Browsing by Author "Mathematics"

Now showing items 21-31 of 31

  • Markov Chains, Random Walks, and Card Shuffling 

    Outlaw, Nolan (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 

    Eidschun, Bradley (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 

    Kirk, Samantha (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 ...

  • Mathematical Techniques for the Analysis of Partial Differential Equations 

    Tran, Kevin K (East Carolina University, 2018-04-25)
    This thesis explores various solution methods for partial differential equations. The heat equation, wave equation and Laplace equation are analyzed using techniques from functional analysis, Fourier series, and Fourier ...

  • Modeling Tsunami Waves Using Q-Advanced Waves in 2-D 

    Cook, Cameron (East Carolina University, 2015-12-15)
    A two-dimensional numerical approximation for modeling tsunamis is developed. New q-advanced functions are used to model the forcing due to an earthquake. These results are used to model the Japanese tsunami of 2011, and ...

  • 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 ...

  • Solutions of an Inhomogeneous MADE using an Analysis of Wavelet Coefficients 

    Faircloth, Dallas Ali (East Carolina University, 2023-12-08)
    In this paper solutions to an Inhomogeneous Multiplicatively Advanced Differential Equation (MADE) of the form $y^\prime(t) - Ay(qt)=f(t)$, for $q>1$ and certain functions $f(t)\in \L^2(\R)$, are provided. Such solutions ...

  • Tackling Student Debt 

    Atkinson, Bradley M (East Carolina University, 2021-04-23)
    Tackling Student Debt is a group project dedicated to finding answers and solutions to the problem of student debt. Many people are uneducated as to how big a problem student debt is. Thousands of dollars in scholarship ...

  • 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 ...