Student Research Papers (Mathematics)http://hdl.handle.net/1957/172642014-09-19T03:52:37Z2014-09-19T03:52:37ZPredicting the most likely state for a basic geophysical flow: theoretical frameworkDuran, Rodrigohttp://hdl.handle.net/1957/468102014-04-10T23:48:40Z2014-03-23T00:00:00ZPredicting the most likely state for a basic geophysical flow: theoretical framework
Duran, Rodrigo
Graduation date: 2013
2014-03-23T00:00:00ZThe Alexander polynomialScherich, Nancyhttp://hdl.handle.net/1957/407912013-07-18T20:03:24Z2013-01-01T00:00:00ZThe Alexander polynomial
Scherich, Nancy
The Alexander polynomial is a well understood classical knot invariant with interesting symmetry properties and recent applications in knot Floer homology. There are many different ways to compute the Alexander polynomial, some involving algebraic techniques and others more geometric or combinatorial approaches. This is an interesting example of how different types of mathematics can be used to describe the same result. While experts understand the relationships between different fields and methods of computation, the subtleties are often omitted in the literature. This paper describes four routes to the Alexander polynomial with the intent to explicate these subtleties and bring clarity to this intersection of subjects.
Graduation date: 2013
2013-01-01T00:00:00ZOn Simpson’s Paradox for Discrete Lifetime DistributionsLebowitz, Danielhttp://hdl.handle.net/1957/403442013-07-12T22:00:03Z2013-06-10T00:00:00ZOn Simpson’s Paradox for Discrete Lifetime Distributions
Lebowitz, Daniel
In probability and statistics, Simpson’s paradox is an apparent paradox in which a trend is present in different groups, but is reversed when the groups are combined. Joel Cohen (1986) has shown that continuously distributed lifetimes can never have a Simpson’s paradox. We investigate the same question for discrete random variables to see if a Simpson’s paradox is possible. With discrete random variables, we first look at those that have equally spaced values and show that Simpson’s paradox does not occur. Next, when observing the discrete lifetimes that are unequally space with identical supports, we similarly discover that a Simpson’s paradox still cannot occur. When the two random variables do not have identical supports, which allows for the flexibility to compare a broad range of different random variables, we discover that a Simpson’s paradox can occur.
Graduation date: 2013
2013-06-10T00:00:00ZPercolation and the bilevel latticeHunt, Jonathanhttp://hdl.handle.net/1957/294522012-05-30T20:37:06Z2012-05-30T00:00:00ZPercolation and the bilevel lattice
Hunt, Jonathan
The paper reviews percolation and some of its important properties, particularly
on the 2-D square lattice. A bilevel lattice is introduced, with a percolation model
representing the spread of a forest fire according to characteristics of the forest. It is
proven that the value of the laddering probability may determine whether a fire fizzles
out or spreads without bound, and a programmed simulation assists in determining a
critical laddering probability.
2012-05-30T00:00:00Z