Mathematics and Statistics

Recent Theses

Students who write theses 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 student theses are located in the Seeley Mudd library.

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"