receive a good deal of personal attention.

The program is currently organized by: Jarl G. Taxerås Flaten, Mayecxiliana Cárdenas Montoya, and Udit Mavinkurve, with the support of Chris Kapulkin and MaCAW.

## Fall 2021

## Winter 2021

- Owen Abma on
*The Logistic Equation and Chaos*(mentor: Udit Mavinkurve); - Clare Bedford on
*Surreal Numbers*(mentor: Apurva Nakade); - Madhav Singhal on
*Building A Scheme in Haskell using Monads*(mentor: Jarl G. Taxerås Flaten); - Saranya Varakunan on
*Knot Theory*(mentor: Torin Carey); - Minghui Wang on
*Markov Chains*(mentor: Nathan Pagliaroli); - Alex Zwart on
*Hyperbolic Geometry*(mentor: Prakash Singh).

## Fall 2020

Due to the ongoing pandemic, in Fall 2020, the Directed Reading Program is offered entirely online. To enhance students' experience, a number of changes are introduced, including a Discord server, a shared Overleaf document, regular check-ins by the organizers, a midterm social event, and more. Some projects include more than one student.

The projects were:

- Amos Elsworthy on
*Mates in Bicategories*(mentor: James Leslie); - Jacob David Ender on
*Monadic Parsing in Haskell*(mentor: Jarl Taxerås); - Lewis Glabush and Wenzhe Wang on
*Topology from a Categorical Approach*(mentor: Mohabat Tarkeshian); - Alex Kazachek on
*Jordan-Brower Separation Theorem*(mentor: Prakash Singh); - Zi Kei Addison Kwong and Saranya Varakunan on
*Quadratic Reciprocity Law*(mentor: Sergio Zapata Ceballos); - Shuja Sayyid and Alex Zwart on
*A Brief Introduction to Infinity*(mentor: Mayecxiliana Cárdenas Montoya); - JoAnna Weil on
*Groebner Bases*(mentor: Avi Steiner); - Sophie Wu on
*Properties and Algebraic Invariants of Knots and Links*(mentor: Torin Carey); - Xinyue Zhang on
*Naive Lie Theory*(mentor: Jeremy Gamble).

The final presentations took place on December 5, 2020.

## Winter 2020

The projects were:

- Jacob Adams on
*Completion in mathematics*(mentor: Prakash Singh); - Daniel Carranza on
*Category theory*(mentor: Brandon Doherty); - Yeonjoon Choi on
*Random matrix theory*(mentor: Nathan Pagliaroli); - Wonsang Chong on
*Theory and practice of machine learning*(mentor: Luis Scoccola); - Julian Drazilov on
*Mordell's theorem*(mentor: Dinesh Valluri); - Jacob Fabe on
*Nielsen-Schreier theorem*(mentor: Apurva Nakade); - Alex Kazachek on
*Manifolds and smooth maps*(mentor: Udit Mavinkurve); - Boyuan Pang on
*Dynamical systems*(mentor: Babak Beheshti); - Jay Shah on
*Universal properties*(mentor: Jarl Taxerås); - Mahima Siali on
*Factoring integers*(mentor: Andrew Herring); - Christopher Vasiu on
*Existence of complete ordered field*(mentor: Arohan Paul); - Amar Venga on
*Gauss-Bonnet theorem*(mentor: Babak Beheshti).

Due to COVID-19 outbreak in Winter 2020, the organizers decided against having final presentations that term.

## Fall 2019

The projects were:

- Szymon Adamus on
*Matroid Theory*(mentor: Udit Mavinkurve); - Jonathan Chang on
*Category Theory*(mentor: James Leslie); - Yeonjoon Choi on
*Feynman Diagrams and Matrix Integrals*(mentor: Nathan Pagliaroli); - Jacob Fabe on
*Universal Properties and the Yoneda Lemma*(mentor: Luis Scoccola); - Charles Hau on
*Kirchhoff’s Matrix Tree Theorem*(mentor: Sergio Zapata); - Paul Norton on
*Category Theory*(mentor: César Martinez); - Boyuan Pang on
*Surface Topology*(mentor: Sergio Chaves); - Mahima Siali on
*Public Key Cryptography: Diffie-Hellman, RSA, and ElGamal*(mentor: Andrew Herring); - Amar Venga on
*Chevalley's Theorem*(mentor: Jeffrey Carlson); - Timothy Yau on
*Tensors and Manifolds*(mentor: Apurva Nakade).

The final presentations took place on November 30, 2019.