Directed Reading Program
Projects from Previous DRPs
Winter 2024
Fall 2023
Spring 2023
Fall 2022
Spring 2022
Fall 2021
Selected for Math Club Session:
Applying Black Scholes to the Real World. Student: Vishal Nayak. Mentor: April Nellis.
Proofs of the Isoperimetric Inequality. Student: Ashvin Pai. Mentor: Shelby Cox.
The Projective Plane and Bezout's Theorem. Student: Yanjun Chen. Mentor: Gary Hu.
Final Presentations (Abstract Booklet):
Applying Black Scholes to the Real World. Student: Vishal Nayak. Mentor: April Nellis.
Proofs of the Isoperimetric Inequality. Student: Ashvin Pai. Mentor: Shelby Cox.
Linear Programming and the Ellipsoid Method with Applications. Student: Wentao Xu. Mentor: Anthony Della Pella.
The Projective Plane and Bezout's Theorem. Student: Yanjun Chen. Mentor: Gary Hu.
Bezout's Theorem for Plane Curves. Student: Audy Lebovitz. Mentor: Carsten Sprunger.
DeRham Cohomology and the Poincare Lemma. Student: Neville Joshua Rajappa. Mentor: Reebhu Bhattacharyya.
Applications of the Crossing Number to Planar Geometry. Student: Henry Fleischmann. Mentor: Will Dana.
Winter 2021
Selected for Math Club Session:
An Introduction to Markov Chains. Student: Karl Goddard. Mentor: Ryan Kohl.
The Prime Number Theorem and the Riemann Zeta Function. Student: Neel Mougdal. Mentor: Patrick Kelley.
The Stoke's Theorem that Calc III Doesn't Teach You. Student: Xuyan Liu. Mentor: Reebhu Bhattacharyya.
Final Presentations (Abstract Booklet):
An Introduction to Markov Chains. Student: Karl Goddard. Mentor: Ryan Kohl.
Random Walks. Student: Renjie Shao. Mentor: Yiwang Chen.
The Prime Number Theorem and the Riemann Zeta Function. Student: Neel Mougdal. Mentor: Patrick Kelley.
Prime Numbers and the Riemann Hypothesis. Student: Rajas Gupta. Mentor: Alex Horawa.
Strategic Games and Nash Equilibria. Student: Yuhan Xiao. Mentor: April Nellis.
Random Matrix Theory and Applications to Portfolio Optimization. Student: Rohit Chakravarty. Mentor: Andrew McMillan.
Rational Points on Elliptic Curves. Student: Jeremy Flics. Mentor: Katja Vassilev.
Hilbert's 10th Problem. Student: Syed Akbari. Mentor: Will Dana.
The Stoke's Theorem that Calc III Doesn't Teach You. Student: Xuyan Liu. Mentor: Reebhu Bhattacharyya.
Knot Invariants. Student: Xun Wang. Mentor: Christopher Zhang.
The Hartman-Grobman Theorem: Approximating Nonlinear Dynamical Systems. Student: Horacio Moreno Montanes. Mentor: Saibal De.
Fall 2020
Selected for Math Club Session:
Data Analysis with Truncated SVD on the Eigenfaces. Student: Chang Wang. Mentor: Saibal De.
Isometries of the Hyperbolic Plane. Student: Cassandra Prokopowicz. Mentor: Christopher Zhang.
Mean-Field Games and their Social Applications. Student: Krista Hart. Mentor: April Nellis.
Final Presentations (Abstract Booklet):
Two Limit Theorems. Student: Yiwei Fu. Mentor: Yili Zhang.
Law Of Large Numbers. Student: Renjie Shao. Mentor: Yiwang Chen.
Symmetries of Symmetric Groups. Student: Matthew Wang. Mentor: Ilia Nekrasov.
Burnside’s Lemma: Using Group Theory to Count Distinct Objects. Student: Huixi Yao. Mentor: Oscar Gonzalez.
Yoneda Lemma and Some Applications. Student: Yingzi Yang. Mentor: Yunze Lu.
You Need a Lemma. Student: Faye Jackson. Mentor: Lukas Scheiwiller.
Finite Difference Methods for Boundary Value Problems. Student: Haijian Wu. Mentor: John Wakefield.
Data Analysis with Truncated SVD on the Eigenfaces. Student: Chang Wang. Mentor: Saibal De.
Demystifying Groups: The Essence of Representation Theory. Student: Antareeksh Deb. Mentor: Carsten Sprunger.
Isometries of the Hyperbolic Plane. Student: Cassandra Prokopowicz. Mentor: Christopher Zhang.
Frobenius Elements in Galois Extensions. Student: Zheng Yang. Mentor: Kannappan Sampath.
Random Walks on Electrical Networks. Student: Joshua Pickard. Mentor: Will Dana.
Mean-Field Games and their Social Applications. Student: Krista Hart. Mentor: April Nellis.
Spring/Summer 2020
Final Presentations (Abstract Booklet):
Trisecting an Angle. Student: Dianhui Ke. Mentor: Attilio Castano.
Introduction to Representations on a Finite Group. Student: Bohan Xu. Mentor: Swaraj Sridhar Pande.
The Coin-Exchange Problem of Frobenius. Student: Zachary Fewkes. Mentor: Rachel Webb.
The Hasse-Minkowski Theorem - Rational Points of a Conic Section. Student: Zijian Rong. Mentor: David Schwein.
The p-adic Numbers and their Applications for Finding Rational Solutions to Conic Equations. Student: Quinn Allchin. Mentor: Jason Liang.
Mahler Expansions for p-adic Functions. Student: Seth Greenfield. Mentor: Eamon Quinlan-Gallego.
Cauchy’s Theorem. Student: Chris Jiang. Mentor: Yueqiao Wu.
Perspectives on Riemann Surfaces: Translating Analysis to Algebra. Student: Vikram Mathew. Mentor: Ruian Chen.
Steiner Symmetrization and Geometric Inequalities. Student: Josh Messing. Mentor: Yonatan Shelah.
What are Manifolds? Student: Wendy Wang. Mentor: Zhan Jiang.
Introduction to Algebraic Geometry. Student: Ziyi Zhang. Mentor: Devlin Mallory.
The Fundamental Group of a Circle. Student: Jonah Weinbaum. Mentor: Karthik Ganapathy.
Introduction to Representation Theory of Finite Groups. Student: Lillian McPherson. Mentor: Kannappan Sampath.
Representing Symmetries with Matrices. Student: Jonah Nan. Mentor: Michael Mueller.
Smooth Manifolds and Lie Groups. Student: Joey Minnella. Mentor: Abigail Finlay.
Compressed Sensing and Non-Parametric Regression. Student: Elizabeth Martin. Mentor: Christiana Mavroyiakoumou.
Reducing Training Variances through Random Forest. Student: Lance Ying. Mentor: Saibal De.
Winter 2020
Note: The program was partially suspended on account of the COVID-19 pandemic.
Selected for Math Club Session (Abstract Booklet):
The Point at Infinity: What is the Degree of 1/z? Student: Faye Jackson. Mentor: Christopher Zhang.
Inequivalent Colorings and How to Count Them. Student: Zihong Yi. Mentor: David Schwein.
Primes of the Form x² + ny². Student: Yuqing Liu. Mentor: Aleksander Horawa.
Devil-Angel Game. Student: Xiaoqi Peng. Mentor: Will Dana.
Student Write-ups:
Representation Theory and Maschke's Theorem. Student: Wen Plotnick. Mentor: Jack Carlisle.
Fall 2019
Final Presentations (Abstract Booklet):
Cheating Fate: Constructing Globally Defined Smooth Maps on Real Manifolds. Student: Christian Capanelli. Mentor: Daniel Irvine.
Curvature, and How to Quantify It. Student: Arav Agarwal. Mentor: Carsten Peterson.
The Teichmueller Space of the Torus. Student: Yichen (Jason) Liu. Mentor: Mark Greenfield.
How Do Algebraic Curves Intersect?. Student: John (Jack) Haviland. Mentor: Aleksander Horawa.
The Zariski Topology. Student: Bencheng Li. Mentor: Jason Liang.
Representability of Group Functors. Student: Zhou Fang. Mentor: Kannappan Sampath.
An Introduction to Mapping Class Groups. Student: Justin Vorhees. Mentor: Christopher Zhang.
Topology of Surfaces. Student: Christopher Tait. Mentor: Jack Carlisle.
How to Turn 3-Dimensional Space into e-Dimensional Space. Student: Josh Messing. Mentor: Ruian Chen.
Introduction to Fourier Transformation and Applications in File Compression. Student: Adam DeHollander. Mentor: Ryan Kohl.
Solving a Boundary Value Problem Using Fourier Series. Student: Trevor Gravely. Mentor: Joseph Kraisler.
Solution Techniques for PDEs and Applications to Fluids. Student: Nasser Mohammed. Mentor: Christiana Mavroyiakoumou.
Graph Embeddings and the Heawood Theorem. Student: Ethan Cohen. Mentor: William Dana.
Central Limit Theorem for Length of Longest Increasing Subsequence. Student: Chen Shang. Mentor: Yuchen Liao.
Arithmetic Functions and Dirichlet Convolution. Student: Andrew Nguyen. Mentor: Angus Chung.
Primes of the Form p = x² + ny² and Euler’s "Convenient" Numbers. Student: Ethan Mook. Mentor: Andrew O’Desky.
Disecting and Trisecting Angles. Student: Avi Tachna-Fram. Mentor: Zhan Jiang.
An Accurate Representation of Linear Representation Theory. Student: Matthew Cunningham. Mentor: Hyung Kyu Jun.
Knots and Knot Invariants. Student: Hannah Moon. Mentor: Farrah Yhee.
Visualizing Complex Numbers and Functions. Student: Shuyang Zhang. Mentor: Michael Mueller.
Elliptic Functions: Meromorphic Functions on the Torus. Student: Zijian Rong. Mentor: David Schwein.
Uniform Convergence and Weierstrass Approximation Theorem. Student: Sai Zheng. Mentor: Sanal Shivaprasad.
Winter 2019
Elliptic Curves and Cryptography. Student: Robert Larese. Mentor: Aleksander Horawa.
Introduction to Probability. Student: Xueyi Zhu. Mentor: Karen Butt.
Visualizing Complex Analysis. Student: Cyril Cordor. Mentor: David Schwein.
Stability of the Predator-Prey System via Phase Portraits. Student: Ziyi Zhou. Mentor: Saibal De.
Fall 2018
Primes of the form x² + ny². Student: Pleum Piriyatamwong. Mentor: David Schwein.
Matrix Groups. Student: Noah McNeal. Mentor: Karen Butt.