Browsing Mathematics by Author "Mathematics"
-
Newton Polygons on p-adic Number Fields
Teller, Jacek (East Carolina University, 2012)This thesis offers a clear introduction to p-adic number fields, and the method of Newton polygons to approximate the size of roots of polynomials in the completion of the algebraic closure of p-adic number fields. Ostrowski's ... -
A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY
Hampton, Earl F. (East Carolina University, 2010)The purpose of this thesis is to define the basic objects of study in algebraic geometry, namely, schemes and quasicoherent sheaves over schemes. We start by discussing algebraic sets as common zeros of polynomials and ... -
Random Walks on Finite Fields and Heisenberg Groups
Zhu, Yi (East Carolina University, 2011)Let H be a finite group and [mu] a probability measure on H. This data determines an invariant random walk on H beginning from the identity element. The probability distribution for the state of the random walk after n ... -
The Spectral Theorem for Self-Adjoint Operators
Chilcoat, Kenneth (East Carolina University, 2016-04-25)The Spectral Theorem for Self-Adjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing ...