About Me
Hello! I am a junior-level mathematics major at the University of West Florida. I enjoy abstract algebra, combinatorial design theory, and number theory. Alongside my studies, I am an active officer for the UWF Math Association and work as a mathematics tutor/mentor, helping students master coursework. My main goal in life is to help as many students as possible as a Math Professor.
Resume
You can view a summary of academic and professional experience below, or read my full CV.
- Education: University of West Florida (Mathematics)
- Experience: Mathematics Tutor, Peer Mentor, Succes Leader, Math Association Vice President
- Skills: Python, SageMath, LaTeX.
- Languages: English and Spanish.
Read Full Resume
Research
Below is a summary of our current and past research projects.
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SURP 2025: Random Construction of Steiner Systems
We wrote several programs to randomly generate these incidence structures using different algorithms in Python that includes dot product between rows of binary incidence matrices and probabilistic analysis to yield better results. Then in C we utilized nauty and traces library to find structures up to isomorphism utilizing canonical labeling algorithm. Additionally, we studied and defined several concepts and proved various theorems related to Design Theory, Algebra and Geometry. The incidence matrices were saved on a database on our website.
Read paper and poster here: Documents and Code -
SURP 2026: Constructing Homology Functors and Tensor Products
Algebraic topology bridges continuous spaces and discrete algebra. This project uses homological algebra to construct homology functors, translating complex geometric properties, like topological “holes,” into solvable algebraic formats. Methodology: Over a twelve-week progression, the focus shifts from point-set topology and the fundamental group to the algebraic prerequisites of homology, specifically emphasizing module theory and tensor products. Weekly mentor meetings will verify all theoretical proofs. Research Objectives: 1. Master the fundamental group. 2. Construct modules and the tensor product to bridge abstract algebra and homological algebra. 3. Apply homology functors and chain complexes to compute surface homology groups. Progress is assessed weekly through independent proofs and calculations. The final results will be given through both a professionally typed LaTeX document serving as a rigorous record of all explored theories, and a poster presentation at the Symposium.
Read paper and poster here: Documents -
Fall 2026: Difference families to construct Steiner Systems
In this project our goal is to construct difference families in Zn with the goal of using them to create Steiner systems that admit a cyclic automorphism group. The difference families can be constructed by brute force using computers, however, we will use theory to make our programs more efficient. We will first focus on Zp, for p prime, and then we will move to more general n. We will be borrowing techniques from group theory, number theory, and finite geometry. In particular, we will be studying and applying Cyclotomic and Fourier analysis. For the programming, we will be using Python, SageMath, and nauty.
Read paper and poster here: Documents and Code
Course Notes
Here you can find our digitized notes and study materials. Links redirect to Google Drive.
Interesting Content
A collection of mathematical resources we recommend.
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Books:
- Fermat's Enigma by Simon Singh
- Introduction to Mathematical Structures by Steven Galovich
- Topology by James Munkres
- Abstract Algebra by Dummit and Foote
- Elementary Number Theory by James Strayer
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Videos:
- History of Math by John Dersch
- Hilbert's hotel by Derek Muller
- Sophie German's work by Oxford University
- Articles & Papers:
- Projective Planes by Eric Moorhouse
- Law of Quadratic Reciprocity by Emily Zhang
- Math News:
Puzzles
Challenging mathematical puzzles.
Geometry Puzzles
- Puzzle 1: In how many different ways can you arrange 4 points in a plane such that there exist ecactly 2 different distances between any 2 points?
Logic Puzzles
- Puzzle 1: There are 12 coins. One of them is false; it weights differently. It is not known, if the false coin is heavier or lighter than the right coins. How to find the false coin by three weighs on a simple scale?
- Puzzle 2: Is it possible to obatain a rational number when an irrational number is raised to an irrational number?
- Puzzle 3: A cat is hiding in one of five boxes that are lined up in a row. The boxes are numbered 1 to 5. Each night the cat hides in an adjacent box, exactly one number away. Each morning you can open a single box to try to find the cat. Can you win this game of hide and seek? What is your strategy to find the cat?
Number Puzzles
- Puzzle 1: Fermat, computers, and a smart boy: A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers: \[x=2233445566 \] \[y=7788990011 \] \[z=9988776655. \] He announces these 3 numbers and calls for a press conference where he is going to present the value of \[n\] (to show that \[x^n + y^n = z^n\] and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug. How did the boy figure out that the scientist was wrong?
- Puzzle 2: Fifteen pirates steal a sack of gold coins. Each coin is of equal denomination. The pirates attempt to divide the coins evenly but find that two coins are left over. A quarrel over these two coins erupts and one pirate is killed. Another attempt is made to divide the coins evenly but this time one coin is left over. Another quarrel erupts and another pirate is killed. A third attempt to divide the coins evenly succeeds. Find the smallest number of gold coins that could have been in the sack initially.