#### Senior Theses from 2011

Noise, Delays, and Resonance in a Neural Network, Austin Quan

Combinatorial Interpretations of Fibonomial Identities, Elizabeth Reiland

Analytic and Numerical Studies of a Simple Model of Attractive-Repulsive Swarms, Andrew S. Ronan

Continued Fractions: A New Form, Donald Lee Wiyninger III

Simulations of Surfactant Spreading, Jeffrey Wong

#### Senior Theses from 2010

Minimal Circuits for Very Incompletely Specified Boolean Functions, Richard Strong Bowen

Combinatorial Proofs Using Complex Weights, Bo Chen

A Multistage Incidence Estimation Model for Diseases with Differential Mortality, Alyssa W. Dray

Optimizing Restaurant Reservation Scheduling, Jacob Feldman

Algebraic Reasoning in Elementary School Students, Ivan Hernandez

Group Frames and Partially Ranked Data, Kwang B. Ketcham

Understanding Voting for Committees Using Wreath Products, Stephen C. Lee

Arithmetic on Specializable Continued Fractions, Ross C. Merriam

Computational Feasibility of Increasing the Visibility of Vertices in Covert Networks, Yaniv J. Ovadia

A Nonlinear ODE Model of Tumor Growth and Effect of Immunotherapy and Chemotherapy Treatment in Colorectal Cancer, Hannah P. Savage

#### Senior Theses from 2009

Mathematical AIDS Epidemic Model: Preferential Anti-Retroviral Therapy Distribution in Resource Constrained Countries, Nadia Abuelezam

Abelian Sandpile Model on Symmetric Graphs, Natalie Durgin

Exploring Agreeability in Tree Societies, Sarah Fletcher

Mathematical Model of the Chronic Lymphocytic Leukemia Microenvironment, Ben Fogelson

Locality and Complexity in Path Search, Andrew Hunter

Fast Matrix Multiplication via Group Actions, Hendrik Orem

Existence of Continuous Solutions to a Semilinear Wave Equation, Ben Preskill

Branching Diagrams for Group Inclusions Induced by Field Inclusions, Tedodore Spaide

#### Senior Theses from 2008

Boundary Cycles in Random Triangulated Surfaces, Kevin Fleming

Wavelets and Wavelet Sets, Sara Gussin

Intrinsic Linking and Knotting of Graphs, Kenji Kozai

An Integrodifferential Equation Modeling 1-D Swarming Behavior, Andrew Leverentz

Dot Product Representations of Graphs, Gregory Minton

Characteristics of Optimal Solutions to the Sensor Location Problem, David Morrison

Functions of the Binomial Coefficient, Sean Plott

Rigid Divisibility Sequences Generated by Polynomial Iteration, Brian Rice

Approximating Solutions to Differential Equations via Fixed Point Theory, Douglas Rizzolo

Sperner's Lemma Implies Kakutani's Fixed Point Theorem, Mutiara Sondjaja

Formation of Labyrinth Patterns in Langmuir Films, George Tucker

Graph Linear Complexity, Jason Winerip

#### Senior Theses from 2007

Applications of the q-Binomial Coefficients to Counting Problems, Jonathan Azose

Hole Closure in Langmuir Fluid Monolayers, Kazh Brito

Analyzing Traveling Waves in a Viscoelastic Generalization of Burgers' Equation, Victor Camacho

Algebra and Phylogenetic Trees, Michael Hansen

Understanding Counterexamples to Lubin's Conjecture, Andrea Heald

Investigating the Use of Brainfingers in Children with Cerebral Palsy for Spatial-Motor Education, Nicholas Herman

Special Cases of Carry Propagation, Alexander Izsak

Voting Paradoxes Caused by Dropping Candidates in an Election, Marie Jameson

A Decimation-in-Frequency Fast-Fourier Transform for the Symmetric Group, Masanori Koyama

Effective Cost Allocation for Deterrence of Terrorists, Eugene Lee Quan

Infinitely Many Radial Solutions to a Superlinear Dirichlet Problem, Chee Meng Tan

An ODE Model of Biochemotherapy Treatment for Cancer, James Moore

Radial Solutions to an Elliptic Boundary Valued Problem, Ivan Ventura

A Tiling Approach to Chebyshev Polynomials, Daniel Walton

#### Senior Theses from 2006

A Fast Fourier Transform for the Symmetric Group, Tristan Brand

The Negs and Regs of Continued Fractions, Alexander Eustis

Turing Pattern Dynamics for Spatiotemporal Models with Growth and Curvature, Julijana Gjorgjieva

Kolmogorov Complexity of Graphs, John Hearn

Foraging Fruit Flies: Lagrangian and Eulerian Descriptions of Insect Swarming, Joesph Majkut

Optimal Control of a Building During an Earthquake, Kenneth Maples

Matrix Representation of Knot and Link Groups, Jessica May

The Singular Values of the Exponientiated Adjacency Matrixes of Broom-Tree Graphs, Tracy Powell

An Exploration in Subtropical Algebra, Nikolas Rauh

Mathematical Models of Image Processing, Tyler Seacrest

An Exploration of Riemann's Zeta Function and Its Application to the Theory of Prime Distribution, Elan Segarra

Succession, Invasion, & Coexistence: PDEs in Ecology, Simon Maccracken Stump

#### Senior Theses from 2005

Constructing a Matrix Representation of the Lie Group G2, Ruben Arenas

Noncommutative Geometry, Steven Avery

An Investigation of Rupture in Thin Fluid Films, Robin Baur

Connections Between Voting Theory and Graph Theory, Deborah Berg

Permutation Routing in the Hypercube and Grid Topologies, Tim Alan Carnes

An Algebraic Approach to Voting Theory, Zajj Daugherty

Solving for Volume-Minimizing Cycles in G2-Manifolds, Jeff Loren Jauregui

Constructing Phylogenetic Trees from Subsplits, Akemi Kashiwada

Generalized Julia Sets: An Extension of Cayley's Problem, Owen Lewis

Decimation-in-Frequency Fast Fourier Transforms for the Symmetric Group, Eric Malm

Cesaro Limits of Analytically Perturbed Stochastic Matrices, Jason Murcko

Combinatorial Consequences of Relatives of the Lusternik-Schnirelmann-Borsuk Theorem, Gwen Spencer

Extensions of Graph Pebbling, Carl Yerger

#### Senior Theses from 2004

Separating Sets for Finite Groups, Melissa Banister

Representation Theoretical Methods in Image Processing, William Chang

Representation Theoretical Approach to n-Candidate Voting, Grant Clifford

Toeplitz Operators on Locally Compact Abelian Groups, David Gaebler

Alexander Polynomials of Tunnel Number One Knots, Robert Gaebler

Modeling Cancer Cell Response to Immunotherapy, Eric Harley

#### Senior Theses from 2003

Convergence of Planar Domains and of Harmonic Measure Distribution Functions, Ariel Barton

Modelling Advection and Diffusion in Microchannels, Dan Beutel

Covering Numbers of the Cubes, Adam Bliss

Modeling Moving Droplets: A Precursor Film Approach, Benjamin Bryant

Shortest Path Problems: Multiple Paths in a Stochastic Graph, Melissa Chase

The Kapitza–Dirac Effect: An Approach from QED, David Clarke

A Combinatorial Analog of the Poincaré–Birkhoff Fixed Point Theorem, John Cloutier

An Eigenspace Approach to Isotropic Projections for Data on Binary Trees, Nate Eldredge

Fluid Drop Coalescence in a Hele-Shaw Cell, Daniel Gianotti

The Hausdorff Dimension of the Julia Set of Polynomials of the Form zd + c, Stephen Haas

The Conformal Center of a Triangle or Quadrilateral, Andrew Iannaccone

Ridge Coarsening in Evaporatively Driven Climbing Films, Peter Lamb

Braids and Juggling Patterns, Matthew Macauley

Eigenvalue Etch-A-Sketch, Jessica Nelson

Turbulence, Magnetics, and Closure Equations, Jane Pratt

Searching for Supersymmetric Cycles: A Quest for Cayley Manifolds in the Calabi–Yau 4-Torus, Christopher Pries

Designing Smooth Motions of Rigid Objects: Computing Curves in Lie Groups, Ross Monet Richardson

Combinatorial Proofs of Congruences, Jeremy Rouse

Geometry and Topology of the Minkowski Product, Micah Smukler

Minkowski Actions of Quaternion Sets and their Applications, Kira Sushkoff