Directed Reading Program - University of Maryland

Summer 2017

"Latent Dirichlet Allocation and Its Application in Grouping Facebook Users Using Labels Extracted from User-Generated Images" Xuejing Wang (mentor: Lijuan Cao)
"Continuity and Connectedness" Jon Bozzonetti (mentor: Steve Balady)
"The Compactness Theorem" Jared Ronning (mentor: Douglas Ulrich)
"Dimension and Measure Theory" Daniel Lay (mentor: Jenny Rustad)

Spring 2017

"Markov Chain Hitting Times" Luke Bender (mentor: Phil Wertheimer)
"Hamiltonian Mechanics and Symplectic Geometry" Alejandro Diaz (mentor: Matt Dellatorre)
"Mathematics of Classification Algorithms " Shravan Sanjiv (mentor: Franck Njeunje)
"Deep Generative Models for Natural Images" Adam Anderson (mentor: Matt Whiteway)
"Linear and Dynamic Programming" Patrick Shan (mentor: Weikun Wang)
"Discrete-Time Dynamical Systems and Chaos" Kevin Braga (mentor: Jenny Rustad)
"Approaches to Building a Recommender System" Joshua Twitty (mentor: Sean Ballentine and Ryan Hunter)
"Comparing Properties of Euclidean and Non-Euclidean Geometries " Andrea Zou (mentor: Corry Bedwell)
"The Mordell-Weil Theorem" Maxim Novak (mentor: Adam Lizzi)
"Making Sense of Special Relativity" Ajeet Gary (mentor: J-P Burelle)
"Golomb's Necklace" Robert Presley (mentor: Steven Reich)
"An Introduction to Elliptical Curve Cryptography" Suteerth Vishnu (mentor: S. Gilles)
"Two cryptographic ciphers: RSA and Vigenere" Beixuan Jia (mentor: Liam Fowl)
"Turing Instabilities and Biological Pattern Formation " Kevin Wittmer (mentor: Stephen Sorokanich)
"Applications of the Blossom Algorithm for Maximal Matching " Alexander Brassel (mentor: Zachary Greenburg)
"Can a countable set contain uncountably many elements? A look into Skolem's paradox " Kyle Reese (mentor: Danul Gunatilleka)
"Visualizing algebraic curves in projective space" Hannah Horng (mentor: Danny Kaufman)
"Complex Analysis on Operators" William Golding (mentor: Sam Punshon-Smith)
"Three Proofs of the Infinity of Primes" Diane Tchuindjo (mentor: Ariella Kirsch)

Fall 2016

TBA Diane Tchuindjo (mentor: Zachary Greenberg)
"Ofurtbeitititilz and Other Procedurally Generated Worlds" Eric Sim (mentor: David Bekkerman)
"The Axiom of Regularity" Sarah Eshera (mentor: Douglas Ulrich)
"Sums of Two Squares" Melanie Abel (mentor: Steve Balady)
TBA Maxim Novak (mentor: Adam Lizzi)
"An Introduction to the Mandelbrot Set" Yotam Yaniv (mentor: Danny Kaufman)
"Convex Optimization and Applications" Edward Nusinovich (mentor: Alex Estes)
"Taylor-Couette Flow" Siddhartha Harmalkar (mentor: Stephen Sorokanich)
"Introduction to Neural Networks for Image Classification" Adam Anderson (mentor: Matt Whiteway)
"Coding Theory: Optimal Error Detection in Binary" Andrew Natarian (mentor: Sean Ballentine)
"Heronian Triangles in the Gaussian Integers" Luxi Huang (mentor: Jesse Milzman)
"The Groebner Basis" Pavani Rannulu (mentor: Weikun Wang)
TBA Xinyang Li (mentor: Phil Wertheimer)

Summer 2016

"Shannon's Information Theory" Zonglin Tian (mentor: Stephen Gilles)
"Fractals and Mobius Transformations" Victor Gonzalez (mentor: Ryan Kirk)
"Voronoi Diagrams: Fortune's Algorithm and Applications" Kevin Wittmer (mentor: Rob Maschal)

Spring 2016

"An Algorithm for Factoring with Quantum Computers" Emily Camardo (mentor: Phil Wertheimer)
"Ito's Formula: a Variation of the Chain Rule" Ankur Patel (mentor: Pratima Hebbar)
"Solving Disentanglement Puzzles with Hints from Topology" Alexa Tsintolas (mentor: Danny Kaufman)
"Neural Networks and Deep Learning" Ramkesh Renganathan (mentor: Franck Ndjakou Njeunje)
"Limit Fractals of Kleinian Groups" Adam Anderson (mentor: JP Burelle)
"Weak Solutions to Partial Differential Equations" William Golding(mentor: Stefan Doboszczak)
"A Philosophical Enquiry of ZFC" Christopher Osterman (mentor: Mark Magsino)
"Hyperbolic Geometry" Victor Gonzalez (mentor: Ryan Kirk)
"Counting in Two Ways" Hunter Johnson (mentor: Zachary Greenberg)
"Gödel's Incompleteness Theorems" Aaron George (mentor: Douglas Ulrich)
"e is Irrational" Anthony Richardson (mentor: Steve Balady)
"Higher Order Homotopy Groups and Postnikov Towers" Liam Fowl (mentor: )
"Primality Testing" Giovanni Fevola (mentor: Rebecca Black)
TBA Ruozhu Li (mentor: Adam Lizzi)
TBA Guillaume Toujas (mentor: Sean Ballentine)
"Graph Algorithms and Their Applications in Maze Solving" Clara Bryant (mentor: Matias G Delgadino)

Fall 2015

"The power of nets" Jaspreet Kaur (mentor: Corry Bedwell)
"Using the random iteration algorithm to create fractals" Adam Anderson (mentor: Kasun Ferrnado)
"Differential geometry: curvature, maps, and pizza" Madelyne Ventura (mentor: Jean-Philippe Burelle)
"Approach of linear regression to machine learning" Jiansong Chen (mentor: Cheng Jie)
"The music of group theory" John Padgett (mentor: Jerry Emidih)
"Linear recurring sequences" Wil Parsons (mentor: Nathan Dykas)
"A group theoretic approach to the helicopter cube" Victor Gonzalez (mentor: Steven Reich)
"Cantor's first uncountability proof" Anthony Richardson (mentor: Steve Balady)
"Return to the origin in simple symmetric random walks" Ankur Patel (mentor: Micah Goldblum)
"Characteristics of planar graphs" George Ge (mentor: Zach Greenburg)
"One dimensional quantum mechanics: the free particle" Luke Corcos (mentor: Jacky Chong)
"Coding theory" Kaman Phamdo (mentor: Sean Ballentine)
"How to beat a small child at dots and boxes" Alexa Tsintolas (mentor: Robert Maschal)
"Hilbert's Nullstellensatz and algebraic curves" Liam Fowl (mentor: Nathaniel Monson)
"Neural network and its applications" Xinyue Liu (mentor: Alex Estes)

Summer 2015

"Ranking Methods" Suyang Xu (mentor: Steve Balady)
"The Heat Equation: Fourier Series and Finite Difference Methods" Liban Mohamed (mentor: Stefan Doboszczak)
"Thinking Mathematically" Samantha Suplee (mentor: Elizabeth Fleming)
"Generalized Linear Models and Their Applications" Ankur Patel (mentor: Matt Whiteway)
"Ito Calculus" Rajath Shetty (mentor: Zhenfu Wang)
"Using Classification Trees to Decide News Popularity" Xinyue Liu (mentor: Xia (Summer) Hu)
"Number Theory" Geri Dunellari (mentor: Tim Mercure)
"Van der Waerden's Theorem: Where topology, dynamics, and number theory meet" Youcef Moumena (mentor: Patrick Daniels)
"Signal Processing with the Fourier and Haar Transform" Colin Emberland (mentor: Sam Punchon-Smith)
"Neural Networks and Machine Learning" Ephraim Rothschild (mentor: Oliver Rourke)

Spring 2015

"Chaos and the Horseshoe Map" Jin Wu (mentor: Jenny Rustad)
"Introduction to Brownian Motion" Yufan Fei (mentor: Mickey Salins)
"Homeomorphism and Topological Properties" David Finder (mentor: Steve Balady)
"Using Queueing Theory and Simulation to Optimise Emergency Department" Henry Addison Euhus (mentor: Summer (Xia) Hu)
"Matrix Groups: Understanding SO(3) in terms of rotations" Liam Fowl (mentor: Ryan Hunter))
"The Riemann Tensor and the Curvature of Space" Miles David Miller-Dickson (mentor: Jon Cohen)
"Can we determine whether an email is spam?" Xinyue Liu (mentor: Mike Kreisel)
"The Lotka-Volterra Model" Rouzhen Ma (mentor: Stephanie Young)
"Relating N ± 1 to the Primality of N" Nate Fulton (mentor: Adam Lizzi)
"Stochastic Differential Equations: When Calculus Fails" Christopher Yeager (mentor: Scott Smith)
"Differential Forms" Zev Kaplowitz (mentor: Danul Gunatilleka)

Fall 2014

Ryan Mazurick, "Time Integration Schemes for the 1D Heat Equation," mentor: Andrew Brandon
Ike Uchenna Chukwu, "Cohomology of an Annulus," Ryan Hunter
Shu Zhu, "Option Pricing Using Fast Fourier Transform," Andreas Roy
Liam Fowl, "The Fundamental Group and Seifert-van Kampen Theorem," Nathaniel Monson
Anurupa Bhonsale, "Optimal Control and Applications to Biomedical Problems," Jim Greene
Chinedum, "Fibonacci Numbers," Sean Ballentine
Samuel Cunningham, "Continuity in Topology," Steve Balady
Becky Vanarsdall, "The Classical Construction Problem and Constructable Numbers," Jonathan Fernandes

Summer 2014

Rajath Shetty, "Sard's Theorem and Gravitational Lensing," mentor: Dan Zollers
Rebecca Hsu, "The Riemann Mapping Theorem and Uses of Conformal Mapping," Minsung Kim
Cooper Strickland, "Five Comments on the Five Lemma," Tim Mercure
Liam Fowl, "Understanding the Prime Number Theorem," Nathaniel Monson
Stephen Semick, "Perceptrons, and Other Methods Perfect for Our Linear World," Oliver Rourke
Nathan Feldman, "Social Networks and Graph Theory," Sean Ballentine
Guoqing Wang, "Fourier Transforms of Tempered Distributions," Jacky Chong
Niko Schultz, "The Glue Function: An Example of How Mathematicians Think," Steve Balady

Spring 2014

Sohan Vartak, "The Stress-Energy Tensor in Special Relativity," mentor: Son Lam Ho
Hasan Touma, "The Mathematics of the Rubik's Cube," Ryan Kirk
Daniel Mourad, "Skolem's 'Paradox'," Tim Mercure
Neil Shah and James Kazmierczak, "Making It Rain with Machine Learning," David Darmon and Chae Clark
Meghana Raja, "Residues and the Basel Problem," James Murphy
Connor Davis, "The Robinson-Schensted Algorithm," Adam Lizzi
William (Brady) Gunnarsson, "Applications of the Laplace Transform in ODE and Modeling DC Circuits," Stefan Doboszczak
Jordan Misra, "The Statistical Mechanics of Money: Modeling Savings and Debt," Joshua Schneider
Mike Houser, "Wave Equations," Jim Greene
Addison Euhus, "An Introduction to Uncertainty Quantification," Edward Phillips
Michael Roberts, "Matrix Groups," Jonathan Fernandes
Olivier Millogo, "Exploring the Golden Ratio," Ariella Kirsch

Fall 2013

Lee Antlefinger-Norton, "A Closer Look at Riemann Integration," mentor: Jacky Chong
James Chen, "Derivative-free Optimization by Simulated Annealing," Virginia Forstall
Connor Davis, "Picard's Theorems," Jon Cohen
Henry Addison Euhus, "Data Mining and Machine Learning," Dan Weinberg
Nathan Ng, "A Remarkable Fact About Gauss Curvature," Rob Maschal
Martin Buck, "Differential Equations on Fractals," Matt Begu�
Lauren Fox, "Markov Chains and the Erogodic Theorem," Mark Magsino
Stephen Semick, "Basic Deblurring of Medical Images," Victoria Taroudaki
Daniel Sun, "Cayley's Theorem: An Invitation to Group Theory," Ryan Kirk
Michael Roberts, "Isometries of Euclidean Space," Jonathan Fernandes
Akira Horiguchi, "Large-Time Behavior of Finite Markov Chains," Zsolt Pajor-Gyulai
Carlos Garcia, "Not Another First-Order Talk: Logic and the Ax-Grothendieck Theorem," Sam Bloom
Anthony McMannis, "Visualizing Spacetime," Jean-Philippe Burelle
Anton Yang, "Lines of Best Fit," Mickey Salins
Mohamad Qadri, "Topology and Geometries on Surfaces," Ryan Hunter

Summer 2013

Joseph Downs, "Control Theory: Feedback and the Pole-Shifting Theorem," Mentor: Edward Phillips
Lee Antlefinger-Norton, "The Baire Category Theorem," James Murphy
Arpan Bhattacharyya, "Lie Algebras to Root Systems," Jon Cohen
Micah Goldblum, "Geodesics on the Torus," Steve Balady
Michael Roberts, "Some Results from the Classical Theory of Recursion," Tim Mercure
Rebecca Hsu, "Proof of Larman, Rogers and Seidel Theorem," Wei-hsuan Yu
Rahul Gogna, "Applications of Sard's Theorem in Electrostatics," Dan Zollers
Rosemary Smith, "Order Statistics of Random Variables," Sean Ballentine

Spring 2013

Arpan Bhattacharyya, "Rubik's Cube Via Group Theory," Mentor: Srimathy Srinivasan
Tim Zulf, "Polynomial Interpolation," Steve Balady
Alex Kandell, "Markov Chain Monte Carlo Estimation of Seismic Attenuation," Tyler Drombowsky
Tolga Keskinoglu, "Concepts in Calculus," Jon Cohen
Addison Euhus, "Options Pricing and Black-Scholes," Zsolt Pajor Gyulai
Michael Roberts, "Nonstandard Arithmetic," Mickey Salins
Kaela MacNeil, "Geometric Constructions of Farey Sequences," Sean Ballentine
Alex Youcis, "Modular Forms and Elliptic Curves," Adam Lizzi
Ilse Haim, "The AKS Primality Test," Jon Huang
Mike Haskel, "L^p Spaces: An Introduction," James Murphy
Carlos Garcia, "Seifert-van Kampen Theorem," Gokhan Civan
Jordan Misra, "A Little Better than Average(s): An Investigation of Nate Silver's Election Prediction Methodology," David Darmon
Alissa Stafford, "Compressive Sensing and Applications," Alex Cloninger
Daniel Smith, "Solutions of Equations by Iteration," Edward Phillips
Mohamad Qadri, "Calculus of Variations and the Brachistochrone Problem," Ryan Hunter
Jun Chu, "Approximating the Black-Scholes Price of an American Put Option," Dan Weinberg

Fall 2012

Savid Sharan, "Singular Value Decomposition and Image Compression," Mentor: Sean Ballentine
Mike Haskel, "Introduction to Homology," James Murphy
Kyle O'Hehir, "Mathematical Finance," Bryant Angelos
Peter Mariani, "Integral Asymptotics and the Stirling Series," Mickey Salins
Jonathan Franck, "Nonlinear Dimensionality Reduction," Alex Cloninger
Lianjun Li, "The Transportation Problem," Gokhan Civan
Chandan Kittur, "Hamiltonian Celestial Dynamics," Ariel Hafftka
Jun Chu, "Gillespie Algorithm of Epidemiology" Daniel Weinberg
Keith Paarporn, "Lebesgue Integration for Signal Processing," Matt Guay
Zeyad Emam, "How Leibniz Squared the Circle," Elizabeth Fleming
Carlos Garcia, "Geometry of Numbers," Jon Cohen
Arpan Bhattacharyya, "Hyperbinary Representations and the Calkin-Wilf Tree," Rebecca Black
Hoyoung Kang, "The Chinese Remainder Theorem," Adam Lizzi
Alex Sherman, "The Classification Theorem for Compact Surfaces," Domingo Ruiz
Ivan Melyakov, "First Order Logic and Definability," Mike Kreisel

Summer 2012

Eddie Lister, "Gauss Sums and Quadratic Reciprocity," Mentor: Jonathan Cohen
Alex Kandell, "A Muliple Scales Approximation to the Korteweg-deVries Equation," Chunting Lu
Ian Magee, "A Return to Calculus," Steve Balady
Andrew Golczynski, "Manifolds and Whitney's Embedding Theorem," Jonathan Fernandes
Anastasiya Belyaeva, "Monte Carlo Methods and Applications," Virginia Forstall
Stephanie Elgart, "The Hairy Ball Theorem," James Murphy
Moming Li, "Spherical Two-Distance Sets," Wei-hsuan Yu
Douglas Ulrich, "A Nice Infinitary Logic," Tim Mercure
Yingquan Li, "Introducting Support Vector Machines for Classification Problems," Greg Laun
Jonathan Franck, "SVM, PCA, and Neural Networks in Machine Learning," Alex Cloninger

Spring 2012

Rohan Bale, "Lorenz Attractors," Mentor: Rodrigo Trevino
Sneha Patel, "Rational Points on Elliptic Curves," Dave Karpuk
Elizabeth Fleming, "The Axiom of Choice in the Measure Problem," Christian Sykes
Ishmael Opong, "An Introduction to the Lorenz Equations," James Greene
Mike Haskel, "Types in Formal Logic," Richard Rast
Alex Sherman, "Irrationality and Transcendence," Adam Lizzi
Brendan Good, "When Curves Collide," Rebecca Black
Saraloys Leroy, "Elements of Complex Numbers," Jon Cohen
Stephanie Barcomb, "Comparison of Time-Marching Methods," Edward Phillips
Huixian Yin, "RSA Public Key Cryptography," Jeremy Bradford
Di Zheng, "The Central Limit Theorem: Proof and Application," Dan Weinberg
Keith Paarporn, "Wavelet Transforms and Image Processing," Matt Guay
Connor Davis, "Properties of Musical Scales," Maxx Cho
Akira Horiguchi, "The Gamma Function and Analytical Continuation," Jon Fernandes
Max Mulitz, "Hypothesis Testing in Sports," Bryant Angelos
Theodore Brennan, "The Poincare Dodecahedral Space," Mike Kreisel

Fall 2011

Joel Pruitt (Scott Schmieding)
Darwin Romero (Bryant Angelos)
Douglas Ulrich (Richard Rast)
Rohan Bhall (Rodrigo Trevino)
Kalkidan Lebeta (Wei-hsuan Yu)
Alicia Stafford (Lucia Simonelli)
Sean Murphy (Dave Shaw)
Eisha Nathan (Dave Karpuk)
Logan Crew (Jonathan Cohen)
Jada Johnson (Mickey Salins)
Michael Thomas (Kanna Nakamura)
Guillaume Cheron (Tim Mercure)