Sample Project Ideas:
- Berkeley’s DRP Project Ideas list
- UNC’s Project Ideas (click on “Directed Reading Program”)
The information we provide at the DRP mentor orientation also has some specific project ideas for students who are relatively new to mathematics.
Past Projects
Spring 2026
- Chaos, Numerical Orbits, and Shadowing Lemmas
Paper: “Numerical Orbits of Chaotic Processes Represent True Orbits” by Hammel, Yorke, and Grebogi
Alan Ye, Mentor: Zach Turner - Measure-Theoretic Probability and Objective Bayesian Priors
Paper: “An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces” by Villa and Walker
Shuyi Jiang, Mentor: Alina Zhu - Learning the Geometry of Data
Paper: “Diffusion Maps” by Coifman and Lafon
Leo Yang, Mentor: Shrikant Chand - Designing a Light Rail Network for the Triangle: A Graph Theory Analysis
Paper: “Network Analysis of World Subway Systems Using Updated Graph Theory” by Derrible and Kennedy
Kate Rampel, Mentor: George Daccache - Computations with Finite State Markov Chains
Book: “Markov Chains and Mixing Times, second edition” by Levin and Peres
Ezechi Anaemereibe, Mentor: Bryan Castillo
Fall 2025
- Spin Geometry and the Positive Mass Theorem From General Relativity
Paper: “On Witten’s Proof of the Positive Energy Theorem” by Parker and Taubes
Jack Qian, Mentor: David Schmidt - Introduction to Stochastic Differential Equations
Book: “Elementary Stochastic Calculus with Finance in View” by Mikosch
Amy Chen, Mentor: Scott McIntyre
Spring 2025
- Applying the Metropolis Hastings Algorithm toward Decryption
Book: “Markov Chains and Mixing Times, second edition” by Levin and Peres
Dhruv Trivedi and Jocelyn Wang, Mentor: Scott McIntyre - Applications of Category Theory to Computer Science
Book: “Categories, Types, and Structures” by Asperti and Longo
Nicholas Popescu, Mentor: Arjun Nigam
Fall 2024
- An Introduction to Category Theory
Book: “Algebra: Chapter Zero” by Aluffi
Patton Galloway, Mentor: Arjun Nigam
Spring 2024
- An Introduction to the Weyl Algebra and the Dixmier Conjecture
Book: “A Primer of Algebraic D-Modules” by Coutinho
Ella Allen, Mentor: Fernando Villegas Negrete - A Beginner’s Guide to Not-So-Beginner Mathematics
Book: “A Readable Introduction to Real Mathematics” by Rosenthal, Rosenthal, and Rosenthal
Catherine Murphy, Mentor: Rena Chu
