Listed below are some old projects that I have worked on. These projects should give you an idea of the variety of projects that an applied mathematician can work on. Please feel free to use the projects listed below for ideas, but please do not copy any of my work. I am not longer actively working on these projects, but I can be reached for questions at email@example.com.
Optimal Number of Parking Permits to Release at UNC (.PDF) (added 1/13/2014)
This was my Master’s Project at UNC, 2011. It was a semester-long consultation project with the Parking Department. Parking departments overbook parking lots, much like airlines overbook seats. This is because different people have different schedules, and it is unlikely that all of the permit holders for a lot will need parking at the same time on a given day. To find the appropriate amount of permits to release at UNC, I used historical data to fit occupancy curves. For a new lot without historical data, I took a sample of occupancy data over two days and extrapolated/simulated based upon the trends I saw at other lots. The goal was to release as many permits as possible, which increases departmental revenue and customer satisfaction, without overflowing the parking lots more than three times in a given school year.
Has the Baseball Hall of Fame Gotten More Selective? (.PDF) (added 1/13/2014)
This was a project for my Exploratory Data Analysis Course, Fall 2013. Baseball Hall of Famers appear to be getting more hits over time. This project used historical data and exploratory data analysis approaches to look at this phenomenon. I found that about half of the trend of increased hits can be explained by certain second-tier Hall of Famers from recent decades not yet gaining HOF entry. Once these players get elected, HOF hit trends should not seem so drastic.
Optimizing a Volleyball Serve (.PDF) (added 1/13/2014)
In Summer 2006, after my freshman year of college, I had a great summer at Hope College’s Mathematics REU (Research Experience for Undergraduates) with Professor Tim Pennings and Dan Lithio. This paper came from our 8 weeks of “research”. We experimented to find the drag and spin coefficients of a volleyball and used these parameters to create a physical model of the dynamics of a volleyball serve. We found the relative importance of the height of the serve, the distance of the serve, and the spin applied to the volleyball. In our free time, we spent time at the beach with Elvis, the dog that does calculus.
Optimal Cross-Linking of Satellites (.PDF) (added 1/29/2014)
In Summer 2008, I did an internship at the Institute for Pure and Applied Mathematics at UCLA. We worked on a project with industry sponsor The Aerospace Corporation, who I ended up interning for in Summer 2009 and 2010. Our team of four created an efficient algorithm capable of generating near-optimal satellite networks given a set of constraints on satellite communication links. An optimal or close-to-optimal network has the traits of high connectivity, fast communication times (i.e. low latency), and high redundancy. The project involved a lot of graph theory, nonlinear optimization using genetic algorithms, and satellites!
Detecting Learning in Sea Slugs (.PDF) (added 1/30/2014)
In Summer 2007, I was among the first students from Case Western accepted into a new internship program. The goal of the program was to study problems at the interface of biology and mathematics. My collaborator, Ari Kanters, and I studied whether it was possible to detect behavioral changes that were representative of learning in sea slugs (Aplysia californica). This project was my first introduction to Matlab and to Markov Chains.
Out-of-Equilibrium Competitive Dynamics between Species (.PDF) (added 1/29/2014)
This is a project for a course titled Dynamics of Biological Systems (II). It studies the mathematics behind competition between species. If an environment can only support a fixed number of individuals, which species will tend to survive?
Plasticity and Pattern Formation in the Visual Cortex with Applications to Stroke Recovery (.PDF) (added 1/29/2014)
Mathematical Neuroscience is a course that I took that studies the dynamics of brain activation channels. This paper looked at a motel of plasticity in the eye that allows stroke victims to recover their functional eyesight.
Nonlinear Least Squares Data Fitting (.PDF) (added 1/30/2014)
This was a course project for a Numerical Methods class. It was also my first introduction to nonlinear optimization, in this case nonlinear least squares.
Presynaptic Modeling of Parkinson’s Disease (.PDF) (added 1/30/2014)
Another project at the interface of biology and mathematics, this time for the course Dynamics of Biological Systems (I).