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## Recent Theses in Mathematics

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 student theses are located in the Seeley Mudd library.

### 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-GAP*q*-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"