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Student Research

Mathematics Menu
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  • Home
Recent Senior Projects in Mathematics
Photo by Scott Barrow

Recent Senior Projects in Mathematics

  • “Applications of Equivariant Topology in Cascading Makeev Problems” 
  • “Centroidal Voronoi Tessellations with Few Generator Points”
  • “Exploring Sequences of Tournament Graphs with Draws”
  • “The Mathematics of Cancer: Fitting the Gompertz Equation to Tumor Growth”

Full Texts of Senior Projects in Digital Commons

Past Senior Projects

  • 2019

    2019


    • Kate Blaine: Determinantal Conditions on Integer Splines
    • Chenyu Chang: Investigations of finding all stable solutions of Stable Marriage Problem
    • Corey Chang: Markov Chains in Music Composition
    • Danielle Degutz: Gerrymandering and the Impossibility of Fair Districting Systems
    • Jintao Fang: The Credit Scorecard Model
    • Jazlyn Johnson: An Algorithmic Approach to Detect Non-injectivity of the Partial Borda Count
    • Meagan Kenney: The Conditional Probability That an Elliptic Curve Has a Rational Subgroup of Order 5 or 7
    • Leah Leiner: Polygonal Analogues to Topological Tverberg-type and van Kampen-Flores-type Theorems
    • Shenze Li: Upper Bounds for the Number of Lattice Edges Needed to Represent 4-Regular Graphs as Lattice Graphs
    • Yushi Pan: From Black-Scholes Model to Pricing Models of American Options: A Performance Comparison
    • Eliot Roske: Analyzing Flow Free with One Pair of Dots
    • Maya Schwartz: Factorization Lengths in Numerical Monoids
    • Edward Skorupa: Time and Finance: An Exploration of Variance in the Black-Scholes Model
    • Ari Spiesberger: Supersymmetry and the Math of Adinkras
    • Sofia Thompson: Econometric Methods for Comparative Case Studies: Lessons From the Dominican Prison Reform
    • Rao Vinnakota: Predicting How People Vote from How They Tweet
    • Jade Waring: A Strength Test for the Borda Count
    • Hsin-Fang Wu: From Constant to Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models
    • Alexis Hao Zheng: Happy Numbers in Iterations of Degree 3
  • 2018

    2018


    • Samuel Baumgartner: Hamilton Paths in the Game of Flow
    • Teagan DeCusatis: Analyzing the Probabilistic Spread of a Virus on Various Networks
    • Yuan Jessica Liu: Graph Replacement Systems for Julia Sets of Quadratic Polynomials
    • Yuming Liu: Stock Price Forecasting Using Stochastic Processes and Machine Learning
    • Andres Mejia: Applications of Equivariant Topology In Cascading Makeev Problems
    • Avery Morris: From Random to Organized: The Architecture of Neural Networks During Development
    • Rachel Nalecz: An Implementation of the Solution to the Conjugacy Problem on Thompson's Group V
    • Nguyen Thuy Linh: Expected Value and Standard Deviation of the Center of Mass of Random Configurations
    • Odett Salcedo: Ties in Ranked Voting Systems
    • Peter Servatius: Concerning the Construction of Fourbar Linkages and Their Topological Configuration-Spaces
    • Kirill Shakhnovskiy: Centroidal Voronoi Tessellations with Few Generator Points
    • Yida Shao: Counting Trees in Ladder Graphs
    • Kaylynn Tran: Exploring Sequences of Tournament Graphs with Draws
    • Christian Yost: Time and Frequency Independent Manipulation of Audio in Real Time
    • Jialin Zhang: Hyperplanes Equipartition with Cascading Makeev Condition
    • Lingxin Zhao: A Stochastic Mass Function on the Edges of a Graph
  • 2017

    2017


    • Victoria Chayes: Maximal Quantum Effects Outside A Spinning Black Hole: An Exploration Of The Kerr Metric
    • Sarah Ghandour: Random Walks on Thomson’s Group F
    • Adrian Gillerman: Equipartitions Using Finite Fourier Analysis
    • Christopher Hawke: Quantifying the Affect of The Shift in Major League Baseball
    • Sadiki Lewis: Exploring Tournament Graphs and Their Win Sequences
    • Finnegan Muller-Hardy: The Expectation for the Center of Mass of Finite Interger Grids
    • Justin Shin: Envy-Free Fair Division With Two Players and Multiple Cakes
    • Stefan Stojanov: An Alternative Formulation for Nonnegative Matrix Factorization
    • Olivia Williams: Modeling Purple Sea Urchin and California Sheephead Populations in Channel Islands Kelp Forests
  • 2016

    2016


    • Margaret Allardice: Orthogonal Projections of Lattice Stick Knots
    • Samuel Audino: Associativity of Binary Operations on the Real Numbers
    • Taylor Boone: Abstractions and Analyses of Grid Games
    • Alexander Goodlad: Proof Theory: The Meta-Meta Framework of Mathematics
    • Christopher Gunnell: The Schur Factorization Property as it Applies to Subsets of the General Laguerre Polynomials
    • Cyril Kuhns: Public Key Cryptography with the Brin-Thompson Group 2V
    • Emmet Mahdavi: Integer Generalized Splines on the Diamond Graph
    • Najee McFarland-Drye: Winning Strategies in The Board Game
    • Eliana Miller: A binary integer programming approach for counting KenKen puzzles
    • Benjamin Moss: The Facilitation of Sound Waves Using Mathematical and Scientific Methods of Digital Signal Processing
    • Xiangying Shuai: Radical Recognition in Off-Line Handwritten Chinese Characters Using Non-Negative Matrix Factorization
    • Ningning Song: A Variational Approach to the Moving Sofa Problem
    • Zexi Song: Cutoff for Lamplighter Markov Chains on Prisms
    • Erin Stuckenbruck: Selecting the Average Alternative: Lose Big, Win Big, and Sum Big
    • Polina Vulakh: McKay Graphs and Modular Representation Theory
  • 2015

    2015


    • Emily Conant: Construction of a Nuclear Shell Model
    • Galen Dorpalen-Barry: Rational Tilings of the Unit Square
    • Rylan Gajek-Leonard: Irreducibility and Galois Properties of Lifts of Supersingular Polynomials
    • Ester Gjoni: Basis Criteria for n-cycle Integer Splines
    • Andy Huynh: Geometry of adinkra embeddings
    • Mohd Ahnaf Khan: Pre-processing for K-means Clustering Algorithm
    • Christiane Koffi: Exploring a Generalized Partial Borda Count Voting System
    • Erik Lovece: Extending the Planar Voronoi Nets of a Set of 6 Sites to Planar Voronoi Nets of a Set of 7 Sites
    • Sharma Maharaj: Resistance on Infinite Networks
    • Van Mai Nguyen Thi: Development and Optimization of a Two-View Model for Anamorphic Projections on Planar Surfaces
    • Joanna Regan: Inferring Connectivity of Neural Networks during Collision Avoidance in Xenopus Tadpoles
    • Jake Weissman: Modeling Stochastic Traps: The Evolution of Preference in a Temporally Heterogeneous Ecological Trap
    • Shuyi Weng: Homeomorphism Groups of Fractals
    • Noah Winslow: On the Realizability and Rigidity of Graphs in Higher Dimensions
    • Xingye Zhang: Aye or Nay: A Study of Opinion Exchange Dynamics
  • 2014

    2014


    • Siddhartha Baral: Investigating Occupancy Using Maximum Likelihood Estimation
    • Celeste Cass: Robots Switching Positions on Graphs
    • Zena Coles: Counting Points on Conics Over Finite Fields
    • Carlos Gadelha: Option Pricing Model on the Discrete World
    • Yushan Jiang: The Analysis of Probabilistic Spread on Complete Graphs
    • Benjamin Kane: The Probabilistic Spread of a Virus on a Network
    • Lara Merling: Fighting Fires on Semi-Regular Tesselations
    • Rajasri Narasimhan: Voter Empowerment and an Exploration of Partial Borda Count
    • Linh Pham: From String Theory to Elliptic Curves over Finite Field Fp
    • Page Redding: Deformations of Conic Sections
    • Carmen Rodriguez: Graphical Model for Three-Way Living Donor Kidney Exchange
    • Nicole Rosato: Fire Containment on Layered In nite Grids
    • Kimberly Sargeant: A Dinner for Two: Winning the Ethiopian Dinner Game
  • 2013

    2013


    • Ian Barnett: Mod 2 Homology of Posets
    • Abhinanda Bhattacharyya: Forbidden Minors for a Pursuit Game on Graphs
    • Lara Bradford: Enumerating Chains for Partially Ordered Sets
    • Emily Carlson: A model of Charge Transport in a Dye-Sensitized Solar Cell
    • Fiona Do Thi: The Firefighter Problem on Grids: Resistant Networks
    • Joe Foy: Inscribed Squares in Taxicab Polygons
    • Nabil Hossain: Implementation of the Solution to the Conjugacy Problem in Thompson's Groups
    • Matt Hughes: Galois Representations from Non-Torsion Points on Elliptic Curves
    • Ruth Lakew: Gaussian Primes Path to Infinity
    • Weiying Liu: Distribution of Prime Numbers in Short Intervals
    • Iliana Maifeld-Carucci: Designing DNA Nanostructures: Optimization of Tetrahedra Stellation
    • Anam Nasim: Spread of a Virus on Networks: A Probabiistic Approach
    • Mark Neznansky: Supersymmetry and Non-Relativistic Quantum Mechanics
    • Jeff Pereira: "SuperSET," a mathematical investigation of a variation of SET
    • Anisha Ramnani: Explorations of the Shannon Switching Game
    • Joy Sebseta: Bard Bipartite Sprouts!
    • Will Smith: Thompson-Like Groups for Dendrite Julia Sets
    • Jacqueline Villers: Counting the Votes: Exploring a Partially Ordered Borda Count
    • Jasper Weinrich-Burd: A Thompson-Like Group for the Bubble Bath Julia Set
    • Layla Wolfgang: Sets of Splines with Boundary Conditions
    • Fanny Wyrick-Flax: Algebraic Relations and Boij-Söderberg Theory
  • 2012

    2012


    • Jeannette Benham: Auditory Perception in Flatland: The Physical Applicability of a Two-Dimensional Cochlear Model
    • Ke Cai: Supersymmetric Gauge Theory
    • Siyao Du: A Linear Algebraic Approach to Information Retrieval
    • Adriana Johnson: Optimal Control of Cell-Cycle-Specific Chemotherapy: An Examination of the Effects of Necrosis
    • Yunxia Jia: Sprouts Game Study
    • Sankapla Khadka: Quantum Codes and Computation
    • Youseung Kim: Micropatterning of Chemical Oscillation Reactions
    • Stergios Mentesidis: Welfare versus Stability in “Stabilizing an Unstable Economy”: A Minskyan Growth Model
    • Mariya Mitkova: Squares on Lattices: an Investigation Inspired by the Square Peg Problem
    • Lindsey Scoppetta: Modules of Splines with Boundary Conditions
    • Evan Seitchik: Trend and Detail: Gap Filling with the Empirical Mode Decomposition
    • Zana Tran: A Module-Theoretic Approach to Supersymmetric Gauge Theory
    • Kimberly Wood: Switching the Shannon Switching Game
    • Zhiwei Wu: Computable Invariants for Quandles
    • Dimin Xu: Extrapolation and Correlation Using the Empirical Mode Decomposition: An Application to Economic Time Series
    • Yuan Xu
    • Yongqing Yuan: The Collision Regions Between Two Epidemic Models: SIR vs. SEIR
    • Changwei Zhou: Bases for representation rings of Lie groups and their maximal tori
  • 2011

    2011


    • Lionel Barrow: A Method for Automatically Generating Network Structure in Bayesian Classifiers
    • Julia Bennet: Filtering Irreducible Clifford Supermodules
    • Lexi Carver: Generically Rigid Bar Frameworks in Three Dimensions
    • Adam Chodoff: Twisted Three-Eared Rabbits: Identifying Topological Quadratics Up To Thurston Equivalence
    • Anastassia Etropolski: Specializations of Jacobi polynomials and their algebraic properties
    • Alex Fragkopoulos: Electron Scattering in Crossed Electric and Magnetic Fields: A Semiclassical Study
    • Diana Khaburzaniya: 
    • Travis McGrath: Elliptic Curves: Minimally Spanning Prime Fields and Supersingularity
    • Jules Moreau: The Mathematics of Change Ringing
    • Madeline Schatzberg: Classifying Derived Voltage Graphs
    • Ben Selfridge: Characters of Combinatorial Hopf Algebras
    • Nathan Smith: Non-Commutative Linear Algebra
    • Jackie Stone: Generalized Adinkra Homology
    • Zhexiu Tu: Square Peg Problem on Lattice Plane
  • 2010

    2010


    • Wui Ming Aldrich-Gan: The Art of Retargeting (or Retargeting of Art): Fitting a Rectangular Peg Into a Square Hole
    • Aleksandar Chakarov:
    • Cedric Cogell:
    • Sarah Farell: Classifying Frequencies of Various Drumheads
    • Jonathan Fivelsdal: Simulating Global Climate Using A Simple Model
    • Elias Halloran: Mathematical Implementations: Modeling Folds in a Real Coordinate Space
    • Xian He: Standing Wave Analysis
    • Liz A. Jiminez-Martinez: Enumerating faces of Zonohedra
    • Huaizhou Jin: Mapping and Localization on Graphs with Particle Filter Algorithm
    • Shun-Yang Lee: Time-Frequency Analysis of the Shepard Tone
    • Paul McLaughlin: Chaos in Bird Vocalizations
    • Samantha Alison Mutter: Happy Numbers: An Exploration of An Iterated Function in Different Bases
    • David Polett: Empowering the Voter: A Mathematical Analysis of Borda Count Elections with Non-Linear Preferences
    • Hannah Quay-de la Vallee: Term Rewriting Systems and Their Corresponding Algebraic Theories
    • Viriya Ratanasangpunth: Clifford Codes
    • Che Ruisi-Besares: Voronoi Diagrams with Non-Linear Bisectors
    • Fang Song: The Impact of China's Unbalanced Sex Ratio on Pre-Marital Education
    • Alexandru Vladoi: Wireless networks: A labeling problem
    • Xinyuan Xu: Whether and When to Purchase an Annuity in China
  • 2009

    2009


    • Scott McMillen: The Indescribable Awesomeness of Vertex Colorings
    • Mona Merling: A Structure Theorem for Plesken Lie Algebras over Finite Fields
    • Nicholas Michaud: A Three-Element Generating Set for Thompson's Group F
    • Sylvia Naples: Classification of Adinkra Graphs
    • Anh Pham: The Effect of Income Inequality and Residential Segregation on Infectious Diseases Transmission (joint with Economics)
    • Tomasz Przytycki: A Generalization of Restricted n-Rotors from Knots to Graphs
    • Serena Randolph: Making Music Visible: The Mathematics behind Chladni Patterns
    • Faqir Usman: Using Graphs to Model the Spread and Containment of Fire
    • Ezra Winston: Modeling Origami Folding with Thick Paper
    • Tina Zhang: Cops and Robbers
    • Dexin Zhou: All About Risk
    • Zhechao Zhou: Analysis of Heterogeneous Patterns and Social Dynamics in Human Communication (joint with Physics)
  • 2008

    2008


    • Zachary Hamaker: Clifford Algebra Representations
    • Andrija Perunicic: Group Structure of Elliptic Curves over Finite Fields
    • Shelley Stahl: Flag h-Vectors of Distributive Lattices
  • 2007

    2007


    • Robert Feinsinger: Enumerating Lattice Paths that Avoid Forbidden Patterns
    • Jordan Volz:
  • 2006

    2006


    • Michael Knight: Primus: Patterns Primes Produce Plugged into the Expanding Product of a Particular Polynomial
    • Benjamin Rin: The Model Theory of Topoi
    • Kenneth Ober: Topological Logics
  • 2000–2005

    2000–2005


    2005

    • David Eisenstadter: Perfect Coloring of Periodic Patterns with Translation Groups
    • Alina Marinova: Robots' Motion on a Graph: Configuration Spaces for a 2-Robot System
    • Janeta Marinova: Closure Operators on Lattices and Boolean Algebras
    • Mariana Raykova: Sequential Dynamical Systems

    2004

    • Rubaba Ali: Application of Grobner Bases to the M-Color Problem for Graphs
    • Catherine Belin: Chip-Firing Games
    • Kerri-Ann Norton: The Game of Life on a Torus
    • Benjamin Rubenstein: Voronoi Tessellations
    • Kathryn Smith: Arrays, Rook Circuits, and Mininal Hamiltonian Graphs

    2003

    • Monica Elkinton: Manipulating Voting Systems: Can We Get There from Hare?
    • Elena Grigorescu: Hilbert Series and Free Resolutions
    • Jill Patterson: Male of Female? The Application of Fuzzy Logic to Simulate a Bard Student's Decision-Making Process When Determining an Individual's Sex?

    2002

    • Imran Ahmed: Does the Out Degree of a Vertex Double When an Oriented Graph is Squared?
    • Sean Callanan: Combining Isometric Subgraphs of Hypercubes
    • Tim Goldberg: Combinatorial Laplacians of Simplicial Complexes
    • Lava Yadav: Chromatic Number of Competition Graphs of Top Split Graphs
    • Jaren Smith: Hilbert Sequences of Monomial Ideals

    2001

    • Luke Nickerson:

    2000

    • Erin Boyer: Forbidden Subgraphs for Edge Domination
    • Shankar Gopalakrishnan: Cutting out the Junk: Breaking up Surfaces with Isolated Singularities
    • Maren Holmen: SET Theory
  • 1995–1999

    1995–1999


    1999

    • Josh Foure: Speed III : Stop that Bus
    • Corina Tanasa: Geodesics Types of Singular Surfaces

    1998

    • Nathan Ryan: Characterising low dimensional simplicial complexes or playing with kids' toys

    1997

    • Brant Jones: Conducting a Tabu Search on the Graph Coloring Problem
    • Esteban Rubens: Partially ordered sets, generalized fences and dimension
    • Rodney Waldhoff: The matching model for routing permutations on graphs
    • Brandon Weber: Uniform approximation of continuous functions using artificial neural networks

    1996

    • Marissa K. Bernstein: Traversability problems in graph theory
    • Dan C. Carroll: Smooth surfaces for computer aided geometric design
    • He Jiang: Transformations of regular polygons
    • Van Anh Nguyen: A binomial model for option pricing
    • Joshua Richman: Three is the loneliest number
    • Kathryn Ryan: Error-detecting codes via group theory

    1995

    • Jason Foulkes: Set Product vs. Coset Product
    • Nil Ozel: List, and list T-Coloring results for 2-chromatic graphs
    • Diego Socolinsky: On the curvature of polyhedra
  • 1990–1994

    1990–1994


    1994

    • Robert Cutler: Edge Domination of G x Qn
    • Weili Wu: The classification of discrete patterns, monohedral tilings and some thoughts about k-anisohedral tiles

    1993

    • Matthew Lee: Counting the subgroups of the dihedral groups : a numerical theoretic approach to abstract algebra
    • Thomas Regner: The significance of neural networks for artificial intelligence

    1992

    • Jeffrey Bolden: Dimension and planarity in partial ordered sets
    • Melissa Cahoon: A Graphic analysis of the hare voting system
    • David Steinberg: Real and complex etheral calculus : or, playing around with these numbers and seeing what works
    • Anne Willig: Three-colorings of cyclic groups

    1990

    • Jade Bingham: Efficient orientations of city street graphs
    • Linda Burgess: Stress Analysis of Axisymmetric Shells
    • Laura Muller: Symmetry groups, perfect colorings, and compound designs : staying within the (guide) lines

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