Random Vectors in the Quadratic Sieve
The study of random objects is a useful one in many applications and areas of mathematics. Randomness is commonly connected to statistics, where a population sample must be random in order for the conclusion from a survey or experiment to be valid. But the concept of randomness is finding its way into other areas of math. Many structures in mathematics have behaviors that are nearly random. We can take advantage of this fact to find results that would not be attainable by using a structure's rigorously defined properties and behaviors. In my dissertation, I considered randomly generated vectors and looked at the probability that the set of vectors produced had a certain interesting property. For this project, I plan to take the results from my dissertation, condense them to article form, and submit the article to a mathematical journal.
Lockard, Shannon (2008). Random Vectors in the Quadratic Sieve. CARS Summer Grants. Item 52.