This page is dedicated to a collection of different technical projects and technical writings. All of these projects were completed during my four years at Wabash College while studying computational mathematics. Classes include Calculus II, Linear Algebra, Abstract Algebra, Machine Learning, Stochastic Simulation, and Numerical Analysis. These classes, along with the parameters of these projects will be outlined in each projects' individual subpage.
Stochastic Simulation is the usage of simulations involving random variables to predict things like expected values and variances. This specific project takes a probability density function and uses different stochastic methods to see which produces the most accurate simulations.
Machine Learning is the process of feeding a computer data and teaching it how to solve certain problems given the data. For this specific project, the task involved teaching a computer to pass Captchas (the things that ask you to identify a random assortment of letters and numbers to prove you aren't a robot). This project showcases use of python coding.
Another project for stochastic simulation. We used polling data from various sites to create a "serious" election predictor. Through this we defined "safe" states that we comfortably felt would be won be one party. We then used data to predict who would win the swing states, these being filled with the random variables and skewed due to polling data.Â
Numerical Analysis is the study of using algorithms to solve complex mathematical problems. For this specific project, we see one of the most practical uses of numerical analysis, interpolating polynomials. Given several data points, how can we predict what goes on between them and beyond. This specific project showcases handwritten and coded computations.
This simple coding project is an example of basic python programming which I completed from scratch while learning python. This project required the creation of a game, as well as separate window that could run the game.
Abstract Algebra is a specific study of mathematics that concerns numbers, variables, and operations, and how they work within set and group theory. This project showcases my abilities in logic and reasoning. I see Abstract Algebra as a series of advanced logic puzzles, and this written assignment provides an example of that.