Browsing Mathematics by Title
Now showing items 13-18 of 18
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Markov Chains, Random Walks, and Card Shuffling
(East Carolina University, 2016)A common question in the study of random processes pertains to card shuffling. Whether or not a deck of cards is random can have huge implications on any game being played with those particular cards. This thesis explores ... -
Mathematical Analysis of Tsunami and Rogue Waves
(East Carolina University, 2012)In this thesis both forced and non-linear wave equations will be studied. Actual data from tsunami and rogue waves will be used and a signal analysis will be performed using wavelets. Main results show that a different ... -
Mathematical Aspects of Image Processing
(East Carolina University, 2014)In this thesis, image processing is explored from a mathematical point of view. After defining a digitized image, techniques for adjusting resolution are discussed. Image transformations defined on a neighborhood centered ... -
Newton Polygons on p-adic Number Fields
(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
(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
(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 ...