Mathematics Honors Papers

AY 2022

SMAH

• "Counting Polynomials over Finite Fields" by Emma Brindley (adviser: Prof. Price)
• "Describing the Effects of Diurnal Forcing on the Kelvin Wave" by Moira Camacho (adviser: Prof. Hottovy)
• "Fractals as Iterated Function Systems" by Aimee Dalsimer (adviser: Prof. Creutz)
• "Random Network Models: With Applications to Marvel Comic Books and More" by Seth Hanson (adviser: Prof. Kenter)
• "Dynamical Systems with Delayed Response" by Rachel Manhertz (adviser: Prof. Popovici)
• "Integers Represented by Ternary Positive Definite Quadratic Forms" by Benjamin Rainear (adviser: Prof. Thompson)
• "Impulse Differential Equations with Applications to the Pulse Vaccination Strategy of the SIR Model" by Joe Spirnak (adviser: Prof. Popovici)
• "A New Result on Almost Universal Quadratic Forms" by Caleb Williams (adviser: Prof. Thompson)

SMPH

• "Neural Network Methods for Solving Differential Equations" by Nico Duchez (adviser: Prof. Soane)
• "An Analytical and Computational Study of the Paraxial Wave Equation" by Kyle Jung (adviser: Prof. Malek-Maldani)
• "The Ensemble Kalman Filter for Complex Nonlinear Systems" by Anna Sawyer (adviser: Prof. Lunasin) (dual major SMOH)

SMOH

• "Allocation of Limited Search Assets in Undersea Warfare" by Gray Benson (adviser: Prof. Svirsko)
• "Solving Interdiction Problems in the South China Sea with Leader/Follower Methods" by Michael Berger (advisers: Prof. Curry and Prof. Alameda)
• "Modeling the Multicommodity Flow Problem with Flow Dependence Constraints" by Katherine Mackle (advsier: CDR Lazzaro)
• "Quantifying and Minimizing the Inequality of Election Resource Allocation" by Joshua Murrell (adviser: Prof. Skipper)
• "Network Analysis of Concussion Symptoms in Collegiate Athletes" by Caroline Turner (adviser: Prof. Svirsko)

AY 2021

SMAH

• "Campaign Advertisement Effects on Candidate Polling" by Derek Bertucci (adviser: Prof. Minut)
• "An Introduction to the Grigorchuk Group and Related Topics" by Joshua Dye (advisor: Prof. Medynets)
• "An Introduction to Supersingular Isogeny Graphs with Cryptographic Applications" by Declan Harrison (advisor: Prof. Thompson)
• "Conic Sections and a Problem in Number Theory" by Catherine Hawkes (adviser: Prof. Ksir)
• "Rank of Random Sign Patterns" by Ping-Yuan Huang (adviser: Prof. Kenter)
• "Analyzing Behaviors of Artificial Intelligence Methods for a Search Game" by Elena Kozak (advisor: Prof. Hottovy)
• "Mixing on Elevated Staircase Transformations" by Shaun Rodock (adviser: Prof. Creutz)
• "A Generalization of Whyburn's Theorem" by Marcos Valdes (adviser: Prof. Zarikian)

SMPH

• "Exploring Links Between Climate Shocks and Migration" by Lillian Baker (advisers: Prof. Hottovy, Prof. Barret, Prof. Peart)
• "Denoising Passive Radar Measurements using Polynomial Systems" by Jacqueline McNulla (advisor: Prof. Bates)
• "Modeling for Optimal Troop Placement in the South China Sea" by Micah Oh (advisers: Prof. Bates, Prof. Curry) (SMOH double major)
• "An Optimal Control Model for Water Pollution" by Philip Smith (adviser: Prof. Soane)

SMOH

• "A Game Theoretic Approach to Solving the Football Endgame" by Logan McGuire (advisor: Prof. Kenter)
• "Data Analysis of Illegal Fishing Networks to Identify Human Trafficking" by Eric Wilson (advisers: Prof. Curry, Prof. Svirsko)

AY 2020

SMAH

• "A Comparison of Different Algorithms for Finding which Vertices in a Graph are Important" by Joseph Farnan (adviser: Prof. Kenter)
• "Exploring Privacy in Cooperative Games" by George Gilliam (adviser: Prof. Uhan)
• "Regression Tree Informed Feature Importance Insights for Near-maritime Optical Turbulence" by Chris Jellen (adviser: Prof. Traves)
• "Synchronization of Coupled Nonlinear Oscillators: Exploring the Asymmetry of East-West Jet Lag" by Hunter McGavran (adviser: Prof. Popovici)
• "Decision Problems in Computational Group Theory" by Aidan Sabety-Mass (adviser: Prof. Medynets)
• "Exploring the Different Stability Functions of the Dynkin Quiver D₄" by Karl Schwarzkopf (adviser: Prof. Allman)

SMPH

• "Landmine Detection as an Inverse Problem" by Max Gelbach (adviser: Prof. Soane)
• "Pathway-based Integrative Modeling of Genomics Data: Accommodating Genes with Multiple Pathway Memberships" by Ani Murali (adviser: Prof. McGuffey)
• "An Overview of Techniques in Lattice Based Cryptography" by Alex Psichas (adviser: Prof. Margulies)
• "Analysis by Dynamic Mode Decomposition: Applications to the Double-Gyre Flow and Laser Data" by Hunter Rice (adviser: Prof. Malek-Madani)

SMOH

• "Integer Programming Methods to Alleviate Human Trafficking in Maritime Settings" by Jamie Miller (adviser: Prof. Curry)
• "Tree-Based Dissimilarity Measures for Statistical Learning" by Marshall Shires (adviser: CAPT Ruth)

AY 2019

SMAH

• "Solving the Inverse Problem Using Combination Random Graph Models" by Samuel Baker (adviser: Prof. Kenter)
• "Classification of Binary Shifts over Finite Fields" by Dylan Cabrera (adviser: Prof. Price)
• "Games on Graphs: Cops and Robbers and Zero Forcing" by Shannon Dillman (adviser: Prof. Kenter)
• "Multi-Dimensional Persistent Homology in Network Science" by Matthew Dods (adviser: Prof. Wakefield)
• "On the Interplay of Self-Dual Matroids and Self-Dual Linear Codes" by Zoe Green (adviser: Prof. Chun)
• "A-Trails in Ribbon Graphs" by Zachary Klein (adviser: Prof. Chun)
• "An Impossibility Theorem for Redrawing Donation Service Areas to Reduce Transplant Rate Geographic Diversity" by Andrew Shu (adviser: Prof. Gentry)

SMPH

• "Simple Probabilistic Model of Lightning Strike Development" by Jacob Santer (adviser: Prof. Hottovy)

SMOH

• "Games on Graphs: Cops and Robbers and Zero Forcing" by Shannon Dillman (adviser: Prof. Kenter)
• "Simple Probabilistic Model of Lightning Strike Development" by Jacob Santer (adviser: Prof. Hottovy)

AY 2018

SMAH

• "Modeling the Rise of Populism" by Matt Baker (advisor: Prof. Minut)
• "The Structure and Topology of Projective and Grassmannian Spaces" by Patrick Coen (adviser: Prof. Agarwala)
• "Matroid Kazhdan-Lustig Polynomials and Structures of Flags" by Trevor Karn (adviser: Prof. Wakefield)
• "Modeling DNA Origami with Ribbon Graphs" by Zachary Klein (adviser: Prof. Chun)
• "Limit Behavior of Swarms of Coupled Agents" by Carl Kolon (adviser: Prof. Medynets)
• "A Proof of the Isoperimetric Inequality with Riemann Mapping" by Bennett Marston (adviser: Prof. Popovici)
• "Understanding the Link Between Khovanov's Cohomology and the Jones Polynomial" by Jacob Pittman (adviser: Prof. Allman)
• "The 'Hot Spots' Conjecture on the Vicsek Set" by Thomas Savage (adviser: Prof. Ionescu)

SMOH

• "Innovations to Increase the Power of State-of-the-Art Graph-Theoretic Two-Sample Statistical Tests" by Michael Wallace (adviser: CAPT Ruth)

AY 2016

SMAH

• "The History and Newman's Proof of the Prime Number Theorem" by Matthew Flores (adviser: Prof. Moen)
• "Critical Groups for Cayley Graphs of Bent Functions" by Thomas Gruebl (adviser: Prof. Joyner)
• "Classical and Quantum Singularities of a Schwarzschild Black Hole Pierced by a Cosmic String" by D. Hanlon (advisers: Prof. Konkowski and Prof. Ita)
• "Fiedler Value Sums Applied to Partition Graphs" by Riley Miller (adviser: Prof. Phillips)
• "Construction of Rational Maps on the Projective Line with Given Dynamical Structure" by Ian Shaw (adviser: Prof. Ksir)
• "Symbolic Dynamics and Coding: Applications to Data Storage" by James Talisse (adviser: Prof. Medynets)
• "Mathematical Modeling: Immune System Dynamics in the Presence of Cancer and Immunodeficiency in vivo" by Thomas Wester (adviser: Prof. Garcia)
• "Sequences of Toeplitz Matrices" by Myles Wortham (adviser: Prof. Price)

SMPH

• "Solutions to Linear and Nonlinear Differential Equations by way of Differential Transforms" by Kyle Packer (adviser: Prof. Seal)

AY 2015

SMAH

• "Cubic Rational Maps Having Everywhere Good Reduction" by Chris Kent (adviser: Stout)
• "Collision Detection of Static Solids" by Adam Shamma (adviser: CAPT McGrath)
• "Pretzel Knots and Tessellations" by J. L. Steves (adviser: Prof. Kidwell)
• "Investigation of Boolean Rings" by Jordan Webster (adviser: Prof. Hanna)

SMPH

• "Methods for Computing PDFs with Applications to Laser Data in the Maritime Domain" by Benjamin Etringer (adviser: Prof. Malek-Madani)
• "Simulation Optimization of the Liver Simulated Allocation Model" by Megan Lewis (adviser: Prof. Gentry)

Note: full text of the papers is only available from the USNA intranet.