**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)