Mathematics Honors Papers

AY 2025

SMAH

• "Noise-Induced Bifurcations in Stochastic Dynamical Systems" by Thomas Jennings (advisers: Prof. Kenter and Prof. Hottovy) (Bowman Project)
• "On Terao’s conjecture: balanced multiplicities and expected codimension" by Tenlea Radack (adviser: Prof. Maxfield) (Trident Project)

SMPH

• "An Optimal Control Problem for a Solid Ignition Fuel Model" by Luke Artz (adviser: Prof. Soane)
• "Generalizing Extended Dynamic Mode Decomposition: Utilizing Phase Space Knowledge for System Identification" by Ivette Ayala (advisers: Prof. Lunasin and Prof. Wiggins) 
• "Enhancing Data-Driven System Identification: Efficient Training Strategy for Noise Resilience and Multi-Attractor Dynamics" 
  by William Nguyen (advisers: Prof. Lunasin and Prof. Wiggins) 
• "The Theory and Implementation of Picard’s Method for Solving ODEs and PDEs" by Sarabeth Joyner
• "Comparison of MJO Predictions Using Simple, Linear Regression, and Neural Network Models" by Aurora Sandoval (adviser: Prof. Hottovy)

AY 2024

SMAH

• "Geometry of Numbers over Real Quadratic Number Fields and Applications to Quadratic Forms" by Andrew Koleslar (Adviser: Prof. Thompson) (Trident Project)
• "Direct Numerical Simulation of Three-Dimensional Flow around a Rotated Cube" by James McAtee (Adviser: Prof. Liakos)
• "Landmine Detection Using Partial Differential Equations" by Michael Wrigley (Adviser: Prof. Melles)

SMPH

• "Prediction and Control of Disease Outbreaks Using Dynamical Modeling: Study of SARS-CoV-2 on Cargo Vessels" by Grace Hastings (adviser: Prof. Popovici)
• "Investigating Schrodinger’s Equation Using Green’s Functions" by Cole Martin (advisers: Prof. Malek-Madani and Prof. Moore (Colgate)) (Trident Project)
• "Efficient Sampling of Bayesian Correlated Probit Models" by David Tonne (adviser: Prof. VanDerwerken) (Dual EAS/SMPH Major)

SMOH

• "Using Optimization and Machine Learning to Improve Weather Modeling" by Jake Cubbler (advisers: Prof. Hottovy, Prof. Hendersen (OAS) and Prof. Taylor (CS))
• "Network Interdiction of the Minimum Cost Multicommodity Flow Problem with Flow Dependence" by Lia Fourakis (adviser: CAPT Lazzaro)
• "Modeling Operational Resilience in the Presence of Climate Disruptions with Bayesian Networks" by Robery Klanac (adviser: Prof. Traves) (Trident Project)
• "Improving Access to Midshipman Development Center Services" by Ford Knippa (adviser: Prof. Svirksko) (Bowman Project)
• "Efficient Exact Linear Programming" by Ram Krishnamoorthy (adviser: Prof. Lourenco) (Trident Project)
•  "A Fast First-Order Method to Calculate the Lovász Theta Function" by Samuel Shin (advisers: Prof. Philips (ONR) and Prof. Uhan) (Dual SMAH/SMOH Major and Trident Project)

AY 2023

SMAH

• "The Bipartite Edge Swapping Problem: Using Eigenvalues and Graph Properties" by Caroline Leal (adviser: Prof. Kenter)
• "WORDLE: A Study in Graphs and Optimization" by Katherine Mendyk (adviser: Prof. Creutz) (Dual SMAH/SMOH)
• "Coupled Multicoloring and Multicommodity Flow" by Jason Weiss (adviser: Prof. Wakefield)
• "Fourier Analysis and Data Science: Multidimensional Scaling" by Paul Zimmer, (advisor: Dr. Will Traves)

SMPH

• "Points to Polynomials: A tale of exactness recovery" by Virendra Ghate (advisers: Prof. Bates, Prof. Peterson)
• "(Debunking) Image Encryption Using Particle Swarm Optimization" by Anna Lesho (advisors: Prof. Margulies, Prof. Park)
• "Modeling the Population Dynamics of Mosquitoes" by Natalia Pavlyk (advisor: Prof. Minut)
• "Numerical Analysis Of A Combustion Model for Layered Media Via Mathematical Homogenization" by Jessica Riggs (adviser: Prof. Soane) (Bowman Project)

SMOH

• "Incorporating Combinatorial Preferences into Course and Instructor Scheduling for the USNA Mathematics Department" by Joshua Douberly (adviser: Prof. Uhan)
• "Maximizing College Football Viewership Under Competitive Constraints" by Oliver Hassler (advisers: Prof. Kenter, Prof. Park)
• "Improving Nonlinear Gas Network Optimization Formulations via Smoothing Techniques" by Geonhee Kim (adviser: Prof. Skipper and Prof. Lourenco)
• "Maximizing Occupied Nodes in Dynamic Network Flow Problems Using Time Indexed Graphs" by Tanner Nixon (adviser: Prof. Curry)
• "Modifying Minimum Fill-In to Find Exact Solutions of Linear Systems" by Jared Perez (adviser: Prof. Lourenco)

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 (adviser: 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 Disparity" 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.