Students who write theses in mathematics spend an entire academic year working on an in-depth study with the help and direction of a faculty member. In addition to writing a thesis, each student gives a seminar late in spring semester. The thesis seminar weeks are busy and exciting times around the department.

Copies of some past student theses are located in the Seeley Mudd library.

2022

  • Anna Dietrich worked with Prof. Rob Benedetto on "Iteration of Rational Functions with Colliding Critical Points"
  • Leah Johnson worked with Prof. Greg Call on "Elliptic Curves and the Ideal Class Pairing"
  • Sophie Launsbach worked with Prof. Sema Gunturkun on "Neural Codes and Neural Rings"
  • Holden Lee worked with Prof. Harris Daniels on "Identifying Complement Subgroups in Finite Group Extensions"
  • Elizabeth (Baz) Pratt worked with Prof. Greg Call on "On The Geometry of Elliptic Pairs"
  • Audrey Rosevear worked with Prof. Michael Ching on "Taut Foliations and Minimal Genus Surfaces in 3 and 4 Dimensions"
  • Amaya Smole worked with Prof. Tanya Leise on "A Network Model for COVID-19"
  • Noah Solomon worked with Professor Nathan Pflueger on "Chip-Firing on Twice-Marked Graphs of Genus 2"

2021

  • Jonah Botvinick-Greenhouse worked with Prof. Ryan Alvarado on "An Introduction to the Theory of the Ergodic Partition"
  • Lianbi Ji worked with Prof. Greg Call on "Torsion Subgroups of Elliptic Curves over Q and over Quadratic Number Fields"
  • Yuuna Klindziuk worked with Prof. Kara Yacoubou Djima on "Fourier Analysis on Graphs"
  • Emily Minus worked with Prof. Tanya Leise on "A Compartmental Model of COVID-19"
  • Andrew Tawfeek worked with Prof. Ivan Contreras on "Discrete Morse Theory: Enumeration of Discrete Gradient Vector Fields"
  • Justin Warring worked with Prof. Amanda Folsom on "On 'Strange' Identities and Quantum Modular Forms: q-hypergeometric Identities and Modular Properties of a Peculiar Function due to Kontsevich"
  • Calvin Woods worked with Prof. Amalia Culiuc on "Lp Weighted Estimates and Matrix Weights"

2020

  • Gregory Carroll worked with Prof. Robert Benedetto on "Prolegomenon to Hrushovski's Stabilizer Theorem"
  • Cameron Chandler worked with Prof. Nathan Pflueger on "Riemann-Roch and Displacement on Chains of Cycles"
  • Sai Chauhan worked with Prof. Yongheng Zhang on "Introduction to the Kontsevich Integral"
  • Max Fox-Jurkowitz worked with Prof. Ryan Alvarado on "Set Representation Using Convex Analysis"
  • Joseph Lupo worked with Prof. Robert Benedetto on "Dynamical Galois Groups, Monodromy Groups, and Three Galois Correspondences"
  • Alexander Mangiafico worked with Prof. Ivan Contreras on "Persistent Homology in Topological Data Analysis"
  • Shashank Sule worked with Prof. Karamatou Yacoubou Djima on "Two Multiresolution Frameworks on Graphs"

2019

  • Katherine Finnerty worked with Prof. Harris Daniels on "Representability of Primes as Sums of Squares An Introduction to Class Field Theory"
  • Caroline MacGillivray worked with Prof. Gregory Call on "Binary Quadratic Forms and the Class Group"
  • Ellie Thieu worked with Prof. David Cox on "The Riemann-Roch Theorem:  Analytic and Algebraic"

2018

  • Michael Barnett worked with Prof. Robert Benedetto on “Modular and Jacobi Forms”
  • Jennifer Cain worked with Prof. Gabriel Sosa on “Detecting Normal Toric Rings Using Gröbner Bases”
  • Lily Fang worked with Prof. Jamie Juul on “An Arboreal Galois Group of a PCF Quadratic Polynomial”
  • Seong Eun Jung worked with Prof. Harris Daniels on “Galois Representations Associated to Torsion Points of Elliptic Curves”
  • Nathanael Lane worked with Prof. David Cox on “Stewart-Gough Kinematics and Homotopy Continuation
  • Fernando Liu Lopez worked with Prof. Yusra Naqvi on “Coxeter Groups from a Combinatorial and Geometric Perspective”
  • Obinna Ukogu worked with Prof. Tanya Leise on “Using Queueing Theory to Model Enzyme-Substrate Interactions”
  • William Wesley worked with Prof. Amanda Folsom on “Combinatorial Proofs of Ramanujan’s Congruences”
  • Bowen Yang worked with Prof. Gregory Call on “Mordell’s Conjecture Canonical Heights and Vojta’s Inequality”
  • Hui Xu worked with Prof. Yao Li (UMass, Amherst) and Prof. Gregory Call on “Comparison of Stochastic Neural Field Models with Corresponding Mean-field Approximations.

2017

  • Fraser Binns worked with Prof. Michael Ching on "The Kervaire Invariant of the Lie-framed Torus"

  • Felipe Pereira Debayle worked with Prof. David Cox on "Interactions between Commutative Algebra, Galois Theory, and Representation Theory"
  • Paul Gramieri worked with Prof. Rob Benedetto on "Applications of Sieve Methods"
  • Caleb Ki worked with Prof. Nick Horton on "Handling Missing Data in Randomized Clinical Trials"
  • Levi Lee worked with Prof. Amy Wagaman on "A Simulation Study Using Graph Models to Fit Social Networks"

  • Emily Masten worked with Prof. Gabriel Sosa on "Matroid Theory and Its Application to Combinatorial Optimization"
  • Jacob Pfau worked with Prof. Yusra Naqvi on "Algebraic and Topological properties of Graph Products"

  • Yen Nhi Truong Vu worked with Prof. Amanda Folsom on "On the Modular Transformations and Asymptotic Behaviors of Mock Modular Forms"

2016

  • Becky Danning worked with Prof. Tanya Leise on "Measuring Centrality in Undirected Valued Networks"
  • Kyle Ferendo worked with Prof. Michael Ching on "The Maximal and Free (∞,n)-Categories of an (∞,n+1)-Category"
  • Hannah Goodwillie worked with Prof. Harris Daniels on "The Ranks of Elliptic Curves with n-isogenies"
  • Cole Hawkins worked with Prof. David Cox on "Boij-Soderberg Theory on Particular Classes of Modules"

2015

  • Dvij Bajpai worked with Prof. Dan Velleman on “Topological Predictors and T-Anonymous Predictors in Hat Problems”
  • Kush Chandra worked with Prof. Greg Call on “The Elliptic Curve Discrete Logarithm Problem and the Weil Pairing”
  • Stephen Hetterich worked with Prof. Rob Benedetto on “The Group of Rational Points on Elliptic Curves”
  • Namyi Kang worked with Prof. Tanya Leise on “A Comparison of Mathematical Models of Decision Making Using Eye Tracking Analysis”
  • Edward Kim worked with Prof. Amanda Folsom on “An Application of the circle Method in Analytic Number Theory to the Partition Function”
  • Sage O’Neil worked with Prof. David Cox on “Group Representations and Applications to Chemistry”
  • Darius Onul worked with Prof. Amy Wagaman on “Using Hidden Markov Models to Predict Stock Pricing”
  • Lucia Minah Yang worked with Prof. Jacqueline Dresch on “An Investigation of Numerical Methods of Solving Linear Problems (Ax=b)”

2014

  • Ruqian Chen worked with Prof. David Cox on “Classification of transitive solvable imprimitive subgroups of symmetric groups of prime squared degrees”
  • Alexander W. Diones worked with Prof. James Henle (Smith College) and Prof. Dan Velleman on “Forcing over Partial Models of ZFC: The Independence of the Continuum Hypothesis”
  • Shanghui Li worked with Prof. Tanya Leise on “Application of Wavelet Methods in the Analysis of Rhythmic Activity and Coupling Relationships in the Suprachiasmatic Nucleus”
  • Yang Xiao worked with Prof. Michael Ching and Prof. Rob Benedetto on “1-2 Quadruples in Self-Similar Unbounded Apollonian Circle Packings”

2013

  • Andrew Erskine worked with Prof. David Cox on "Binomial Edge Ideals and the Characterization of Closed Graphs"
  • Anya Goldberg worked with Prof. Robert Benedetto on "The Hasse-Minkowski Theorem on Quadratic Forms"
  • Taylor Grant-Knight worked with Prof. Daniel Velleman on "Categorizing Computability:  A Study of Recursively Enumerable Degrees"
  • R. Henry Weaver worked with Prof. Daniel Velleman on "Elusive Points:  Topics in Constructive Analysis"
  • David (Hao) Zhang worked with Prof. Amy Wagaman on "Compositional Data Analysis"

2012

  • Trevor Hyde worked with Prof. David Cox on "Dividing the Lemniscate An interplay of elliptic functions, class field theory, and complex multiplication"
  • Brian Kim worked with Prof. Shu-Min Liao and Prof. Daeyoung Kim (UMass) on "Perfect Pitch:  An analysis of Pitchers Using Pitch F/X Data"
  • Ariah Klages-Mundt worked with Prof. Robert Benedetto and Prof. Paul Gunnells (UMass) on "Computing Elliptic Curves over Complex Cubic Fields"
  • Yordanka Kovacheva worked with Prof. Robert Benedetto on "Serre Duality"
  • Dang Trinh worked with Prof. Tanya Leise on "Stock Volatilities:  Long Memory and Common Factors"

2011

  • Adam Humphries worked with Prof. Velleman on "ρ-GAPq-CSP is NP-hard"
  • Samuel Smith worked with Prof. R. Benedetto on "Measure-Theoretic Entropy, Topological Entropy, and the Variational Principle"

2010

  • Ben Krause worked with Prof. Cox on "Plane Curves and their Singularities"
  • Michael Kreisel worked with Prof. Cox of Amherst and Prof. Rob Kusner (UMass) on "A Classification of Euclidean Surfaces with Conical Singularities"
  • Sam Schiavone worked with Prof. Leise on "Cloaking and Invisibility By Change Of Variables"
  • Andrey T. Tagarev worked with Prof. Leise on "Speech Recognition with Artificial Neural Networks"

2009

  • Maya Miller-Vedam worked with Prof. Benedetto on "The Riemann Hypothesis for Curves Over Finite Fields"
  • Stephen O. Oloo worked with Prof. Cox on "The Gelfand Representation of Unital Commutative Banach Algebras"

2008

  • Benjamin Dickman worked with Prof. Benedetto on "On a Theorem of Dwork"
  • Sasha E. Joseph worked with Prof. Benedetto on "Algebraic Number Theory and Density Theorems"
  • Jeremy Newton worked with Prof. Tranbarger on "Prototype Patterns of a Poisson Process"
  • Gina Turrini worked with Prof. Tranbarger on "Sex and Statistics:  A Bootstrap Study Using Multiple Logistic Regressions Modeling and Odds Ratios to Explore Sexual Attitudes and Behaviors in the National Survey of Family Growth"
  • Austin Yim worked with Professor Velleman on "Relevance Logic and Relevant Arithmetic"

2007

  • Sarah G. Cotter worked with Prof. Velleman and Prof. Jim Henle (Smith College) on "Elementary Embeddings and Left-Distributive Algebras"
  • Benjamin Purkis worked with Prof. Cox on "Ergodic Theory and Continued Fractions"

 2006

  • Tsvetelina V. Petkova worked with Prof. Starr and Prof. Ruth Haas (Smith College) on "Nonisomorphic Graph Colorings"

 2005

  • Wing L. Mui worked with Prof. Cox on "An Introduction to Polynomial Knots"
  • Mathew A. Wechter worked with Prof. Starr on "An Analytic Proff of the Prime Number Theorem"

2004

  • Mihailis E. Diamantis worked with Prof. Velleman on "The Independence of the Continuum Hypothesis"
  • Andrew K. Gilette worked with Prof. Benedetto on "Searching for Small Canonical Heights: Finding A Minimum Speed Limit On the Road to Infinity"
  • Adam M. Lowrance worked with Prof. David Cox on "Solutions of Equations over Finite Fields"
  • Paul Reschke worked with Prof. Benedetto on "Rational Periodic and Preperiodic Points of Polynomial Functions"

2003

  • Richard P. Laurberg worked with Prof. Call on "A Primer on the Birch-Swinnerton-Dyer Conjecture"
  • Michael A. Stevens worked with Prof. Call on "The Ideal Class Pairing on Elliptic Curves"

2002

  • Brian Carty worked with Prof. Velleman on "Non-Standard Times Call for Non-Standard Analysis: An Introduction to Infinitesimal Reasoning"

2001

  • William E. Gryc worked with Prof. Cox on "Wavelets and Multiresolution Analysis"
  • Anushka Krishnachander worked with Prof. Velleman on "An Introduction to Combinatorial Game Theory and the Game of Hackenbush"

2000

  • James D. Hunter worked with Prof. Velleman on "On the Structure of the Recursively Enumerable Degrees"
  • Thomas B. Wexler worked with Prof. Starr and Prof. Haas (Smith College) on "Some Results on Signed Domination in Graphs"

1999

  • David S. Spiegel worked with Prof. Cox on "Symmetries of the Helmholtz Equation"

1998

  • Ben Brubaker worked with Prof. Cox on "An Investigation of Singularities of the Evolute"
  • Dan Golosovker worked with Prof. Call on "Preperiodic Points of Polynomials in Number Fields"
  • Spencer Hamblen worked with Prof. Call on "Calculating the Circle Pairing over Families of Elliptic Points"
  • Chris Hardin worked with Prof. Velleman on "Reverse Mathematics and the Mean Value Theorem"
  • Raphael Jones worked with Prof. Armacost on "The Frattini Subgroup"

1997

  • Chris Hale worked with Prof. Call on "Preperiodic Points of Morphisms over Function Fields"

1996

  • Lawrence Snyder worked with Prof. Starr and Prof. Haas (Smith College) on "Combinatorial Rigidity and the Path Decomposition of Isostatic Graphs"
  • Michael Stanfield worked with Prof. Cox on "Polynomial Equations and Abstract Algebra"
  • William Wasik worked with Prof. Velleman on "The Suslin Problem and Whitehead's Problem are Undecidable"