What did you do on your summer vaction?: Math Edition
Mathematics professors and majors had a productive summer working on various research projects. Here are a few:
Professor Whieldon and Alison Schuetz
Last summer, Alison Schuetz and Robert Vaughn worked with Dr. Whieldon on projects connecting points in the Mandelbrot set to several different combinatorial objects.
This summer, Alison and Dr. Whieldon have been finishing the write-up of oneof the results from the summer involving connections between points in the Mandelbrot set and the Fuss-Catalan numbers. They are currently finishing a paper containing this result, along with bijective proofs that these generalized Catalan numbers count other neat sets of objects.
The picture illustrates why the number of ways of breaking an octagon into pieces with four sideseach should be the same as the number of rooted trees with threesets of three-leaved branches.
Dr. Parson has been working on completing a book with Brian Conrad from Stanford University. The book is about the proof of the "Ramanujan Conjecture," which is a problem in number theory posed by the Indian mathematician Srinivasa Ramanujan in 1916 andsolved by the Belgian mathematician Pierre Deligne in the 1960s and 1970s. The book is aimed at graduate students in number theory and will give an exposition of the part of Deligne's proof that is currently not easily accessible to those first learning the subject.
Professors Dunham and Stewart, Tarang Hirani, and Skyler Stasiewicz
Our team spent the summer exploring large networks (what are known to mathematicians as graphs.) First, we gathered and learned a lot of background material on graph theory. We also spent a lot of time honing our Matlab programming skills so we could solve graph theory problems on large data sets. We chose
two complicated and very different data sets: the network of global air travel and the network of interactions among yeast proteins.
We spent some of our summer analyzing the many graph theoretic properties of these data sets like shortest paths and largest cliques. We coded visualizations in Matlab as well as making some very data-rich visualizations using
the open-source software package Gephi." width="249" height="205" align="right"/>
In our research, we found two theorems on Erdȍs-Renyi random graphs containing two undefined constant terms, which we eventually named gamma (γ) and kappa (κ). By isolating these terms, we developed two new measures to be used on graphs to demonstrate their "distance from randomness." We even used what we learned in Math 112 (Applied Statistics) to interpret the data from our many simulations, which we needed in order to calculate values for these measures.
For more information on summer research, ask anyone mentioned in this article! Each of these projects was funded at least in part by a BOA or SRI grant.
Math Seminar Series Returns!
The very popular mathematics seminar series returns this fall with two speakers. Professor Jonelle Hook from Mount St. Mary's University will speak on Friday, September 27th at 12:10 pm. Her talk is entitled "Finding Patterns Among the Stars: A Mathematical Search for Order."
Professor Stephen Casey from American University will speak on Tuesday, October 1st at 12:40 pm. His talk is entitled "Pi, the Primes, Periodicities, and Probability: Using Probability to Compute Values of the Zeta Function." You can find out more in his article in the American Mathematical Monthly: bit.ly/1fVwWyH
Mark your calendars and keep an eye on the third floor bulletin board for more upcoming events!
Cumberland Valley Math Modeling Challenge
The fifth annual Cumberland Valley Math Modeling Challenge (CVMMC) will take place at Shippensburg University on September 28th and 29th. Hood has sent teams every year, and we won the entire contest in 2009. Each year, teams arrive with sleeping bags and laptops on a Saturday afternoon and work through the night on a mathematical modeling challenge. Last year teams chose from two modeling problems: one problem asked teams to design a strategy for Pennsylvania to respond to possible changes in the Electoral College; the other problem asked students to model the long-term effects of urban and suburban development of agricultural land.
Each team competing writes a one-page executive summary of their model's conclusions and prepares a ten-minute Power-Point presentation on what its members figured out in their busy night. The panel of judges, which includes everyone from mathematicians to English professors, ranks teams' written reports and oral presentations, and finally the entire group of competitors picks the winners.
If you are interested in competing this year, tell Dr. Parson that you want to come along. The modeling will be fun, and you will enjoy meeting students from
around the region. For further information, see the CVMMC web site: bit.ly/1fOxrKU
If you are busy in September, but you are still interested in participating, keep the annual COMAP contest (February 2014) in mind.
- Sept. 11, 12:30 p.m. Whitaker Center Multicultural Room
National Security Scholars Program Informational Meeting
- Sept. 28-29, Shippensburg University
- Sept. 28, James Madison University, Harrisonburg, VA
SUMS Conference (for undergrad research)
Oct. 16-18, Baltimore
NCTM Regional Conference
- Oct. 27, 9-11:30 a.m.
VA Tech Regional Mathematics Competition
Nov. 1-2 Hampden-Sydney and Farmville, VA
MAA Fall Section Meeting at Longwood Univ.