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Filtering by: Advisor Swisher, Holly Remove constraint Advisor: Swisher, Holly Resource Type Capstone Project Remove constraint Resource Type: Capstone Project

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  • De Bruijn graphs and their applications to fault tolerant networks

    Creator:
    Baker, Joel
    Abstract:
    The goal of this expository paper is to introduce De Bruijn graphs and discuss their applications to fault tolerant networks.
    Resource Type:
    Capstone Project

  • The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms

    Creator:
    Smith, Karen
    Abstract:
    As indicated by the title The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms, this paper leads us to an understanding of the relationship between these three areas of study. In [4], Zagier gives the results of an intriguing example of the relationship between these areas. However there...
    Resource Type:
    Capstone Project

  • The j-Function and the Monster

    Creator:
    Scherer, Asa
    Abstract:
    The first published notion that the j-function was in any way related to the Monster came in 1979, when Conway and Norton noted in [CN79] that each coefficient in the q- expansion of the j-function could be written as a (nontrivial) integral linear combination of the dimensions of irreducible representations...
    Resource Type:
    Capstone Project

  • Burnside's Theorem

    Creator:
    Linman, Julie
    Abstract:
    Just as prime numbers can be thought of as the building blocks of the natural numbers, in a similar fashion, simple groups may be considered the building blocks of finite groups. Burnside considered the following questions: 1. Do there exist non-abelian simple groups of odd order? 2. Do there exist...
    Resource Type:
    Capstone Project
    Full Text:
    Advisor: Holly Swisher April 2010 Contents 1 Introduction 2 2 Group Theory Background 4 2.1

  • Class Number One Problems

    Creator:
    Bunnell, Elijah
    Abstract:
    In this paper we examine some of the developments concerning the Gauss class number problems and build a solid understanding of the class number. First we will develop some background knowledge necessary to understand the problem, specifically the theory of quadratic forms and quadratic fields and how the class number...
    Resource Type:
    Capstone Project

  • The Partition Function and Ramanujan Congruences

    Creator:
    Bucher, Eric
    Abstract:
    The study into specific properties of the partition function has been a rich topic for number theorists for many years. Much of the current work involving the arithmetic properties of the partition function and their seed in some keen observations of Ramanujan.In particular he discovered what are referred to as...
    Resource Type:
    Capstone Project