### Senior Theses from 2015

Synthesis of the Tetracyclic Scaffolds of the Endiandric Acids, Eun Bin Go

A Combinatorial Exploration of Elliptic Curves, Matthew Lam

Chromatic Polynomials and Orbital Chromatic Polynomials and their Roots, Jazmin Ortiz

An Exposition of Kasteleyn's Solution of the Dimer Model, Eric Stucky

Perturbation Dynamics on Moving Chains, Ksenia V. Zakirova

### Senior Theses from 2014

Experimental Realization of Slowly Rotating Modes of Light, Fangzhao A. An

There and Back Again: Elliptic Curves, Modular Forms, and L-Functions, Allison F. Arnold-Roksandich

A Mathematical Framework for Unmanned Aerial Vehicle Obstacle Avoidance, Sorathan Chaturapruek

Infinitely Many Rotationally Symmetric Solutions to a Class of Semilinear Laplace-Beltrami Equations on the Unit Sphere, Emily M. Fischer

Characterizing Forced Communication in Networks, Samuel C. Gutekunst

Energy-Driven Pattern Formation in Planar Dipole-Dipole Systems, Jaron P. Kent-Dobias

A New Subgroup Chain for the Finite Affine Group, David Alan Lingenbrink Jr.

Fast Algorithms for Analyzing Partially Ranked Data, Matthew McDermott

Experiments on Surfactants and Thin Fluid Films, Peter Megson

Reed's Conjecture and Cycle-Power Graphs, Alexa Serrato

Cycle lengths of θ-biased random permutations, Tongjia Shi

Using Topology to Explore Mathematics Education Reform, Carling Sugarman

Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem, Jeremy Usatine

### Senior Theses from 2013

A Discrete Approach to the Poincare-Miranda Theorem, Connor Thomas Ahlbach

On Toric Symmetry of P1 x P2, Olivia D. Beckwith

Voter Compatibility In Interval Societies, Rosalie J. Carlson

Extortion and Evolution in the Iterated Prisoner's Dilemma, Michael J. Earnest

Chip Firing Games and Riemann-Roch Properties for Directed Graphs, Joshua Z. Gaslowitz

Simulations of Surfactant Driven Thin Film Flow, Shreyas Kumar

Analysis of Time-Dependent Integrodifference Population Models, Taylor J. McAdam

Lines in Tropical Quadrics, Kevin O'Neill

Hypergraph Capacity with Applications to Matrix Multiplication, John Lee Thompson Peebles Jr.

Mathematical Knowledge for Teaching and Visualizing Differential Geometry, Nathan Pinsky

A Comparison and Catalog of Intrinsic Tumor Growth Models, Elizabeth A. Sarapata

Structured Matrices and the Algebra of Displacement Operators, Ryan Takahashi

### Senior Theses from 2012

Approval Voting Theory with Multiple Levels of Approval, Craig Burkhart

Nonlinear Wave Equations and Solitary Wave Solutions in Mathematical Physics, Trevor Caldwell

Counting Vertices in Isohedral Tilings, John Choi

A Refined Saddle Point Theorem and Applications, Harris Enniss

Approval Voting in Box Societies, Patrick Eschenfeldt

Switching Between Cooperation and Competition in Social Selection, August Guang

A Combinatorial Approach to $r$-Fibonacci Numbers, Curtis Heberle

Searching Stars for a Moving Hider, Jennifer Iglesias

Flatterland: The Play, Kym Louie

Uniquely Solvable Puzzles and Fast Matrix Multiplication, Palmer Mebane

Explorations of the Aldous Order on Representations of the Symmetric Group, Jack Newhouse

Detecting Covert Members of Terrorist Networks, Alice Paul

Algebraic Methods for Log-Linear Models, Aaron Pribadi

Gromov-Witten Theory of Blowups of Toric Threefolds, Dhruv Ranganathan

Analysis of Swarm Behavior in Two Dimensions, Louis Ryan

Russian Mathematical Pedagogy in Reasoning Mind, Maia Valcarce

### Senior Theses from 2011

Finding the Beat in Music: Using Adaptive Oscillators, Kate M. Burgers

Swarm Control Through Symmetry and Distribution Characterization, Georgi Dinolov

Markov Bases for Noncommutative Harmonic Analysis of Partially Ranked Data, Ann Johnston

Group Actions and Divisors on Tropical Curves, Max B. Kutler

Extending List Colorings of Planar Graphs, Sarah Loeb

Martingale Couplings and Bounds on Tails of Probability Distributions, Kyle Luh

Verification of Solutions to the Sensor Location Problem, Chandler May

Comparing the Cognitive Demand of Traditional and Reform Algebra 1 Textbooks, Allison M. Park

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