Algebraic and Discrete Mathematics
Topics and Advisors
| Topic Area | Faculty Advisor(s) |
|---|---|
| Coding Theory and Cryptography | W. J. Martin, B. Servatius |
| Combinatorics | P. R. Christopher, W. J. Martin, B. Servatius |
| Discrete Optimization | W. J. Martin, B. Servatius |
| Finite Fields | W. J. Martin, B. Servatius |
| Graph Theory and Applications | P. R. Christopher, B. Servatius |
| Group Theory | P. R. Christopher, B. Servatius |
| Linear Algebra | P. R. Christopher, W. J. Martin, B. Servatius |
| Number Theory | W. J. Martin, B. Servatius |
Some Recent Algebraic and Discrete Mathematics MQPs
- Combinatorial Structures in Cryptography
- Student: Hardy, Seth Michael
Advisor: MARTIN, W. J. (MA)
Error correcting codes, such as Reed-Solomon codes, can be used to create authentication codes based on orthogonal arrays. These codes are provably secure up to a certain number of uses; however, as the number of desired uses goes up, so does the keylength. This project researches the security of a code whose messages (which function as private keys) have specific form that allows them to be represented in a more compact fashion. Specifically, messages with low Hamming weight are considered. - Distance Sequences in Graph Theory
- Student: Donovan, Elizabeth Ann
Advisor: CHRISTOPHER, P. R. (MA)
This project investigates problems involving the concept of distance in graph theory. Applications of these problems exist in such areas as optimizing facility locations. Defining the status of a vertex as the sum of the distances to all other vertices in a graph, we explore certain variations of this parameter, such as total status, minimum average distance and minimum and maximum chromatic status. We compute these parameters for various families of graphs, and obtain bounds for more general results.
Last modified: August 16, 2006 15:07:21