# Directed Reading Program (prior semesters)

#### DRP Activities - Fall 2022

- 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 )

#### DRP Activities - Spring 2022

- 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 )

#### DRP - Fall 2021

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 )

#### Organizers (2021-2022)

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

- 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

#### DRP Activities - Fall 2020

- 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 *)

The Fall 2020 participants and their projects were:

- 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

#### Organizers (2020-2021)

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

- 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

#### DRP Activities - Fall 2019

- 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

#### Organizers (2019-2020)

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

- 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

#### DRP Activities - Fall 2018

- 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"