A Collection of Projects from Diverse Motivations
I am a proud math nerd, a photographer, and someone who likes adding third phrases to written lists out of love for the Oxford comma.
More specifically, I graduated as valedictorian from Gettysburg College in the spring of 2021 with a BA mathematics, and am now a PhD student at Stony Brook University studying... you guessed it... Mathematics.
When I'm not proving various things that I am instructed to prove (as is the life of a math graduate student) I enjoy elimintating projects from my mile-long "to do" list. These can include math or CS research, programming web tools, composing music, developing games, or writing philosophy and fiction. Of course, not every idea results in a masterpiece, but this website includes the things I am most proud of.
If you are interested in working together, please contact me!
P.S. Click on one of those buttons on the top left of your screen!
Abstract: In this article, we describe various approaches to opponent hand estimation in the card game Gin Rummy. We use an application of Bayes' rule, as well as both simple and convolutional neural networks, to recognize patterns in simulated game play and predict the opponent's hand. ...
American writer, teacher, and comedian Sam Levenson gives us the following warning. "Somewhere on this globe, every ten seconds, there is a woman giving birth to a child. She must be found and stopped."...
Abstract: The finite abelian group G is type I if |G| has a prime divisor congruent to 2(3), type II if |G| is divisible by 3 but has no divisors congruent to 2(3), and type III if all divisors of |G| are congruent to 1(3).... (Presentation)
Abstract: A subset A of a given finite abelian group G is called weakly (k, l)-sum-free if the set of all sums of k distinct elements of A is disjoint with set of all sums of l distinct elements of A.... (Presentation)
Abstract: Just a few random numbers and 2-by-2 matrices can be used in unison to create spectacularly beautiful images of planar fractals. These iterated function systems (IFS) are easy to understand, but lead to deep constructions...
Abstract: Möbius transformations are a convenient group of maps to study. We will explore a specific kind of Möbius transformation used to generate particular discrete subgroups of Möbius transformations called Schottky Groups. We will then use Schottky Groups to explain and make fractal-like images out of circles.
While serving as a PLA for a Calculus 2 class, I realized that the students were not understanding the origin of the formulas they were trying to memorize and use, which motivated me to write this short tutorial.
(In Progress) "Lights Out" is a game using binary-state cellular automota. This paper explores the algebraic structures the game admits.
(In Progress) After taking a math methods course for Physicits, I realized that the 1333-page textbook that we used covered far more material than a semseter of undergraduate math for physics majors requires. This textbook will include coverage of 4 important topics that every physics major should be familiar with: Fourier Analysis, Vector Calculus, Linear Algebra, and Partial Differential Equations.
A showcase and collection of the Mathematics and beauty of fractals generated with iterated function systems. This web app allows for the creation and sensitivity investigations of IFS fractals.
is a javascript library for additive combinatorics calculation. This web app allows has four Additive combinatorics tools free for use: a function calculator, sumset calculator, table generator, and playground Jupyter-style notebook.
This web app plots functions f from the complex plane to itself by first coloring the plane and then recoloring the plane, assigning to z the color at f(z). I believe this is an improvement on software written in MatLab: with this tool, you can upload your own image to be used as domain coloring.
This tool is an interface for some javascript that colors pixels on an HTML canvas element.
This is a web app that can create, edit, convert, export, and save table files, such as CSV, TSV, and others.
Here is an assortment of random generators that I have been requested to make.
graphPlot is a Python module (released on PyPi) that uses physical simulation to find ideal plotting coordinates for graphs.
ifsFractals is a Python module (released on PyPi) that can be used to generate fractals that are fixed point sets of contraction mappings.
Sedario is a short two-person strategy game of my own invention, with simple rules and few materials. I had fun developing this client-side online interface to play the game.
This is a collection of games that are all made using the HTML5 canvas element and javascript. They are intended to be fun as well as instructional for somone wanting to make thier own.
This is a Texas Holdem' web application that allows users to create and join games. My intention is that players use Zoom (or equivalent) simultaneously.
I was annoyed when I struggled to find a simple web-based Bingo Caller that would be good to project on a screen, so I made one.
Quadegories!™ is an extremely challenging, clue-based trivia game that works the brain's executive funtion. It was developed by Brook Zelcer.
(Always in Progess) This CoCalc folder contains some of my "backburner" projects and ideas. Some subfolders have unanswered questions and probelems, so feel free to take a look!
I made this animation as a demonstration of the way to animate solutions to three-dimmensional systems of ODEs.
After hearing the chair of the Math Department at Gettysburg College (Dr. Ben Kennedy) asses the "math weather" at the beginning of each colloquium, I decided to make a web app to do it everyday!
Everyone who has done it knows that learning LaTeX can be a struggle at first, but the rewards are huge! I made these templates so that people who have never learned a markup language before can get started with typesetting.
Building and using Desmos Graphs can give great intuitive and visual understaing of various topics. These are some of the graphs that I have made that I either find helpful or nice to look at.
(In progress) This is the homepage for an introduction to Python Programming course (and textbook) I wrote and have taught a few times upon request.
I started photography in high school, and I started working professionally for the office of Communications and Marketing at Gettysburg College in 2018.
I enjoy shooting portaits and events, but I have also done wildlife, landscape, and travel photography.
# of photos | Price per photo |
1-2 | $12 each |
3-9 | $11 each |
10+ | $10 each |
unlimited | $150/hour |
Although 'The Scientific Method' is a fairly ubiquitous phrase, we will begin to see that the poseter flowchart that we recall adorning the wall of our fifth grade classroom does not do it justice. What is the Scientific Method? aims to take the reader through notable episodes of the history of particle physics while examining the ongoing philosophical discussion on the scientific method.
In 1967, the heart of the Cold War, a lanky Russian Jewish mathematician from the United States sat at a piano in front of a large audience in Copenhagen, singing a satire about mutually assured destruction and nuclear holocaust, that was televised to viewers around the world. Should we be that surprised?...
World War II induced a fear in American-Jewish communities, which instigated a sharp turn from the chaotic energy that had been driving the subversive Jewish comedy in America. However, the common and blatant sexism of the time affected Jewish male and female comedians in opposite ways.... (Photo Slides)
(In progress) I have always enjoyed writing short stories, and I have begun collecting and organizing them into a book.
(In progress) A Short Melody to the End is a one Act Play that I am writing. I hope to be able to announce the debut soon!
I have arranged and composed for various groups including marching band, choir, piano, and small chamber ensembles. Here you can access my Noteflight Marketplace as well as view all of my public scores.