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Senior Theses from 2011

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

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Combinatorial Interpretations of Fibonomial Identities, Elizabeth Reiland

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

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Continued Fractions: A New Form, Donald Lee Wiyninger III

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Simulations of Surfactant Spreading, Jeffrey Wong

Senior Theses from 2010

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

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Combinatorial Proofs Using Complex Weights, Bo Chen

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

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Optimizing Restaurant Reservation Scheduling, Jacob Feldman

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Algebraic Reasoning in Elementary School Students, Ivan Hernandez

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Group Frames and Partially Ranked Data, Kwang B. Ketcham

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

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Arithmetic on Specializable Continued Fractions, Ross C. Merriam

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

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

Senior Theses from 2009

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

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Abelian Sandpile Model on Symmetric Graphs, Natalie Durgin

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Exploring Agreeability in Tree Societies, Sarah Fletcher

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Mathematical Model of the Chronic Lymphocytic Leukemia Microenvironment, Ben Fogelson

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Locality and Complexity in Path Search, Andrew Hunter

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Fast Matrix Multiplication via Group Actions, Hendrik Orem

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

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

Senior Theses from 2008

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Boundary Cycles in Random Triangulated Surfaces, Kevin Fleming

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Wavelets and Wavelet Sets, Sara Gussin

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Intrinsic Linking and Knotting of Graphs, Kenji Kozai

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

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Dot Product Representations of Graphs, Gregory Minton

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

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Functions of the Binomial Coefficient, Sean Plott

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Rigid Divisibility Sequences Generated by Polynomial Iteration, Brian Rice

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

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

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Formation of Labyrinth Patterns in Langmuir Films, George Tucker

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Graph Linear Complexity, Jason Winerip

Senior Theses from 2007

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

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Hole Closure in Langmuir Fluid Monolayers, Kazh Brito

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

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Algebra and Phylogenetic Trees, Michael Hansen

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Understanding Counterexamples to Lubin's Conjecture, Andrea Heald

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

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Special Cases of Carry Propagation, Alexander Izsak

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

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

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Effective Cost Allocation for Deterrence of Terrorists, Eugene Lee Quan

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

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An ODE Model of Biochemotherapy Treatment for Cancer, James Moore

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Radial Solutions to an Elliptic Boundary Valued Problem, Ivan Ventura

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A Tiling Approach to Chebyshev Polynomials, Daniel Walton

Senior Theses from 2006

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A Fast Fourier Transform for the Symmetric Group, Tristan Brand

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The Negs and Regs of Continued Fractions, Alexander Eustis

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

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Kolmogorov Complexity of Graphs, John Hearn

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

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Optimal Control of a Building During an Earthquake, Kenneth Maples

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Matrix Representation of Knot and Link Groups, Jessica May

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

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An Exploration in Subtropical Algebra, Nikolas Rauh

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Mathematical Models of Image Processing, Tyler Seacrest

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

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

Senior Theses from 2005

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

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Noncommutative Geometry, Steven Avery

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An Investigation of Rupture in Thin Fluid Films, Robin Baur

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Connections Between Voting Theory and Graph Theory, Deborah Berg

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

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An Algebraic Approach to Voting Theory, Zajj Daugherty

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

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Constructing Phylogenetic Trees from Subsplits, Akemi Kashiwada

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

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

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Cesaro Limits of Analytically Perturbed Stochastic Matrices, Jason Murcko

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

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Extensions of Graph Pebbling, Carl Yerger

Senior Theses from 2004

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Separating Sets for Finite Groups, Melissa Banister

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Representation Theoretical Methods in Image Processing, William Chang

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Representation Theoretical Approach to n-Candidate Voting, Grant Clifford

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Toeplitz Operators on Locally Compact Abelian Groups, David Gaebler

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Alexander Polynomials of Tunnel Number One Knots, Robert Gaebler

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Modeling Cancer Cell Response to Immunotherapy, Eric Harley

Senior Theses from 2003

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

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Modelling Advection and Diffusion in Microchannels, Dan Beutel

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Covering Numbers of the Cubes, Adam Bliss

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Modeling Moving Droplets: A Precursor Film Approach, Benjamin Bryant

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

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

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

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

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

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

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The Conformal Center of a Triangle or Quadrilateral, Andrew Iannaccone

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Ridge Coarsening in Evaporatively Driven Climbing Films, Peter Lamb

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Braids and Juggling Patterns, Matthew Macauley

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Eigenvalue Etch-A-Sketch, Jessica Nelson

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Turbulence, Magnetics, and Closure Equations, Jane Pratt

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

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

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Combinatorial Proofs of Congruences, Jeremy Rouse

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Geometry and Topology of the Minkowski Product, Micah Smukler

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Minkowski Actions of Quaternion Sets and their Applications, Kira Sushkoff