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Browsing by Degree "Mathematics"

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Browsing by Degree "Mathematics"

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  • Walsh, Danielle Marie (Wake Forest University, 2014)
    We explore the concept of dimension using mathematical tools. We start by providing definitions, examples, and basic properties for two types of topological dimension: small inductive dimension and large inductive dimension. ...
  • Southwick, Jeremiah T. (Wake Forest University, 2016)
    The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, ...
  • Vashaw, Kent Barton (Wake Forest University, 2016)
    We consider group-gradings of noncommutative algebras with the following question in mind: for what groups $G$ does there exist an Artin-Schelter regular algebra $A$ with $G$ grading $A$ such that $A_e$, the identity-graded ...
  • Thorner, Jesse (Wake Forest University, 2013)
    We prove a completely explicit version of the Sato-Tate Conjecture for newforms f(z) on Gamma_0(N) with squarefree level. This result assumes that the symmetric power L-functions of f(z) are automorphic and satisfy the ...
  • Palesis, Eleni Panayiota (Wake Forest University, 2015)
    A \emph{knot} is the image of an embedding of $S^1$ into $\R^3$, and a \emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with ...
  • Goedhart, Eva (2005-04-26)
    This thesis provides explicit, applicable bounds for solutions of a wide class of second-order difference equations with nonconstant coefficients. Among the applications is an affirmative answer to a question of Stevi´c. ...
  • Meek, Thomas (Wake Forest University, 2023)
    The polynomial-algorithms package is a computer algebra system written in Haskell. This package implements a polynomial type as well as several algorithms which use that type. These include a recursive version of Buchberger's ...
  • Liu, Yihua (Wake Forest University, 2011)
    The construction of networks that model biological activities is an important open question. In this thesis, we explore the modeling of biological networks using Fuzzy Logic. Fuzzy Logic models allow for genes to not only ...
  • Barnett, Joel Andrew (Wake Forest University, 2014)
    Graph pebbling involves determining the minimum number of pebbles needed so that regardless of the initial arrangement of pebbles on a graph, a pebble can be moved to any vertex using specified ``pebbling moves.'' This ...
  • DeBenedetto, Joshua Albert (Wake Forest University, 2011)
    This thesis explores the use of Bayesian statistical methods and hierarchical modeling in order to analyze massive data sets of Peruvian tree growth data. The study is important in finding connections between different ...
  • Newman, Jonathan (Wake Forest University, 2009-05-07)
    Higher Dimensional Convex Brunnian Links and Other Explorations in Knots. Thesis under the direction of Hugh N. Howards, Ph.D., Associate Professor of Mathematics. This thesis will examine two areas of knot theory. The ...
  • Yu, Chuanyang (Wake Forest University, 2023)
    In this thesis, we work on generalized homology theory and go over the proof of Poincare Duality in the first part. In the second part we work over the basic ideas of Lie algebras and algebraic geometry. In the third part, ...
  • Sizemore, Robert Kelly (Wake Forest University, 2013)
    In this thesis, we examine a ranking method called HodgeRank. HodgeRank was introduced in 2008 by Jiang, Lim, Yao and Ye as ``a promising tool for the statistical analysis of ranking, especially for datasets with cardinal, ...
  • Viazzo, Giacomo (Wake Forest University, 2023)
    Serre's Open Image Theorem states that the image of the adelic Galois representation of a non-CM elliptic curve $E$ over a number field $k$ is open in $\GL_2(\hat{\Z})$, and hence has finite index. Thus, the adelic image ...
  • Varlack, Japheth Abiah (Wake Forest University, 2024)
    We are interested in answering the question: What is the smallest positive integer K such that the equation x^5 + y^5 = K has no integer solutions but does have rational solutions? To this end, suppose K is a positive ...
  • Atkins, James Cameron (Wake Forest University, 2012)
    Let <italic>k</italic> be a field of characteristic zero, and let <italic>R= k<sub>-1</sub>[x<sub>1</sub>, ..., x<sub>n</sub>]</italic>
  • Beam, Kristy (Wake Forest University, 2009-05-06)
    There exist polynomials Cn(q,t) known as the q,t-Catalan polynomials. We know from work in representation theory by Haglund, Haiman, and Garsia that the q,t-Catalan polynomials are symmetric; that is, that Cn(q,t) = ...
  • Pickard, Emma Hollan (Wake Forest University, 2023)
    In 1999, Mikhail Khovanov introduced Khovanov homology as a knot invariant. The aim of this research is to provide a way in which less experienced students can explore Khovanov Homology, and to provide detail on representatives ...
  • Blankenship, David Cordell (Wake Forest University, 2024)
    The aim of this thesis is to present the basics of Einstein’s theory of relativity andthe relevant differential geometry. The first chapter will cover special relativity which will introduce some of the basic ideas in ...
  • Dixon, Kari Crowell (Wake Forest University, 2013)
    In any ecological community, the probabilities for observance (capture) of individual animals often differ both within and between species. Previous research involving multiple species' abundances have largely ignored ...