Project Showcase

Written work, including research papers and course-based analytical writing. These documents reflect my skills in mathematical reasoning, applied analysis, and structured academic communication.

Bachelor of Science in Mathematics Thesis

Title:  Irreversible k-Threshold Dynamics on Corona and Base-b Corona Product Graphs

— Fort Hays State University Mathematics and Computer Science Capstone Seminar

Irreversible k-Threshold Dynamics on Corona and Base-b Corona Product Graphs 

— Submitted for Peer Review in Discussiones Mathematicae Graph Theory (Available via ArXiv)

Taxicab Trigonometric Functions: Exploring Trigonometric Structure in Taxicab Geometry 

— Report for MATH 620: Modern Geometry

Enhancing Work Zone Safety with Roadside Camera-Based Tracking and Truck-Aware Traffic Co-Simulation

— Research conducted at UNL (REU 2025). Full paper available upon request to respect the intellectual property of the research team.

Aerial Photographs and Remote Sensing Portfolio

— Course Portfolio for  Geosciences 674: Aerial Photographs and Remote Sensing

Slides from oral presentations delivered at regional and national mathematics conferences, as well as academic seminars. These materials reflect my ability to structure and communicate technical ideas clearly in a live setting  my ability to structure and communicate technical ideas clearly in a live setting, with a focus on mathematical reasoning and applied research. 

Bachelor of Science in Mathematics Thesis Presentation (View Defense)

— Fort Hays State University Mathematics and Computer Science Capstone Seminar

Irreversible k-Threshold Dynamics on Corona and Base-b Corona Product Graphs

— 2026 Kansas Section of the Mathematics Association of America (KSMAA) Conference

Irreversible k-threshold number of Corona Product and Double Corona Product Graphs

— 2025 American Mathematical Society (AMS) Fall Eastern Virtual Section Meeting

Irreversible k-threshold number of Corona Product and Double Corona Product Graphs

— 2025 KSMAA Conference

Research posters presented at undergraduate conferences and campus events. These works visually summarize key findings from selected academic projects and highlight major findings, methods, and outcomes. 

Irreversible k-Threshold Dynamics on Corona and Base-b Corona Product Graphs

— 2026 John Heinrich's Scholarly and Creative Activities Days (SACAD)

A 4-Dimensional Rubik’s Cube You Can Hold: How It’s Possible and the Math Behind It

— 2026 SACAD

Irreversible k-Threshold Number C k (G) and Saturation Probability P [G] for Corona Product and Double Corona Product Graphs

— 2025 SACAD

Enhancing Work Zone Safety with Roadside Camera-Based Tracking and Truck-Aware Traffic Simulation

Additional Interactive Media & Simulation Visuals

— 2025 Nebraska Summer Research Symposium and Engineering Summer Research Fair 

This section includes computational, programming-based, and web-oriented projects that complement my academic work in mathematics. These projects range from research-support tools and graph visualizations to interactive web applications and creative digital experiments. While they differ in format, they collectively reflect my interest in using code to model structures, visualize dynamic processes, communicate ideas clearly, and make abstract patterns more accessible. Several of these projects were developed to support my research, explain mathematical ideas more effectively, or explore how emerging tools such as AI can be used responsibly in academic and technical work. 

Graph Visualizer and Irreversible k-threshold Simulator

An interactive web tool developed to support my research on irreversible k-threshold processes. The visualizer allows users to build and explore graph families that appear in my thesis work, including corona products, double corona products, and base-b corona products, along with classical, random, and custom graphs.

Counting Partitions with sum n − 2 x and length 2 x  —  Python   ( or C++ )

A computational project developed alongside my graph theory research to generate and organize partitions of n−2x under the constraints used in the probabilistic analysis of my research at FHSU. This program helped translate a combinatorial counting problem into a concrete algorithmic procedure, allowing me to examine partition structures, frequency patterns, and cases that arise in the study of irreversible k-threshold processes. 

Farm Operations Center — AI Hackathon Winning Project

Developed as part of Fort Hays State University’s first annual AI Hackathon, an 8-hour, one-day innovation challenge where teams used artificial intelligence to prototype practical solutions to real-world problems. The event encouraged interdisciplinary teamwork, rapid prototyping, and the use of AI as part of the development process. My team created a farm operations web application designed for agricultural decision-making in northwest Kansas. The project includes a dashboard for Hays, Kansas, with live weather information and market prices, crop rotation tools, balance sheet, equipment tracking, and an AI farm assistant named Walter. Our team, consisting of Ryan Casey (K-State), Alexiya Moore (FHSU), and myself, won first place at the event.

Audio Visualizer

A creative web-based project built for fun to explore how sound can be transformed into animated visual patterns. The visualizer captures audio from a selected browser tab and displays several real-time views of the sound, including waveform motion, frequency bars, spectrogram-style color patterns, and abstract music-reactive animations. The project uses browser-based audio analysis to separate sound into time-based and frequency-based data, allowing the visuals to respond to rhythm, intensity, and changes in pitch or frequency content.

Hyper Flappy Bird

A creative browser-based game project inspired by Flappy Bird, expanded with multiple 2D and 3D modes, reverse-direction challenges, dimension-shift mechanics, score tracking, achievements, and unlockable customization options. This project was built mostly for fun, while also giving me practice with interactive design, animation, game logic, user controls, and persistent browser-based data.

Complex Mapping Studio

An interactive complex-function visualization tool built to explore mappings from the complex plane to the complex plane. Users can enter expressions as complex functions of z, view domain coloring, compare input and output planes, trace paths, export images, and examine how grids and contours transform under a complex function. The project also includes support for several special functions and analytic continuations when available.