Independent Study & Honors Theses

The faculty of our large Mathematics Department has a wide variety of interests. Typically, 30-40 students each year complete the A.B. or B.S. major in mathematics or the A.B. joint major in mathematics and economics.

Independent StudY

Independent study courses are usually offered at the request of interested students. Course topics have included statistics, topology, differential equations, geometry, the history of mathematics, Galois theory, matroids, combinatorics, transcendental numbers, differential geometry, fluid dynamics, number theory, and probabilistic models.

Honors Theses

Below is a list of some recent honors theses. For a longer list (dating back to 1938), visit the Lafayette library catalog.

Class of 2022

  • Beth Anne Castellano ’22,  Young tableaux and the irreducible representations
    of the symmetric group – Advisors Prof. Bloom & Prof. McMahon
  • Xinyu Hu ’22, Investigating Evolutionary Game Theory: the Replicator Dynamics for Small Symmetric Games – Advisor Prof Root
  • Yutian Huang ’22, Assessing the flexibility of deterministic tumor-immune ODE models for fitting stochastic synthetic dat – Advisor Prof. Lewis
  • Kevin Manogue, ’22, Spinors, spacetime and the positive mass theorem, Advisor Professor Corvino
  • Deniz Ozbay, ’22, On the geometry and Morse index of a free boundary minimal surface in the Schwarzschild Anti-de Sitter metric in 3 dimensions, Advisor Professor Corvino
  • Ru Wang ’22, A Glance at Mainstream Cryptosystems – Advisor Prof Reiter
  • Anna Zittle ’22, Analyzing the trade-offs between model complexity and parameter identifiability in math modeling of tumor dynamics, Advisor Prof. Lewis

Class of 2021

  • Zixuan Jin ’21, The One-Child Policy and Female Labor Force Participation in China – Advisors Profs Larsen & Liebner
  • Elene Karangozishvili, ’21: On a free boundary minimal surface in the Schwarzschild Anti-de Sitter metric, Advisor Professor Corvino

Class of 2020

  • Ryan Barnett ’20, LIBOR transition: estimating forward-looking term rates for SOFR (joint with Economics) – Advisors Prof. Lu & Prof. Kelly
  • Xiaonan Chen: ’20: On a free boundary minimal surface in the Schwarzschild geometry, Advisor Professor Corvino
  • Mike Van Ness ’20, Lattice basis reduction and the NTRU cryptosystem – Advisor Prof Smith
  • Sijia Du ’20, A one dimensional probabilistic packing problem – Advisor Prof. Fisher

Class of 2019

  • Ben Adenbaum ’19,  Investigating the signed Laplacian matrix of a graph – Advisor Prof. Smith
  • Hoa Duong ’19, Vertical Wage Gap Structure in the Retail Industry and Its Effects on Firms’ Performance (joint with Economics) – Advisors Prof. Liebner & Prof. Ruebeck
  • Michelle Foley ’19, Developing a Sustainable Food Pantry System at Cheston Elementary School – (joint with Economics) Advisors Profs. Gaugler & Ruebeck
  • Kathryn Haglich ’19, Modeling and Detecting Cancerous Cell Free DNA – Advisor Prof. Liebner

Class of 2018

  • Oanh Doan ’18, Impact of Neighborhood Quality on Airbnb Prices (joint with Economics) – Advisors Prof. Liebner & Prof. Stifel
  • Morgan Hoeft ’18, An Analysis of the Use of of Starting Pitchers in Major League Baseball – Advisor Prof. Liebner
  • Samantha Miller-Brown ’18, Wedderburn’s Theorem and the Representations of \(S_n\) – Advisor Prof. Bloom
  • Joshua Radack ’18, Improving Baseball Lineups with Markov Chain Monte Carlo – Advisor Prof. Liebner
  • M. E. Shelton ’18,  Using Neural Networks to Evaluate Policy Implications on the Treatment of Multiple Sclerosis – Advisor Prof. Hammarsten
  • Dana J. Smith ’18, Studying income inequality via innovative estimation methods: a case study in Latin America – Advisor Prof Root
  • Emily Smith ’18, Medical Marijuana Laws and Their Effect on Opioid-Related Mortality (joint with Economics) – Advisors Prof. Liebner & Prof. Averett
  • Xiaoshi Wang ’18, The Stretch Factor of the Delaunay Triangulation – Advisor Prof. McMahon

Class of 2017

  • Joshua Arfin ’17, Reweighting Schemes for Bootstrapping U-Statistics: An Empirical Investigation for Practitioners – Advisor Prof. Gaugler
  • Tamerlane Asher ’17, What Have You Done for Me Lately?  A Model of Past Performance on Major League Baseball Player Compensation (joint with Economics) – Advisors Prof. Liebner & Prof. Larson
  • Sonia Bhala ’17, Effects of Quantitative Literacy on Healthcare Decision-Making: An Aural Context – Advisor Prof. Root
  • Blake Bortnick ’17, Modules, Vector Spaces, Rings and Decomposition –  Advisor Prof. McMahon
  • My Bui ’17, Stochastic Volatility Option-pricing Models and
    Bayesian Parameter Estimation (joint with Economics) – Advisors Prof. Lu & Prof. Kelly
  • Benjamin Draves ’17, Treelet Covariance Smoothers – Advisor Prof. Gaugler
  • Andrew Eickemeyer, ’17: A Tour of Classical Results on Minimal surfaces: On the Plateau Problem and Osserman’s Theorem on the Gauss Map, Advisor Professor Corvino
  • Dehua Sun ’17, Measuring an NBA Player’s Impact Outside the Box Score – Advisor Prof. Liebner

Class of 2016

  • Jawad Awan ’16 (joint with Economics), Volatility Surfaces – Advisors Prof. Lu & Prof. Chambers
  • Kaitlin Geraghty ’16, Using LEGO robots to improve middle school math achievement – Advisor Prof. Root
  • Jason Saied ’16, Outer Automorphisms and Transitive Actions of \( S_6 \) – Advisor Prof. McMahon
  • Dantong Zhu ’16,  Combinatorial ways of understanding automorphisms of \(S_6\) – Advisor Prof. Gordon

Class of 2015

  • Anni Gao ’15: Hidden Markov Models: Theory and Application – Advisor Prof. Fisher
  • Yemai Liu ’15: A Brief History of Linear Algebra and Two Important Theorems – Advisor Prof. Traldi
  • Juan Posso ’15: A Tour of Geometric Measure Theory – Advisor Prof. Corvino
  • Patrick Pozzi ’15: A Monte Carlo Investigation of the Behavior of Information Criteria for Model Selection in repeated Measures Models – Advisor Prof. Gaugler
  • Bridget Rauch ’15: The Perception of an Extortionate Strategy as a Human Opponent within the Iterated Prisoners’ Dilemma (joint with Psychology) – Advisors Profs. Root & Talarico

Class of 2014

  • Rachel Gordon ’14: Techniques and Applications of the Traveling Salesman Problem – Advisor Prof. Stonesifer
  • Linyi Jia ’14: Life Contingency Models and an Epidemiological Application – Advisor Prof. Fisher
  • Shannon Nitroy ’14: A Study of a New Curriculum: The Effect of Easton Weed and Seed’s ‘Summer Nights’ Program on Summer Learning Loss (joint with Economics) – Advisors Profs. Liebner & Ruebeck
  • Michael Pinkard ’14: The Min-Oo Conjecture – Advisor Prof. Corvino

Class of 2013

  • Andrew Brady ’13: Density Estimation through Bayesian Regression Splines – Advisor Prof. Liebner
  • Bonnie Harvey ’13: Using Markov Models to Estimate the NHL Scoring Rate – Advisor Prof. Liebner
  • Christopher Miles ’13: Network Coding Theory And Matroid Representability (joint with ECE) – Advisors Profs. Gordon & Jouny
  • Liang Zhang ’13: Cyclic Covers of Knot Complements and the Alexander Polynomial – Advisor Prof. Zulli
  • Rujie Zhou ’13: Markovian Models In Insurance With Applications In Joint-Life Mortality – Advisor Prof. Fisher

Class of 2012

  • Bidur Dahal ’12: A Survey of Tutte Polynomials and T-uniqueness – Advisors Profs. Gordon & Traldi
  • Felix Hutchison ’12: Neuron Modeling and Spiking Network Realization (joint with ECE) – Advisors Profs. Hornfeck & Root
  • Jiaqi Li ’12: Survival Analysis: A Theoretical Understanding and its Application to Breast Cancer – Advisor Prof. Teboh-Ewungkem
  • Kelly Sullivan ’12: Mathematical Exploration of Sudoku with an Emphasis on the 4×4 Case – Advisor Prof. McMahon
  • Heidi Verheggen ’12: Two Open Problems in Diophantine Analysis – Advisor Prof. Smith

Class of 2011

  • Farhan Abedin ’11: The Riemannian Positive Mass Theorem – Advisor Prof. Corvino
  • Ramona Fittipaldi ’11: Exploring Outer Automorphisms in S6 through Geometric Shapes – Advisor Prof. McMahon
  • Rachel Ingber ’11: Gifts, Gift Cards, Deadweight loss: Using the Holiday Helpers Program to Improve the Economic Benefit of the Holiday Season (joint with Economics) – Advisors Profs. Liebner & Ruebeck
  • Peiyuan Mao ’11: Invariant Subspaces of Some Operators in Hilbert Space – Advisor Prof. Hill
  • Peter McGrath ’11: Lattices, Lattice Reduction, and the LLL algorithm – Advisor Prof. Smith
  • Alyssa Smith ’11: Quantitative Reasoning for True Democracy (for an interdisciplinary major) – Advisor Prof. Root
  • Qi Sun ’11: Copula Correlation, Default Correlation, and Copula Method with Mixture Normal Model on Asset-Backed Security (joint with Economics) – Advisors Profs. Chambers & Lu

Class of 2010

  • Xing Yan ’10: Predicting the Volatility of the U.S. Housing Market: an Application of the GARCH model (joint with Economics) – Advisors: Profs. Chambers & Liebner
  • Jorge Sawyer ’10: Spaces, Rings, and Subsets of the Stone-Cech Compactification – Advisor Prof. Kimber
  • Shelvean Kapita ’10: An Introduction to Comparison Geometry – Advisor Prof. Corvino

Class of 2009

  • Jim Stoholski ’09: Analyzing Baseball Strategy through MCMC Simulations – Advisor Prof. Liebner
  • Shiliang Cui ’09: Martingales and Sequence Patterns Generated by a Markov Chain – Advisor Prof. Fisher
  • Joseph Dudek ’09: Robot Groups in Algebraic Topology – Advisor Prof. Meier
  • Ying Quan ’09: A Tree Model for Pricing Mortgages with Prepayment and Default Options (joint with Economics) – Advisors Profs. Chambers & Lu
  • Hayley Rosado ’09: Applications of Origami in Mathematics – Advisor Prof. Berkove

Class of 2008

  • George Armah ’08: Constructing Cayley Graphs of Coxeter Groups – Advisor Prof. McMahon
  • Kristen Mazur ’08: Permutation Groups – Advisor Prof. McMahon
  • Jinjin Qian ’08: An Analysis of Correlation in Copula’s Model of Pricing CDO’s (joint with the Economics and Business Department) – Advisors Profs. Chambers & Lu
  • Jordan Tirrell ’08: Color My Numbers: Van der Waerden’s Theorem – Advisor Prof. Gordon

Class of 2007

  • Lindsay M. Bryant ’07: A Copula Approach to Valuing Credit Default Obligations (joint with the Economics and Business Department) – Advisors: Profs. Kelly & Lu
  • Brian G. Kronenthal ’07: Combinatorial Game Theory: Analyzing Games with “Nimbers” – Advisor: Prof. Smith
  • Frank A. Patane ’07: A Brief Introduction to the Prime Number Theorem – Advisor: Prof. Kimber
  • Haotian Wu ’07: An Introduction to Hamilton’s Ricci Flow on Closed Surfaces and Three-Manifolds with Positive Ricci Curvature – Advisor: Prof. Corvino

Class of 2006

  • Stacey Altrichter ’06: Hamiltonian Dynamics of a Mechanical Example of Coupled Nonlinear Oscillators – Advisor: Prof. Root
  • Ibrahima Bah ’06: Space-Time Interactions from Virasoro and Kac-Moody Algebra (joint with Physics) – Advisor: Profs. Corvino & Novaco
  • Kari Barkley ’06: A Model of a Vertically Transmitted Disease with a Delay Due to Partial Immunity – Advisor: Prof. Hill
  • Jenna Bratz ’06: A Mathematical Model of a Vertically Transmitted Disease with a Maturation Delay – Advisor: Prof. Hill
  • Jacob Carson ’06: The Growth of Paths in Seifert-Weber Dodecahedral Space – Advisor: John Meier
  • Kevin Ehly ’06: Topology of the Reflection Poset – Advisor: Prof. Meier
  • Maureen Jackson ’06: The Mathematics Behind the Game of SET – Advisor: Prof. McMahon
  • Ekaterina Jager ’06: Space-Time Block Codes – Advisor: Prof. Smith
  • Alex Kadel ’06: Achieving Mutual Cooperation: An Investigation into Prisoner’s Dilemma and Other Non-Zero Sum Games – Advisor: Prof. Gordon
  • Erica Morabito ’06: Probabilistic Modeling of Biological Sequences – Advisor: Prof. Fisher
  • Brian Regan ’06: Game Theory and a Generalization of Cooperative Games – Advisor: Prof. Gordon
  • Gregory P. Rodebaugh ’06: Lagrangian Vortex/Impulse Method Applied to a Sunfish (joint with Mechanical Engineering) – Advisor: Prof. Root
  • Jose Tano ’06: A Non-Fiction Prediction of Fiction : An Economic Model of Hardcover Novels (joint with Economics and Business) – Advisor: Prof. Bruggink

Class of 2005

  • Farhan Ahmed ’05: Pruning algorithm to reduce the search space of the Smith-Waterman algorithm & kernel extensions to the uC/OS-II Real-Time Operating System (joint with ECE) – Advisors: Profs. Gum & Nestor
  • Prince Chidyagwai ’05: Convergence of Fourier Series – Advisor: Prof. Hill
  • Gregory Francos ’05: An Introduction to Matroid Theory and Invariants – Advisor: Prof. Gordon
  • Usman Khan ’05: A Binomial Tree Approach to Price Callable Convertible Bonds – Advisor: Prof. Lu
  • Robert McEwen ’05: Algorithms for Recursively Generating Ortho-projections – Advisor: Prof. Zulli
  • Trent Mohney ’05: The Poisson Point Process and Applications – Advisor: Prof. Fisher
  • Kevin Penderghest ’05: The Unilateral Shift Operator – Advisor: Prof. Hill
  • Blerta Shtylla ’05: Newton’s Method with Stochastic Perturbations of the First Derivative – Advisors: Prof. Berkove & Root
  • Katharine Wolchik ’05: Stock Portfolio Continuous Trading Strategies by Simulation – Advisor: Prof. Lu

Class of 2004

  • Carrie Abildgaard ’04: The Markowitz Model, Transaction Costs, and Utility Functions in the Theory of Financial Decision Making – Advisor: Prof. Smith
  • Elisabeth Edwards ’04: Isometries and Wallpaper Groups – Advisor: Prof. Gordon
  • Douglas Schiz ’04: An Econometric Location And Gate Revenue Model For The National Football League (joint with Economics and Business) – Advisor: Bruggink

Class of 2003

  • Alexandru Balan ’03: An Enhanced Approach to Network Reliability Using Boolean Algebra (joint with Computer Science) – Advisors: Profs. Liew & Traldi
  • Joshua Grubman ’03: A Comparison of Relative Abilities of Multiple Regression Analysis and Artificial Neural Networks to Predict House Prices in a Hedonic Model (joint with Economics and Business) – Advisor: Bruggink
  • Lazar Nikolic ’03: The Generalized Riemann Integral – Advisor: Prof. Hill
  • Christopher Reich ’03: The Effects of U.S. News and World Report Annual College Rankings on Top, Private National Universities and Liberal Arts Colleges (joint with Economics and Business) – Advisor: Bruggink
  • Crystal Taylor ’03: Pareto Efficient Exchange and Urban Development (joint with Economics and Business) – Advisors: Profs. Hutchinson, Gordon & McMahon

Class of 2002

  • Ned Allis ’02: Public Key Cryptography and Factoring – Advisor: Prof. Reiter
  • Lindsay Carifi ’02: Markowitz Model: Finding the Efficient Frontier Using the Current Stock Market – Advisors: Profs. Handy & Lu
  • Andrew Colton ’02: A Mathematical Model of an Immunological Experiment – Advisor: Prof. Gorman
  • Steven A. DiMauro ’02: An Introduction to Game Theory and Variations in the Game of Nim – Advisor: Prof. Smith
  • Timothy A. Fargus ’02: Knot Theory: The Jones Polynomial and the Knot Group – Advisor: Prof. Zulli
  • Nicholas Jacobi ’02: Dynamical Systems and Chaos – Advisor: Prof. Yuster

Class of 2001

  • Bruce Adcock ’01: Fractional Derivatives – Advisor: Prof. Berkove
  • Sarah Bellows ’01: Measuring Productivity in the Labor Market: The Impact of the Free Agent Year on Baseball Players (joint with Economics and Business) – Advisor: Bruggink
  • Mark Coslett ’01: The Magic Behind the Black-Scholes Option Pricing Model – Advisor: Prof. Lu
  • Jeffrey P. Dumont ’01: The 3x+1 Problem, Generalizations and Visualization – Advisor: Prof. Reiter

Class of 2000

  • Paul Harmon ’00: Markov Chains: Theory and Applications – Advisor: Prof. Fisher