Senior Capstone Projects

Caitlin Moser

“The Relationship Between Realized and Implied Volatility”

Financial professionals use many different tools and measurements to help with investment decisions. One such tool is a measurement called volatility; a measurement determined by the amount of change and the rate of that change observed in a stock price. This talk will discuss the way in which financial professionals are able to calculate and then use volatility to aid them in their decision processes. We will also look at how reliable this evaluation process is by using an application of regression analysis.

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Andrew Wolenter

“An Exploration into the Boolean Lattice”

Have you ever heard a piece of juicy gossip and then told a few people, who each tell one person, who tells one person, and this pattern continues until the subject of the gossip hears the rumor? This network of people and communication connections has a striking similarity to a Boolean lattice. Come find out what exactly a Boolean lattice is and how it operates. This talk will go over multiple theorems already proven dealing the Boolean lattice and introduce new ways of viewing an already proven theorem using linear algebra and combinatorics.

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Paul Crone

“A Talk On Odd Perfect Numbers”

In this talk we will take an investigative look at the mathematics involved in the search for odd perfect numbers, a problem that has stumped mathematicians for over three hundred and seventy years. In particular, we will examine an early theorem from Euler and see how it describes the congruency class of odd perfect numbers. We will also look at some mathematical techniques that can be used to create a lower bound for the total number of divisors of an odd perfect number. Finally, we will review the most recent results concerning odd perfect numbers.