Directed Reading Program (prior semesters)

• Kick-off event (January 21 at 5:00 [grad students] and 5:30 [undergrad students] in Blocker 169)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Tuesday, April 8 at 5:30 pm in Blocker 628)
• (Optional) Practice presentations (Tuesday and Wednesday, April 15-16 at 5:00)
• Final presentations by undergraduate participants, DAY ONE (Wednesday, April 23 at 5:00 pm in Blocker 624 and 628)
• Final presentations by undergraduate participants, DAY TWO (Thursday, April 24 at 5:00 pm in Blocker 624 and 628)

• Stephen Berg - The Fixed Point Proportion for d Regular Trees (mentor: Santiago Radi)
• Vainavi Chilukuri - Neural Network Applications to Finance (mentor: Ben Warren)
• Aires Cuatle-Gonzalez - A Proof of the Prime Number Theorem (mentor: Yongming Li)
• Marvin Fung - Motivation for Elliptic Curves (mentor: Somak Dutta)
• Cory Greger - The Probabilistic Method (mentor: Deven Gill)
• Joshua Im - The Quadratic Excess Theorem (mentor: William Taylor)
• Ryan Jung - Continuous Functional Calculus on C*-algebras (mentor: Ajay Kumar Karri)
• Prathik Kannan - An introduction to elliptic functions and modular forms (mentor: Erik Davis)
• Smriti Kolar - Mathematical Methods in Economic Modelling: Applications of Static, Comparative, and Dynamic Analysis (mentor: Nazif Muhammed Nafi)
• Kevin Lei - Introduction to Category Theory (mentor: Aatmun Baxi)
• Athasi Madabhushi - Graph Algorithms and the Four Color Theorem (mentor: Seth Hoisington)
• Anna Mastylo and Ryan Lee - Unraveling Randomness: The Mathematics of Stochastic Calculus and Brownian Motion (mentor: Chris Pecaroro)
• Kimberly Maxwell - Introduction to Game Theory (mentor: Niklas Day)
• Major McIlvain - Basic Algebra and Facts About Curves (mentor: Ruzho Sagayaraj)
• Luca Nealon - Distribution Theory (mentor: Bingheng (Benjamin) Yang)
• Isabella (Izzi) Oaks - Differential Geometry and Applications to Physics (mentor: Jose Lopez)
• John Scott - Finite Difference Methods in solving the Heat Equation (mentor: Vaso Micheas)
• Shreya Shankar - Counting Isomers of Molecules using Group Theory (mentor: Derek Wu)
• Aaryan Sharma - Smooth manifolds and the connection between de Rham cohomology and singular cohomology. (mentor: Kai Huang)
• Nick Vantine - The Isoperimetric Inequality (mentor: Siddharth Sabharwal)
• Karthik Venkat - Classifying hyperbolic isometries and realising surfaces as quotients of R2 or H2 (mentor: Viraj Joshi)

• Kick-off event (August 20 at 5:15 [grad students] and 5:30 [undergrad students] in Blocker 302)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Wednesday, October 30 at 5:15pm in Blocker 166)
• Final presentations by undergraduate participants, DAY ONE (Wednesday, November 20 at 5:30 pm)
• Final presentations by undergraduate participants, DAY TWO (Thursday, November 21 at 5:00)

• Adam Authur - Markov Chains and the Gambler’s Ruin (mentor: Aditya Nambiar)
• Craig Cabrera - Introduction to the Calculus of Variations (mentor: David Pecoraro)
• Gabriel Gomez - Introduction to Functional Calculus (mentor: Junchen Zhao)
• Rafael Gomez - Bounding The Graphic Metric Traveling Salesman Problem (mentor: Youngho Yoo)
• Max Kurbanov - p-adic numbers and their applications (mentor: Santiago Radi)
• Saketh Marrapu - Graph Theory and Some Gnarly Applications Within Mathematics (mentor: Garrett Tresch)
• Connor McGuire - Mathematical Advances in Portfolio Optimization: Integrating Convex and Stochastic Programming for Enhanced Asset Allocation (mentor: Youngho Yoo)
• Colin Neaville - Numerical methods for PDEs (mentor: Seth Hoisington)
• Anish Sant - Introduction to Spectral Theory and the Spectral Measure (mentor: Ajay Kumar)

• Kick-off event (August 31 at 5:15 [grad students] and 5:30 [undergrad students] in Blocker 306)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Tuesday, April 2 at 5:00pm in Blocker 628)
• Final presentations by undergraduate participants, DAY ONE (Monday, April 29 at 5:00 pm)
• Final presentations by undergraduate participants, DAY TWO (Tuesday, April 30 at 5:00 

• Emily Baker - Algebraic Geometry (mentor: Erik Davis)
• Anders Bahrami - An Introduction to Qualitative Theory of ODEs (mentor: Alexandros Kazantzidis)
• Lucian Chauvin - Turing Machines and Undecidability (mentor: Ben Warren)
• William Echols - Clifford Algebra for Graph Theory (mentor: Alex Weygandt)
• Tom Haque - Monte Carlo Integration (mentor: Jose Lopez Garcia)
• Preston Kouyoumdjian - Density of primes dividing an infinite sequence (mentor: Santiago Radi)
• Arthur Mayo III - Topological reduction in chemical reaction networks (mentor: Jordy Lopez Garcia)
• Rock Mundada - Understanding Random Walks in Finance (mentor: Angelique Morvant)
• Ananya Nambiar - The Mathematical Framework of Relativity (mentor: Seth Hoisington)
• Lance Preston and Christofer Hardcastle - Chemical Reaction Networks and the Deficiency Zero Theorem (mentor: Wyatt Smith)
• Mckinley Xie - A Gentle Introduction to Algebraic Geometry (mentor: Jing Ye)

• Kick-off event (August 31 at 5:15 [grad students] and 5:30 [undergrad students] in Blocker 306)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Tuesday, November 7 at 5:00pm in Blocker 302)
• Final presentations by undergraduate participants, DAY ONE (Wednesday, November 29 at 4:30 pm in Blocker 624)
• Final presentations by undergraduate participants, DAY TWO (Thursday, November 30 at 5:00 pm in Blocker 624)

• - Victoria Abell (mentor: Luis Aceves )
• - Kamilia D. Aguilar (mentor: Tanuj Gupta )
• - Luke Brenner (mentor: Thomas Winckelman )
• - David Cates (mentor: Tushar Pandey )
• - Samuel Hernandez (mentor: Seth Gerberding )
• - Mikayla Hill (mentor: Agniva Dasgupta )
• - Catherine Huang (mentor: Jordan Hoffart )
• - Jennifer Mackenzie (mentor: Yung-Chieh Hsieh )
• - Noah Maiorino and Jackson Schwedler (mentor: Chris Pecoraro )
• - Joshua Rojas (mentor: Erik Davis )
• - Abhinav Sairam (mentor: Erik Davis )
• - Landon Ueslmann (mentor: Seth Hoisington )

• Kick-off event (January 19 at 5:15 [undergrads] and 5:30 [grad students] in Blocker 306)
• Welcome Event (Wednesday, February 15 at 5:00 pm in Blocker 302)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Tuesday, March 28 at 5:30pm in Blocker 302)
• Final presentations by undergraduate participants, DAY ONE (Tuesday, April 25 at 5:10 pm in Blocker 302)
• Final presentations by undergraduate participants, DAY TWO (Thursday, April 27 at 5:30 pm in Blocker 628)

• - Andrew Hoyt (mentor: Derek Wu )
• - Oli Oney (mentor: Erik Davis )
• - Sydney Mason (mentor: Jose Lopez )
• - Samantha Brink (mentor: Tim Bates )
• - Christian Flewelling (mentor: Bennett Clayton )
• - Celeste Mills (mentor: Xin Su )
• - Adam Garsha (mentor: Kanan Gupta )

• Kick-off event (August 30 at 5:30 pm)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Wednesday, October 19 at 5:30 pm in Blocker 150)
• Final presentations by undergraduate participants (November 29 and 30)

• Jason Hirsch - The Discrete Fourier Transform and its Applications (mentor: Ryan Budahazy )
• Christian Lambert - Gauss-Bonnet Theorem for Hyperbolic Triangles (mentor: Siddharth Sabharwal )
• Ethan Luo - Approximating Graph Algorithms Using Metric Embeddings (mentor: Garrett Tresch )
• Qingrui Meng - Conservation Laws with Finite Difference Methods (mentor: Bennett Clayton )
• Jade Wirz - Invariants of Knots and their N-Parallel Cabling (mentor: Tushar Pandey )
• Daniel Duong and Jacinto Rodriguez Shahin - Introduction to Virus Dynamics and Immunity (mentor: Mansi Bezbaruah )
• Mason Honeycutt and Matthew Harvey - Modelling Chemotaxis With PDEs (mentors: Chunyang Liao and Madison Sheridan )
• Carl Leonardh Schmidt and Cindy Zhuang - Mathematical Modeling for Population Dynamics in Biological Systems (mentor: Seth Gerberding )

• Kick-off event (Jan. 25 at 5:15 pm [mentors] and 5:30 pm [mentees] - at the benches outside of Blocker, second floor)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Thurs. Feb. 17 [5:00 pm] - Blocker 117)
• Final presentations by undergraduate participants (Tues. Apr. 26 [around 5:00 pm] and Wed. Apr. 27 [around 5:00 pm] - Blocker 117 [and a nearby classroom]) 

• Timothy Bates - Computational Topology (mentor: Tushar Pandey )
• Oliver Carver - Derivative Pricing in Discrete Time: American and European Options (mentor: Yongming Li )
• Luke Duane-Tessier - Eigenvalue Interlacing on Quantum Graphs (mentor: Marshall King )
• Lindsey Goodwin - An Introduction to p-adic Numbers (mentor: Erik Davis )
• Wesley Halstead - Dots and Lines (mentor: Kanan Gupta )
• Daehee Han - Turing Machine and Halting Problem (mentor: Joshua Goldstein )
• Logan Knudsen - Group Actions and Minimal Homeomorphisms (mentor: Alex Weygandt )
• Sarah Malinowski - An Introduction to Knot Theory (mentor: Andrea Barton )
• Devon Maywald - An introduction to Potential Flow And Analytic Functions (mentor: Mansi Bezbaruah )
• Jack Molenhouse - Introduction to Complex Dynamics (mentor: - Tanuj Gupta )
• Savannah Pinner - Generating FUNctions (mentor: Agniva Dasgupta )
• Lauren Porter - The Deutsch-Jozsa Algorithm (mentor: Valentia Fragkiadaki )
• Johnathan Purser - Axiomatic Music Theory (mentor: Tushar Pandey )
• Inaara Tejani - Category Theory and the Yoneda Lemma (mentor: Aatmun Baxi )
• Dilan Trivedi - The Fourier Series with Applications (mentor: Derek Wu )
• Samuel Valle - Philosophy of Mathematics (mentor: Matthew Faust )
• Iker Vita - Selected Topics From Differential Topology (mentor: Jose Lopez )
• Aldus Verastegui - Time Complexity of Algorithms (mentor: Jordan Hoffart )
• Yahan Xu - Introduction to Machine Learning (mentor: Arpan Pal )

The Fall 2021 participants, topics, and mentors were:

• Steven Danen - Decomposition of Minkowski Sums (mentor: Elise Walker )
• Spencer Ellis - Anti-de Sitter Space (mentor: Priyanga Ganesan )
• Vishwam Khapre - Introduction to Knot Theory (mentor: Tanuj Gupta )
• Megan Novak - Introduction to the Analysis of Algorithms (mentor: Benjamin Warren )
• Massaro Ochoa (mentor: Tushar Pandey)
• Jesse Peterson - Using Algebraic Curves to Solve Problems in Number Theory (mentor: Erik Davis )
• Austin Pritchett (mentor: Josiah Owens )
• Jonah Robinson - Topological Crystals (mentor: Matthew Faust )
• Mitchell Sisk (mentor: Siddharth Sabharwal )
• Collin Stafford - Introduction to Graph Theory and its Applications Through Search Algorithms (mentor: Zhaobidan Feng )

The 2021-2022 DRP was organized by Jordy Lopez and Angelique Morvant, with faculty mentor Anne Shiu.

• Kick-off event (Jan. 21 at 5:00 pm [mentors] and 5:15 pm [mentees] - * online via Zoom *)
• A presentation on "How (not) to give a talk", plus a tutorial on Overleaf and Beamer (Thurs. Mar. 25 [5:00 pm] - * online via Zoom *)
• Final presentations by undergraduate participants (Tues. Apr. 20 [5:00 pm] and Thurs. Apr. 22 [5:00 pm] - * online via Zoom *)

• Tessora Stefan (mentor: Jordy Cheyem Lopez Garcia ) - Topological Proof of the Infinitude of Primes
• Christian De Los Santos (mentor: Alexander Ruys de Perez ) - Neural Codes and Max Intersection-Completeness
• Austin Pritchett (mentor: James O’Quinn ) - Becoming the King of Games with Mathematics
• Fang Shu (mentor: Tushar Pandey ) - Linear Algebra in Finance and Risk Management
• David Cruz (mentor: Erik Davis ) - Casinos and Games of Chance: Applications of Probability and Expected Value
• Wells Hero (mentor: Tanuj Gupta ) - Whitney Embedding Theorem
• Jackson West (mentor: Zhaobidan Feng ) - An Introduction to Combinatorial Reasoning

• Kick-off event (Aug. 25 at 4:45pm [mentors] and 5:00 [mentees] - * online via Zoom *)
• A presentation on "How (not) to give a talk" (Mon. Oct. 26 [5:00] - * online via Zoom *)
• Final presentations by undergraduate participants (Mon. Nov. 16 [5:00pm], Tues. Nov. 17 [5:45 pm], and Mon. Nov. 23 [6:15 pm] - * online via Zoom *)

• Alex Behne (mentor: Tolulope Oke)
• Alexis Foster (mentor: Jennifer Zhu) - Applications of Linear Algebra in Biomathematics
• Michael Grantham (mentor: James O’Quinn) - Chaotic Dynamical Systems
• Callie Lansing (mentor: Alexander Ruys de Perez) - Local Obstructions and Nonconvexity in Neural Codes
• Yeojoon Moon (mentor: Priyanga Ganesan) - Stability Analysis of Linear Systems
• Mark Olvera (mentor: John Weeks) - A brief overview of how graphs and groups can interact
• Nicole Peltier (mentor: Zhengye Zhou) - Fourier Analysis on Finite Groups
• Robert Todora (mentor: Mansi Bezbaruah) - Cryptography with Elliptic Curves
• Tanvi Vishwanath (mentor: Lauren Snider) - An Epidemiological Application of Percolation Theory
• Jackson West (mentor: Konrad Wrobel) - ZFC and the Continuum Hypothesis

The 2020-2021 DRP was organized by Kari Eifler, Angelique Morvant, and Pablo Sanchez Ocal, with faculty mentor Anne Shiu.

• Kick-off event (Jan. 21 at 5pm [mentors] and 5:30 [mentees] - Blocker 220)
• A presentation on "How (not) to give a talk" (Thursday, April 2 at 5pm - * online via Zoom *)
• Final presentations by undergraduate participants (April 20 and 23 and 27 at 5pm - * online via Zoom *)

• Soohee Bae (mentor: Mahmood Ettehad) - Data driven framework for dynamical system identification. This project resulted in the following manuscript submitted for publication: On Vertex Conditions In Elastic Beam Frames: Analysis on Compact Graphs
• Dillon Berry (mentor: Joshua Goldstein) - The Foundations of Probability
• Alexander Crabtree (mentor: Erik Davis) - An Introduction to Simple Continued Fractions
• Riley Decker (mentor: Zheng Kuang) - Groups Isomorphic to a Proper Subgroup
• Thomas Dexter (mentor: Petr Naryshkin) - Isometries of the Hyperbolic Plane
• Alicia Duran (mentor: Kelly Maluccio) - TBA
• Thomas Flowers (mentor: Matthew Faust) - Quantum Graphs
• William Frendreiss (mentor: Agniva Dasgupta) - A new ordering of the rational numbers
• Jaqueline Gonzalez (mentor: Priyanga Ganesan) - One- and two-dimensional flows
• Daniel Kimble (mentor: John Weeks) - Quantum Error Correcting Codes
• Logan Perry (mentor: Amudhan Krishnaswamy-Usha) - Markov Chains and Their Applications
• Sofia Pineda (mentor: Mansi Bezbaruah) - Solvability and Algorithms
• Neel Reddy Pochareddy (mentor: Tushar Pandey) - Convex Optimization: From theory to the Endless Applications
• Fengqiao Wang (mentor: Haoshen Li) - Compute Geodesic Using Heat Method
• Jackson West (mentor: Changningphaabi Namoijam) - Basics of P-adic Analysis
• [Anonymous student] (mentor: Byeongsu Yu) - Random Walks and Catalan Numbers

• Kick-off event (Sept. 3 at 5pm)
• A presentation on "How (not) to give a talk" (Wednesday, November 6 at 5 pm in Blocker 624)
• Final presentations by undergraduate participants (Monday, November 25 and Monday, December 2 at 5pm in Blocker 220) 

• William Frendreiss (mentor: Aleksandra Sobieska) - Triangulations and Properties
• Yun Lun (mentors: Priyanga Ganesan and Quyuan Lin) - Unsupervised Learning: K-Mean Clustering and Principle Component Analysis
• Patrick Maedgen (mentor: Changningphaabi Namoijam) - Elliptic Curve Cryptography
• Cristian Meraz (mentor: Konrad Wrobel) - Amenability and the Growth of Groups
• Olumayowa Olowomeye (mentor: Byeongsu Yu) - An introduction and application of Topological Data Analysis
• Isaac Ray (mentor: Pablo Sanchez Ocal) - Introduction to Group Theory
• Claudio Romero (mentor: Alex Weygandt) - Quasi-Isometries Through Milnor-Schwarz Lemma
• Braden Yosko (mentor: Weston Baines) - Introduction to the Theory of Computation

The 2019-2020 DRP was organized by Kari Eifler and Taylor Brysiewicz, with faculty mentor Anne Shiu.

• Kick-off event (Jan. 16 at 5pm)
• A presentation on "How (not) to give a talk" (Wed. Apr. 3 at 5pm in Blocker 605 AX)
• Final presentations by undergraduate participants (Wed. and Thurs. April 24 and 25 at 5pm in Blocker 220 [Wed.] and 628 [Thurs.])

• Maryam Almaskin (mentor: Ayo Adeniran) - Introduction to Graph Theory
• Melissa Cruz (mentor: Weston King) - Non-Crossing Partitions
• Jackson Haynes (mentor: Oguz Gezmis) - The Birch and Swinnerton-Dyer conjecture
• Trevor Hollister (mentor: Wei-Lun, Tsai) - The Zeroes of the Riemann Zeta Function
• Bailey Johnson (mentor: John Griffin) - Set theory Applications
• Brent Loving (mentor: Weston Baines) - Introduction to deep learning and neural networks
• Yifei Liang (mentor: Jianyan Ye) - An Introduction To Markov Chains
• Kate McCollough (mentor: Nida Obatake) - Topology and the Neural Code
• Nathan Medrano (mentor: Eric Tovar) - Hyperbolic Partial Differential Equations and Methods
• Jonathan Reed (mentor: Sheagan John) - Transcending Rationality: A Discussion of Transcendental Numbers in Mathematics
• Guadalupe Vallers (mentor: Pablo Sanchez) - Classical Theorems in Affine Space
• James Woodcock (mentor: Priyanga Ganesan) - Convergence of Series in Banach Spaces

• Kick-off event (Wed. Sept. 5 at 5pm in Blocker 605AX)
• A presentation on "How (not) to give a talk" (Wed. Nov. 7 at 5pm in Blocker 605 AX)
• Final presentations by undergraduate participants (Wed. Nov. 28 at 5pm in Blocker 220)

• William Brett Boyer (mentor: Quyuan Lin) - "Some mathematical theories to fluid dynamics"
• Chase Colbert (mentor: Wei-Lun Tsai) - "The distribution of prime numbers"
• Tyson Mailloux (mentor: Weston Baines) - "Survey of machine learning With applications"
• Kristopher Rakestraw (mentor: Konrad Wrobel) - "Percolation theory"

The 2018-2019 DRP was organized by Kari Eifler and Eric Tovar, with faculty mentor Anne Shiu.