Student Research Papers (Mathematics)http://hdl.handle.net/1957/172642017-07-27T12:33:32Z2017-07-27T12:33:32ZClassifying Octonionic-Linear OperatorsPutnam, Alexanderhttp://hdl.handle.net/1957/617072017-07-05T18:19:59Z2017-07-05T00:00:00ZClassifying Octonionic-Linear Operators
Putnam, Alexander
The goal of this paper is to classify linear operators with octonionic coefficients and octonionic variables. While building up to the octonions we also classify linear operators over the quaternions and show how to relate the linear operators over the quaternions and octonions to matrices. We also construct a basis of linear operators that maps to the canonical basis of matrices for each space. Finally, we discuss automorphisms of the octonions, a special subset of the linear operators.
June 2017
2017-07-05T00:00:00ZKACZMARZ AND RANDOMIZED KACZMARZ METHODAbubakari, Nurideenhttp://hdl.handle.net/1957/614792017-06-20T21:29:29Z2017-06-20T00:00:00ZKACZMARZ AND RANDOMIZED KACZMARZ METHOD
Abubakari, Nurideen
2017
2017-06-20T00:00:00ZPredicting the most likely state for a basic geophysical flow: theoretical frameworkDuran, Rodrigohttp://hdl.handle.net/1957/468102015-01-28T20:59:59Z2015-01-09T00:00:00ZPredicting the most likely state for a basic geophysical flow: theoretical framework
Duran, Rodrigo
Graduation date: 2013
2015-01-09T00:00:00ZThe 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
2013-01-01T00:00:00Z