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Mathematics Projects


Explorations in Number Theory and Cryptography

Dr. Charles Lam

This program explores the evolution of cryptology from simple substitution ciphers to public-key cryptography. Students will be introduced to basic number theory, and its use in modern-day encryption methods. In addition, different uses of cryptography in cases such as authentication and digital signatures will be explored. Participants will investigate on weaknesses in encryption schemes using basic cryptanalysis techniques.

How to use Chaos to Control Insect Populations

Dr. Maureen Rush

Explore the world of chaos by looking at discrete models that erupt with unpredictable behavior. This chaotic behavior is commonly associated with weather patterns and stock market volatility, but we consider how insect populations behave when other insects interact with them. In particular, we’ll take a look at the population dynamics of the Glassy Winged Sharpshooter (GWSS) in the presence of a population of wasps (Gonatocerus) using a predator-prey model. In this model, the wasp is a predator, or a GWSS egg parasite.  Under certain conditions of the infectivity rate of the wasp, the GWSS population becomes chaotic, and for other rates, the population can be eradicated. The principal reason for controlling the glassy-winged sharpshooter is to prevent the spread of the Xylella bacterium to susceptible plants and destroys some Central Valley crops.