# 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.

As of Winter 2024, the program is organized by Adrian Chitan, Mac Martin, and Nathan Pagliaroli with the support of Chris Kapulkin (faculty mentor) and Curtis Wilson (alumni support).

## 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.

## Winter 2024

The projects were:

- Chris Blackwell on
*Hilbert Space and Riesz’s Representation Theorem*(mentor: Michael Francis); - Joe Choi
*on Fractional Dimensions? I "Cantor" Believe it! A brief discussion on the Cantor Set, the Hausdorf dimension, and the Dimensionality of the Cantor Set*(mentor: Adrian Chitan); - Jayden D’Costa on
*Basics of Markov Chains*(mentor: Curtis Wilson); - Adam Gale on
*The Lambda Calculus: Building Turing Completeness*(mentor: Ben Connors); - Meagan James
*on Cofibrations, H-Spaces, and Triviality of the Fundamental Group’s Action*(mentor: Sebastian Gomez Rendon); - David Johnson on
*Enumeration of the wallpaper groups*(mentor: Aaron Huntley); - Spencer Kelly on
*Riemannian Geometry and the Hopf-Rinow Theorem*(mentor: Adrian Chitan); - Kate Juhee Kim on
*Topological Groups*(mentor: Mac Martin); - Manuel Romero on
*Introduction to Stability Theory*(mentor: Xiangyuan Liang); - Brayden Smith on
*Counting Surfaces with Random Matrix Theory*(mentor Nathan Pagliaroli); - Noah Vale on
*The Separation Theorems and Farkas’ Lemma*(mentor: Jason Palombaro);

## Fall 2023

The projects were:

- Christopher Blackwell on
*Bezout’s Theorem in the Plane*(mentor: Sayantan Roy Chowdhury); - Kiara Burcher on
*Deutch’s Algorithm and Quantum Supremacy*(mentor: Manimugdha Saikia); - Joe Choi on
*Azuma Inequality*(mentor: Adrian Chitan); - Chloe Clohosey on
*Category Theory and Universal Properties*(mentor: Aaron Noel Huntley); - Adam Gale on
*Parallelism and Multi-Threading: Optimizing mathematical computations*(mentor: Javaad Akhtar); - Adrien Grenier on
*The Construction of a Differentiable Monster*(mentor: Harshith Sairaj Alagandala); - Meagan James on
*Introduction to Homotopy Theory*(mentor: Sebastian Gomez Rendon); - David Johnson on
*Of Prime Importance: A Survey of Primality Tests*(mentor: Kumar Shukla); - Spencer Kelly on
*Smooth Manifolds and Frobenius’ Theorem*(mentor: Adrian Chitan); - Eleanor Khamneli on
*Statistical Modelling*(mentor: Nathan Harris Kershaw); - Abigail Kushnir on
*Genetic Hitchhiking: Evolution’s Carpool for DNA*(mentor: Zahra Shafiei); - Daxing Li on
*Natural Numbers and Formal Proofs*(mentor: Thomas Thorbjornsen); - Vera Lluka on
*Order Theory*(mentor: Sterling Ebel); - Laura Pulgarin on
*The infinity of infinities*(mentor: Alexander Zwart); - Brayden Smith on
*Smooth Manifolds as Locally Ringed Spaces*(mentor: Amos Elsworthy).

## Winter 2023

The projects were:

- Owen Abma on
*The Weierstrass Function*(mentor: Sinan Nurlu); - Chris Blackwell on
*The Irrational and Transcendent Nature of e and π*(mentor: Reid Ciolfi); - Chloe Clohosey on
*Isomorphisms in Group Theory*(mentor: Marios Velivasakis); - Dhruv Dhoum on
*Euclidean Geometry*(mentor: Mac Martin); - Sterling Ebel on
*An introduction to p-adic geometry*(mentor: Curtis Wilson); - Meagan James on
*Knot Theory and Seifert Surfaces*(mentor: Mahan Moazzeni); - Abigail Kushnir on
*Maximizing Cuts and Minimizing Deviation: Azuma’s Inequality Applied to the Max-Cut Problem*(mentor: Adrian Chitan).

## Fall 2022

- Murtaza Asrani on
*Algorithms in Computational Geometry — Convex Hull and Voronoi Diagrams*(mentor: Kumar Shukla); - Chris Blackwell on
*The Gamma Function: The Unique Extension of The Factorials*(mentor: Reid Ciolfi); - Chloe Clohosey on
*Group Theory and Symmetries of the Platonic Solids*(mentor: Marios Velivasakis); - Sterling Ebel on
*The Yoneda Lemma*(mentor: Chirantan Mukherjee); - Amos Elsworthy on
*The Geometry of Elliptic Curves*(mentor: Jarod Palubiski); - Brayden Smith on
*The Classification of Compact Connected Surfaces*(mentor: Adrian Chitan); - Richard Yeh on
*Continued Fractions*(mentor: Curtis Wilson).

## Winter 2022

- Jackson Edward Howe on
*Primality Testing — with Algorithm Implementation in Python*(mentor: Kumar Sannidhya Shukla); - Arjayn Piratheeparatnam on
*Image Classification using Convolutional Neural Networks*(mentor: Elham Kianiharchegani); - Chloe Madeleine Clohosey on
*Introducing Quantum Mechanics: How Symmetry Shapes Science*(mentor: Karthik Boyareddygari); - Matia Lee on
*Understanding Turing Machines*(mentor: Prajwal Dhondiram Udanshive).

## Fall 2021

The Directed Reading Program was held in-person during Fall 2021. The projects were:

- Clare Bedford on
*Diophantine Equations and Fermat's Last Theorem*(mentor: Marios Velivasakis); - Sina Babaei Zadeh on
*Differential Geometry of Curves and Surfaces*(mentor: Udit Ajit Mavinkurve); - Jing Xuan Chen on
*Sheaves in Complex Analysis*(mentor: Jarl G. Taxerås Flaten); - Tianhao Li on
*Image Classification*(mentor: Elham Kianiharchegani); - Steven Elliott Kunz on
*Lagrange's Four-Square Theorem*(mentor: Sergio Zapata Ceballos); - Joseph Li on
*General Relativity*(mentor: Nathan Joseph Pagliaroli); - Saranya Varakunan on
*Convex Geometry*(mentor: Mohabat Tarkeshian).

## Winter 2021

Due to the ongoing outbreak, in Winter 2021, the Directed Reading Program was offered entirely online.

The projects were:

- 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).