**Fall 2023**

Erin Hopper,
"Modeling Biological Sequence Alignment"
(mentor: Valerie Wray)

Joseph Heavner,
"Modular Forms & Their Applications"
(mentor: Emilio Dominguez)

May Piatt,
"The H-Cobordism Theorem and its Applications"
(mentor: Keith Mills)

Cheng-Yuan Lee,
"Spectral Graph Theory"
(mentor: Prakhar Gupta)

Siddhant Mittal,
"Unraveling Stochastic Processes: From Basics to the Black-Scholes Theorem"
(mentor: Brooke Weston)

Rowan Weiss,
"An Introduction to Computability Theory and the Halting Problem"
(mentor: Connor Lockhart)

Michael Belluscio,
"Classification of Dynamical Systems with Entropy"
(mentor: Spencer Durham)

Alejandro Escoto,
"Geometric Flows"
(mentor: Vlassis Mastrantonis)

Hung Anh Vu,
"Unveiling the magic of Denoising Diffusion Probabilistic Models"
(mentor: Ke Chen)

**Spring 2023**

Brooke Guo,
"The Isoperimetric Inequality: From Antiquity to Steiner"
(mentor: Vlassis Mastrantonis)

Jacob Lin,
"Grobner Basis and Division of Multivariate Polynomials"
(mentor: Yu-Chi Hou)

Koray Bailey,
"An Overview of Grover's Search Algorithm and Random Walks"
(mentor: Junaid Aftab)

Andy Pavlosky,
"A Sweep of Computational Geometry"
(mentor: Max Springer)

Kevin Flanary,
"The Geometry of Riemann Surfaces and the Riemann Hurwitz Theorem"
(mentor: Sam Bachhuber)

David Song,
"Introduction to Options, Arbitrage, and the Black-Scholes Equation"
(mentor: Arpith Shanbhag)

Robert Sargent,
"The Banach-Tarski Paradox"
(mentor: Connor Lockhart)

Neil Shah,
"Understanding a Spin 1/2 Particle in a Magnetic Field through Representation Theory and Lie Algebra"
(mentor: Jackson Hopper)

Sarah Hwang,
"Rudin's Proof of the Stone-Weierstrass Theorem"
(mentor: Vasanth Pidaparthy)

Avi Kedia,
"Topologies on Finite Sets"
(mentor: Keith Mills)

Nowrin Nuzhat,
"Categorical Proof of Cayley's Theorem"
(mentor: Shin Eui Song)

**Fall 2022**

Robert Sargent,
"Intro to Geometric Algebra"
(mentor: Prakhar Gupta)

Ryan Khan,
"Exploring Mathematical Finance with a Focus on The Black-Scholes Formula"
(mentor: Melanka Wedige)

Kevin Flanary,
"Foundational Mathematics of Quantum Error Correction"
(mentor: Ian Teixeira)

Henry Denson,
"Morse Theory"
(mentor: Sze Hong Kwong)

Ezra Aylaian,
"Integration on Manifolds and the de Rham Cohomology"
(mentor: Geoffrey Sangston)

Matthew Cimerola,
"Neural Networks and Their Applications"
(mentor: Junaid Aftab)

Alejandro Escoto,
"On the de Rham Cohomology"
(mentor: Vlasios Mastrantonis)

**Spring 2022**

Zachary Gurwitz,
"Why does 19^41 end in 19?"
(mentor: Keith Mills)

Victoria Shumakovich,
"Unconstrained Optimization"
(mentor: Zhirui Li)

Eric O'Leary,
"Classification of Surfaces"
(mentor: Jay Desai)

Tianyu You,
"Decoupling of Spin Error"
(mentor: Kwong Sze Hong)

Adam Melrod,
"An Ultraproduct Proof of the Compactness Theorem"
(mentor: )

John Brownfield,
"Consequences of Hilbert's Nullstellensatz"
(mentor: Nicholas Hiebert-White)

Matthew Simmons,
"Banach-Tarski Paradox and Tarski's Circle-Squaring Problem"
(mentor: )

Daniel Schug,
"Image Processing: Linear Filtering,Variational Techniques, and More"
(mentor: Lucas Bouck)

Abdulrahman Alenazi,
"On Mahler's 2D conjecture"
(mentor: Vlasios Mastrantonis)

Changbin Ko,
"Numerics for Data Science"
(mentor: Rachel Lee)

Karthik Sellakumaran Latha,
"Root Systems and Weyl Groups"
(mentor: Arghya Sadhukhan)

Xueyi An,
"Ramanujan Graph: Connection between Linear Algebra and Graph Theory"
(mentor: Shin Eui Song)

Chenhongshu Yu,
"Quantum Computation of Shor'sAlgorithm in Cryptography"
(mentor: Jackson Hopper)

**Fall 2021**

Joshua Liu,
"Elliptic Curves"
(mentor: Foivos Chnaras)

Marisa Cofie,
"Distributions and Their Application to PDEs"
(mentor: Prakhar Gupta)

Neelam Akula,
"Investigating Repeating Decimals"
(mentor: Alexander Suarez-Beard)

Cole Saborio,
"Restricted Boltzmann Machines:statistical physics for machine learning"
(mentor: Stavros Papathanasiou)

David Fang,
"Algebraic Groups and Chevalley's Theorem"
(mentor: Shin Eui Song)

Darsh Shah,
"Dirichlet's Unit Theorem"
(mentor: Jackson Hopper)

Xinyue Li,
"Introduction to Graph Theory"
(mentor: Arghya Sadhukhan)

Karthik Sellakumaran Latha,
"Symmetric Groups and Schur-Weyl Duality"
(mentor: Chengze Duan)

Jeffrey Zhang,
"Markov Chains and Ergodic Convergence"
(mentor: Zhirui Li)

Turner McLaurin,
"Category Theory and Universal Constructions"
(mentor: Keith Mills)

Sophia Hu,
"Applications of Linear Algebra in Data Science:SVDs and Recommender Systems"
(mentor: Lucas Bouck)

**Spring 2021**

Marie Brodsky,
"Games and Nash Equilibria"
(mentor: Brandon Gontmacher)

Ryan Tse,
"Universal Bundles"
(mentor: Keith Mills)

Aryan Kaul,
"The Brouwer Fixed Point Theorem"
(mentor: Vlassis Mastrantonis)

Andrew Craun,
"Linear Statistical Models with R: Modeling Teenage Gambling Expenditures"
(mentor: Pei Zhang)

Sophia Chen,
"Furstenberg's Proof of the Infinitude of Primes"
(mentor: Kwong Sze Hong)

Zongxia Li,
"Neural Networks and their Applications"
(mentor: Eric Oden)

Abdulrahman Alenazi,
"The Remarkable Theorem of Gauss"
(mentor: Prakhar Gupta)

Jackson Reynolds,
"Geometry of Root Systems"
(mentor: Arghya Sadhukhan)

**Fall 2019**

Yashas Lokesh,
"Exploring Coxeter Groups"
(mentor: Dani Kaufman)

Siddarth Balaji,
Riemann Sphere and Schottky Transformations
(mentor: Keith Mills)

Kat Georgantas,
"Transformations in Hyperbolic Space"
(mentor: Zachary Greenberg)

Bryce Toole,
"Percolation and Epidemic Modeling on Networks"
(mentor: Brandon Alexander)

Yunmeng Wu,
"Persistent Homology"
(mentor: Laura Iosip)

Ares Shackleford,
"Data Assimilation"
(mentor: Brooke Herzog)

Jiahui Luo,
"Modeling the Stock Price of Facebook using Stochastic Calculus"
(mentor: Ayushi Saxena)

Steven Jin,
"Elliptic Curves over Finite Fields"
(mentor: Professor Lawrence Washington)

Luke Roepe,
"Projective Space: How Cameras See the World"
(mentor: Jerry McDermott)

Matthew Firth,
"Hidden Markov Models: Applications to Computer Vision and Speech Recognition"
(mentor: Stavros Papathanasiou)

Rohit Krishnagopal,
"Bayesian Games"
(mentor: Blake Fritz)

Kyle Reese,
"The Classification of Semisimple Lie Algebras"
(mentor: Arghya Sadhukhan)

**Spring 2019**

Steven Jin,
"Riemann's Inequality for Algebraic Curves and its Consequences"
(mentor: Professor Amin Gholampour)

Troy Cary,
"Generative Adversarial Networks"
(mentor: Chenzhi Zhao)

Samuel Howard,
"Error-Correcting Codes"
(mentor: Tahseen Rabbani)

Zifan Yu,
"Markov Chains and Random Walks"
(mentor: Pranava Jayanti)

Matthew Chung,
"A Sampling of Wavelet Theory"
(mentor: Jerry Emidih)

Nicholas Hiebert-White,
"An Introduction to Schemes"
(mentor: Patrick Daniels)

Kusal De Alwis,
"Rotations in 3D Using Geometric Algebra"
(mentor: Laura Iosip)

Joseph Cleary,
"Special Case of Fermat's Last Theorem"
(mentor: Shin Eui Song)

Siddarth Taneja,
"A Little Lie (Theory) Never Hurt Anyone"
(mentor: Arghya Sadhukhan)

Shu-Huai Lin,
"Erdős Distance Problem on the Plane"
(mentor: Jacky Chong)

Henry Meade,
"Neural Nets: Theory and Implementation"
(mentor: Shahnawaz Khalid)

Leonard Unger,
"Holes, Homology, and Fixed Point Theorems"
(mentor: Yiannis Markakis)

**Fall 2018**

Teddy Hersey,
"Fourier Analysis and Sound"
(mentor: Dani Kaufman)

Jiateng Wang,
"Stochastic Calculus"
(mentor: Pratima Hebbar)

Nicholas Hiebert-White,
"Bezout's Theorem and Applications"
(mentor: Yiannis Markakis)

Meghana Doddapaneni,
"Elliptic Curve Cryptography"
(mentor: Steven Reich)

Nicholas Falcon,
"How to Use Support Vector Machines"
(mentor: Catherine Schwartz)

Ifeanyi Iyke-Azubogu,
"Elliptic Curves and their Applications"
(mentor: Arghya Sadhukhan)

Lanqi Fei,
"Construction of Q_{p} with Two Approaches"
(mentor: Shin Eui Song)

Aaron Benda,
"A Topological Proof of the Fundamental Theorem of Algebra"
(mentor: Zachary Greenberg)

John Freal,
"Application of Fourier Series to PDEs"
(mentor: Keagan Callis)

Nathan Hayes,
"Groups of Rotations in 3 Dimensions"
(mentor: Jacky Chong)

**Summer 2018**

Tenzin Sonam,
"Elementary Topological Properties of R^{p}"
(mentor: Ishfaaq Imtiyas)

Zachary Star,
"Using Residue Theory to Evaluate Infinite Sums"
(mentor: Keagan Callis)

Alexander Davydov,
"Computability Theory and Big Numbers"
(mentor: David Bekkerman)

Adheep Joseph,
"Exploring Transcendental Extensions"
(mentor: Jordan Hirsh)

Alexander Brunmayr,
"The Ising Lattice Spin Model"
(mentors: Nick Paskal and Stephen Sorokanich)

**Spring 2018**

Marc Eichenwald,
"Introduction to Group Theory via Rubik's Cubes"
(mentor: Dani Kaufman)

Andrew Miller,
"Computing Real Integrals using Complex Analysis"
(mentor: Allan Yashinski)

Elizabeth O'Callaghan,
"Big Graphs and Menger's Theorem"
(mentor: Zachary Greenberg)

Douglas Post,
"Understanding Spaces with a Case Study in the Banach-Mazur Game"
(mentor: Kevin Quigley)

Brandon Kwintner,
"The Cauchy Integral Formula"
(mentor: Noah Chrein)

Evan McIntire,
"Expander Families and Cayley Graphs"
(mentor: Arghya Sadhukhan)

Deena Postol,
"Sums of Distinct Squares"
(mentor: Steve Balady)

Rahul Reddy,
"Network Flows and Cuts"
(mentor: Laura Iosip)

Thomas Bishop,
"Quantifier Elimination over Algebraically Closed Fields"
(mentor: Danul Gunatilleka)

Nina Jacobsen,
"Wavelets and Image Processing Applications"
(mentor: Mark Magsino)

Tyler Hoffman,
"Immersions, Embeddings, and the Klein Bottle"
(mentor: Jacky Chong)

Matthew Watson,
"The Pohlig-Hellman Algorithm"
(mentor: Phil Wertheimer)

Rachel Kim,
"Gaussian Integers and Sums of Squares"
(mentor: Allan Yashinski)

Scott Stanich,
"Ergodic Theory and Weyl's Theorem"
(mentor: Kasun Fernando)

Ganesh Chandrasekaran,
"An Information-theoretic Analysis of Neural Signals"
(mentor: Jesse Milzman)

Hunter Dement,
"Model Theory and the Compactness Theorem"
(mentor: Douglas Ulrich)

**Fall 2017**

Ryan Synk,
"General Relativity and Differential Forms"
(mentor: Stephen Sorokanich)

Jared Ronning,
"The Prime Number Theorem and Dirichlet's Theorem on Primes in Arithmetic Progressions"
(mentor: Sam Bloom)

Matt Kukla,
"Bertrand's Postulate"
(mentor: Steve Balady)

John Nolan,
"The Fundamental Group"
(mentor: Dani Kaufman)

Tianchu Xie,
"Neural Networks and Optimization"
(mentor: Micah Goldblum)

Junran Yang,
"Konig’s Theorem About Vertex Cover and Matchings"
(mentor: Zachary Greenberg)

Ajeet Gary,
"Understanding the Generalized Stokes' Theorem with Differential Forms"
(mentor: Ryan Kirk)

Linden Yuan,
"Ergodic Theory and an Application to Number Theory"
(mentor: Kasun Fernando)

Emmanuel Benyam,
"Modular Arithmetic and Applications to Primality Testing"
(mentor: Nathan Dykas)

Xinyang Li,
"The Fundamental Group"
(mentor: Douglas Ulrich)

Sujith Vishwajith,
"Reinforcement Learning and Applications"
(mentor: Jerry Emidih)

Christopher Pilotte,
"Lights Out Puzzle"
(mentor: Charles Daly)

Shivam Agrawal,
"Training A Neural Network to Recognize Digits"
(mentor: Nathaniel Monson)

Sinikiwe Gurupira,
"Chaos and Bifurcations"
(mentor: JT Rustad)

Kevin Gima,
"Quantum Teleportation or Not"
(mentor: David Bekkerman)

Vlada Dementyeva,
"Graph Theory"
(mentor: Danul Gunillateka)

**Summer 2017**

Xuejing Wang,
"Latent Dirichlet Allocation and Its Application in Grouping Facebook Users Using Labels Extracted from User-Generated Images"
(mentor: Lijuan Cao)

Jon Bozzonetti,
"Continuity and Connectedness"
(mentor: Steve Balady)

Jared Ronning,
"The Compactness Theorem"
(mentor: Douglas Ulrich)

Daniel Lay,
"Dimension and Measure Theory"
(mentor: JT Rustad)

**Spring 2017**

Luke Bender,
"Markov Chain Hitting Times"
(mentor: Phil Wertheimer)

Alejandro Diaz,
"Hamiltonian Mechanics and Symplectic Geometry"
(mentor: Matt Dellatorre)

Shravan Sanjiv,
"Mathematics of Classification Algorithms"
(mentor: Franck Njeunje)

Adam Anderson,
"Deep Generative Models for Natural Images"
(mentor: Matt Whiteway)

Patrick Shan,
"Linear and Dynamic Programming"
(mentor: Weikun Wang)

Kevin Braga,
"Discrete-Time Dynamical Systems and Chaos"
(mentor: JT Rustad)

Joshua Twitty,
"Approaches to Building a Recommender System"
(mentor: Sean Ballentine and Ryan Hunter)

Andrea Zou,
"Comparing Properties of Euclidean and Non-Euclidean Geometries"
(mentor: Corry Bedwell)

Maxim Novak,
"The Mordell-Weil Theorem"
(mentor: Adam Lizzi)

Ajeet Gary,
"Making Sense of Special Relativity"
(mentor: J-P Burelle)

Robert Presley,
"Golomb's Necklace"
(mentor: Steven Reich)

Suteerth Vishnu,
"An Introduction to Elliptical Curve Cryptography"
(mentor: S. Gilles)

Beixuan Jia,
"Two cryptographic ciphers: RSA and Vigenere"
(mentor: Liam Fowl)

Kevin Wittmer,
"Turing Instabilities and Biological Pattern Formation"
(mentor: Stephen Sorokanich)

Alexander Brassel,
"Applications of the Blossom Algorithm for Maximal Matching"
(mentor: Zachary Greenberg)

Kyle Reese,
"Can a countable set contain uncountably many elements? A look into Skolem's paradox"
(mentor: Danul Gunatilleka)

Hannah Horng,
"Visualizing algebraic curves in projective space"
(mentor: Dani Kaufman)

William Golding,
"Complex Analysis on Operators"
(mentor: Sam Punshon-Smith)

Diane Tchuindjo,
"Three Proofs of the Infinity of Primes"
(mentor: Ariella Kirsch)

**Fall 2016**

Diane Tchuindjo,
"An Inquiry into Eulerian and Hamiltonian Cycles"
(mentor: Zachary Greenberg)

Eric Sim,
"Ofurtbeitititilz and Other Procedurally Generated Worlds"
(mentor: David Bekkerman)

Sarah Eshera,
"The Axiom of Regularity"
(mentor: Douglas Ulrich)

Melanie Abel,
"Sums of Two Squares"
(mentor: Steve Balady)

Maxim Novak,
"Quadratic Residues and Gauss’s Lemma"
(mentor: Adam Lizzi)

Yotam Yaniv,
"An Introduction to the Mandelbrot Set"
(mentor: Dani Kaufman)

Edward Nusinovich,
"Convex Optimization and Applications"
(mentor: Alex Estes)

Siddhartha Harmalkar,
"Taylor-Couette Flow"
(mentor: Stephen Sorokanich)

Adam Anderson,
"Introduction to Neural Networks for Image Classification"
(mentor: Matt Whiteway)

Andrew Natarian,
"Coding Theory: Optimal Error Detection in Binary"
(mentor: Sean Ballentine)

Luxi Huang,
"Heronian Triangles in the Gaussian Integers"
(mentor: Jesse Milzman)

Pavani Rannulu,
"The Groebner Basis"
(mentor: Weikun Wang)

Xinyang Li,
"The RSA Algorithm"
(mentor: Phil Wertheimer)

**Summer 2016**

Zonglin Tian,
"Shannon's Information Theory"
(mentor: Stephen Gilles)

Victor Gonzalez,
"Fractals and Mobius Transformations"
(mentor: Ryan Kirk)

Kevin Wittmer,
"Voronoi Diagrams: Fortune's Algorithm and Applications"
(mentor: Rob Maschal)

**Spring 2016**

Emily Camardo,
"An Algorithm for Factoring with Quantum Computers"
(mentor: Phil Wertheimer)

Ankur Patel,
"Ito's Formula: a Variation of the Chain Rule"
(mentor: Pratima Hebbar)

Alexa Tsintolas,
"Solving Disentanglement Puzzles with Hints from Topology"
(mentor: Dani Kaufman)

Ramkesh Renganathan,
"Neural Networks and Deep Learning"
(mentor: Franck Ndjakou Njeunje)

Adam Anderson,
"Limit Fractals of Kleinian Groups"
(mentor: JP Burelle)

William Golding,
"Weak Solutions to Partial Differential Equations"
(mentor: Stefan Doboszczak)

Christopher Osterman,
"A Philosophical Enquiry of ZFC"
(mentor: Mark Magsino)

Victor Gonzalez,
"Hyperbolic Geometry"
(mentor: Ryan Kirk)

Hunter Johnson,
"Counting in Two Ways"
(mentor: Zachary Greenberg)

Aaron George,
"Gödel's Incompleteness Theorems"
(mentor: Douglas Ulrich)

Anthony Richardson,
"e is Irrational"
(mentor: Steve Balady)

Liam Fowl,
"Higher Order Homotopy Groups and Postnikov Towers"
(mentor: Nathaniel Monson)

Giovanni Fevola,
"Primality Testing"
(mentor: Rebecca Black)

Ruozhu Li (mentor: Adam Lizzi)

Guillaume Toujas (mentor: Sean Ballentine)

Clara Bryant,
"Graph Algorithms and Their Applications in Maze Solving"
(mentor: Matias G Delgadino)

**Fall 2015**

Jaspreet Kaur,
"The power of nets"
(mentor: Corry Bedwell)

Adam Anderson,
"Using the random iteration algorithm to create fractals"
(mentor: Kasun Fernando)

Madelyne Ventura,
"Differential geometry: curvature, maps, and pizza"
(mentor: Jean-Philippe Burelle)

Jiansong Chen,
"Approach of linear regression to machine learning"
(mentor: Cheng Jie)

John Padgett,
"The music of group theory"
(mentor: Jerry Emidih)

Wil Parsons,
"Linear recurring sequences"
(mentor: Nathan Dykas)

Victor Gonzalez,
"A group theoretic approach to the helicopter cube"
(mentor: Steven Reich)

Anthony Richardson,
"Cantor's first uncountability proof"
(mentor: Steve Balady)

Ankur Patel,
"Return to the origin in simple symmetric random walks"
(mentor: Micah Goldblum)

George Ge,
"Characteristics of planar graphs"
(mentor: Zachary Greenberg)

Luke Corcos,
"One dimensional quantum mechanics: the free particle"
(mentor: Jacky Chong)

Kaman Phamdo,
"Coding theory"
(mentor: Sean Ballentine)

Alexa Tsintolas,
"How to beat a small child at dots and boxes"
(mentor: Robert Maschal)

Liam Fowl,
"Hilbert's Nullstellensatz and algebraic curves"
(mentor: Nathaniel Monson)

Xinyue Liu,
"Neural network and its applications"
(mentor: Alex Estes)

**Summer 2015**

Suyang Xu,
"Ranking Methods"
(mentor: Steve Balady)

Liban Mohamed,
"The Heat Equation: Fourier Series and Finite Difference Methods"
(mentor: Stefan Doboszczak)

Samantha Suplee,
"Thinking Mathematically"
(mentor: Elizabeth Fleming)

Ankur Patel,
"Generalized Linear Models and Their Applications"
(mentor: Matt Whiteway)

Rajath Shetty,
"Ito Calculus"
(mentor: Zhenfu Wang)

Xinyue Liu,
"Using Classification Trees to Decide News Popularity"
(mentor: Xia (Summer) Hu)

Geri Dunellari,
"Number Theory"
(mentor: Tim Mercure)

Youcef Moumena,
"Van der Waerden's Theorem: Where topology, dynamics, and number theory meet"
(mentor: Patrick Daniels)

Colin Emberland,
"Signal Processing with the Fourier and Haar Transform"
(mentor: Sam Punshon-Smith)

Ephraim Rothschild,
"Neural Networks and Machine Learning"
(mentor: Oliver Rourke)

**Spring 2015**

Jin Wu,
"Chaos and the Horseshoe Map"
(mentor: JT Rustad)

Yufan Fei,
"Introduction to Brownian Motion"
(mentor: Mickey Salins)

David Finder,
"Homeomorphism and Topological Properties"
(mentor: Steve Balady)

Henry Addison Euhus,
"Using Queueing Theory and Simulation to Optimise Emergency Department"
(mentor: Summer (Xia) Hu)

Liam Fowl,
"Matrix Groups: Understanding SO(3) in terms of rotations"
(mentor: Ryan Hunter))

Miles David Miller-Dickson,
"The Riemann Tensor and the Curvature of Space"
(mentor: Jon Cohen)

Xinyue Liu,
"Can we determine whether an email is spam?"
(mentor: Mike Kreisel)

Rouzhen Ma,
"The Lotka-Volterra Model"
(mentor: Stephanie Young)

Nate Fulton,
"Relating N ± 1 to the Primality of N"
(mentor: Adam Lizzi)

Christopher Yeager,
"Stochastic Differential Equations: When Calculus Fails"
(mentor: Scott Smith)

Zev Kaplowitz,
"Differential Forms"
(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" (mentor: Ryan Hunter)

Shu Zhu, "Option Pricing Using Fast Fourier Transform" (mentor: Andreas Roy)

Liam Fowl, "The Fundamental Group and Seifert-van Kampen Theorem" (mentor: Nathaniel Monson)

Anurupa Bhonsale, "Optimal Control and Applications to Biomedical Problems" (mentor: Jim Greene)

Chinedum, "Fibonacci Numbers" (mentor: Sean Ballentine)

Samuel Cunningham, "Continuity in Topology" (mentor: Steve Balady)

Becky Vanarsdall, "The Classical Construction Problem and Constructable Numbers" (mentor: 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" (mentor: Minsung Kim)

Cooper Strickland, "Five Comments on the Five Lemma" (mentor: Tim Mercure)

Liam Fowl, "Understanding the Prime Number Theorem" (mentor: Nathaniel Monson)

Stephen Semick, "Perceptrons, and Other Methods Perfect for Our Linear World" (mentor: Oliver Rourke)

Nathan Feldman, "Social Networks and Graph Theory" (mentor: Sean Ballentine)

Guoqing Wang, "Fourier Transforms of Tempered Distributions" (mentor: Jacky Chong)

Niko Schultz, "The Glue Function: An Example of How Mathematicians Think" (mentor: 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" (mentor: Ryan Kirk)

Daniel Mourad, "Skolem's 'Paradox'" (mentor: Tim Mercure)

Neil Shah and James Kazmierczak, "Making It Rain with Machine Learning" (mentors: David Darmon and Chae Clark)

Meghana Raja, "Residues and the Basel Problem" (mentor: James Murphy)

Connor Davis, "The Robinson-Schensted Algorithm" (mentor: Adam Lizzi)

William (Brady) Gunnarsson, "Applications of the Laplace Transform in ODE and Modeling DC Circuits" (mentor: Stefan Doboszczak)

Jordan Misra, "The Statistical Mechanics of Money: Modeling Savings and Debt" (mentor: Joshua Schneider)

Mike Houser, "Wave Equations" (mentor: Jim Greene)

Addison Euhus, "An Introduction to Uncertainty Quantification" (mentor: Edward Phillips)

Michael Roberts, "Matrix Groups" (mentor: Jonathan Fernandes)

Olivier Millogo, "Exploring the Golden Ratio" (mentor: Ariella Kirsch)

**Fall 2013**

Lee Antlefinger-Norton, "A Closer Look at Riemann Integration" (mentor: Jacky Chong)

James Chen, "Derivative-free Optimization by Simulated Annealing" (mentor: Virginia Forstall)

Connor Davis, "Picard's Theorems" (mentor: Jon Cohen)

Henry Addison Euhus, "Data Mining and Machine Learning" (mentor: Dan Weinberg)

Nathan Ng, "A Remarkable Fact About Gauss Curvature" (mentor: Rob Maschal)

Martin Buck, "Differential Equations on Fractals" (mentor: Matt Begué)

Lauren Fox, "Markov Chains and the Erogodic Theorem" (mentor: Mark Magsino)

Stephen Semick, "Basic Deblurring of Medical Images" (mentor: Victoria Taroudaki)

Daniel Sun, "Cayley's Theorem: An Invitation to Group Theory" (mentor: Ryan Kirk)

Michael Roberts, "Isometries of Euclidean Space" (mentor: Jonathan Fernandes)

Akira Horiguchi, "Large-Time Behavior of Finite Markov Chains" (mentor: Zsolt Pajor-Gyulai)

Carlos Garcia, "Not Another First-Order Talk: Logic and the Ax-Grothendieck Theorem" (mentor: Sam Bloom)

Anthony McMannis, "Visualizing Spacetime" (mentor: Jean-Philippe Burelle)

Anton Yang, "Lines of Best Fit" (mentor: Mickey Salins)

Mohamad Qadri, "Topology and Geometries on Surfaces" (mentor: Ryan Hunter)

**Summer 2013**

Joseph Downs, "Control Theory: Feedback and the Pole-Shifting Theorem" (mentor: Edward Phillips)

Lee Antlefinger-Norton, "The Baire Category Theorem" (mentor: James Murphy)

Arpan Bhattacharyya, "Lie Algebras to Root Systems" (mentor: Jon Cohen)

Micah Goldblum, "Geodesics on the Torus" (mentor: Steve Balady)

Michael Roberts, "Some Results from the Classical Theory of Recursion" (mentor: Tim Mercure)

Rebecca Hsu, "Proof of Larman, Rogers and Seidel Theorem" (mentor: Wei-hsuan Yu)

Rahul Gogna, "Applications of Sard's Theorem in Electrostatics" (mentor: Dan Zollers)

Rosemary Smith, "Order Statistics of Random Variables" (mentor: Sean Ballentine)

**Spring 2013**

Arpan Bhattacharyya, "Rubik's Cube Via Group Theory" (mentor: Srimathy Srinivasan)

Tim Zulf, "Polynomial Interpolation" (mentor: Steve Balady)

Alex Kandell, "Markov Chain Monte Carlo Estimation of Seismic Attenuation" (mentor: Tyler Drombowsky)

Tolga Keskinoglu, "Concepts in Calculus" (mentor: Jon Cohen)

Addison Euhus, "Options Pricing and Black-Scholes" (mentor: Zsolt Pajor Gyulai)

Michael Roberts, "Nonstandard Arithmetic" (mentor: Mickey Salins)

Kaela MacNeil, "Geometric Constructions of Farey Sequences" (mentor: Sean Ballentine)

Alex Youcis, "Modular Forms and Elliptic Curves" (mentor: Adam Lizzi)

Ilse Haim, "The AKS Primality Test" (mentor: Jon Huang)

Mike Haskel, "L^p Spaces: An Introduction" (mentor: James Murphy)

Carlos Garcia, "Seifert-van Kampen Theorem" (mentor: Gokhan Civan)

Jordan Misra, "A Little Better than Average(s): An Investigation of Nate Silver's Election Prediction Methodology" (mentor: David Darmon)

Alissa Stafford, "Compressive Sensing and Applications" (mentor: Alex Cloninger)

Daniel Smith, "Solutions of Equations by Iteration" (mentor: Edward Phillips)

Mohamad Qadri, "Calculus of Variations and the Brachistochrone Problem" (mentor: Ryan Hunter)

Jun Chu, "Approximating the Black-Scholes Price of an American Put Option" (mentor: Dan Weinberg)

**Fall 2012**

Savid Sharan, "Singular Value Decomposition and Image Compression" (mentor: Sean Ballentine)

Mike Haskel, "Introduction to Homology" (mentor: James Murphy)

Kyle O'Hehir, "Mathematical Finance," Bryant Angelos

Peter Mariani, "Integral Asymptotics and the Stirling Series" (mentor: Mickey Salins)

Jonathan Franck, "Nonlinear Dimensionality Reduction" (mentor: Alex Cloninger)

Lianjun Li, "The Transportation Problem" (mentor: Gokhan Civan)

Chandan Kittur, "Hamiltonian Celestial Dynamics" (mentor: Ariel Hafftka)

Jun Chu, "Gillespie Algorithm of Epidemiology" (mentor: Daniel Weinberg)

Keith Paarporn, "Lebesgue Integration for Signal Processing" (mentor: Matt Guay)

Zeyad Emam, "How Leibniz Squared the Circle" (mentor: Elizabeth Fleming)

Carlos Garcia, "Geometry of Numbers" (mentor: Jon Cohen)

Arpan Bhattacharyya, "Hyperbinary Representations and the Calkin-Wilf Tree" (mentor: Rebecca Black)

Hoyoung Kang, "The Chinese Remainder Theorem" (mentor: Adam Lizzi)

Alex Sherman, "The Classification Theorem for Compact Surfaces" (mentor: Domingo Ruiz)

Ivan Melyakov, "First Order Logic and Definability" (mentor: 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" (mentor: Chunting Lu)

Ian Magee, "A Return to Calculus" (mentor: Steve Balady)

Andrew Golczynski, "Manifolds and Whitney's Embedding Theorem" (mentor: Jonathan Fernandes)

Anastasiya Belyaeva, "Monte Carlo Methods and Applications" (mentor: Virginia Forstall)

Stephanie Elgart, "The Hairy Ball Theorem" (mentor: James Murphy)

Moming Li, "Spherical Two-Distance Sets" (mentor: Wei-hsuan Yu)

Douglas Ulrich, "A Nice Infinitary Logic" (mentor: Tim Mercure)

Yingquan Li, "Introducting Support Vector Machines for Classification Problems" mentor: Greg Laun)

Jonathan Franck, "SVM, PCA, and Neural Networks in Machine Learning" (mentor: Alex Cloninger)

**Spring 2012**

Rohan Bale, "Lorenz Attractors" (mentor: Rodrigo Trevino)

Sneha Patel, "Rational Points on Elliptic Curves" (mentor: Dave Karpuk)

Elizabeth Fleming, "The Axiom of Choice in the Measure Problem" (mentor: Christian Sykes)

Ishmael Opong, "An Introduction to the Lorenz Equations" (mentor: James Greene)

Mike Haskel, "Types in Formal Logic" (mentor: Richard Rast)

Alex Sherman, "Irrationality and Transcendence" (mentor: Adam Lizzi)

Brendan Good, "When Curves Collide" (mentor: Rebecca Black)

Saraloys Leroy, "Elements of Complex Numbers" (mentor: Jon Cohen)

Stephanie Barcomb, "Comparison of Time-Marching Methods" (mentor: Edward Phillips)

Huixian Yin, "RSA Public Key Cryptography" (mentor: Jeremy Bradford)

Di Zheng, "The Central Limit Theorem: Proof and Application" (mentor: Dan Weinberg)

Keith Paarporn, "Wavelet Transforms and Image Processing" (mentor: Matt Guay)

Connor Davis, "Properties of Musical Scales" (mentor: Maxx Cho)

Akira Horiguchi, "The Gamma Function and Analytical Continuation" (mentor: Jon Fernandes)

Max Mulitz, "Hypothesis Testing in Sports" (mentor: Bryant Angelos)

Theodore Brennan, "The Poincare Dodecahedral Space" (mentor: Mike Kreisel)

**Fall 2011**

Joel Pruitt (mentor: Scott Schmieding)

Darwin Romero (mentor: Bryant Angelos)

Douglas Ulrich (mentor: Richard Rast)

Rohan Bhall (mentor: Rodrigo Trevino)

Kalkidan Lebeta (mentor: Wei-hsuan Yu)

Alicia Stafford (mentor: Lucia Simonelli)

Sean Murphy (mentor: Dave Shaw)

Eisha Nathan (mentor: Dave Karpuk)

Logan Crew (mentor: Jonathan Cohen)

Jada Johnson (mentor: Mickey Salins)

Michael Thomas (mentor: Kanna Nakamura)

Guillaume Cheron (mentor: Tim Mercure)