Now showing items 1-8 of 8

  • Characteristics of Counter Example Loops in the Collatz Conjecture 

    Allen, Thomas W., II (2012-06-07)
    This thesis was undertaken in order to obtain new results about the Collatz Conjecture: that (4; 2; 1) is the only loop created by the Collatz function. We look at some past results and generalize one of them. We discover ...
  • Diophantine monoids defined by a single linear equation 

    Brock, Trey (2013-11-15)
    This project focuses on factorization properties of submonoids of N(r); for some positive integer r; de ned as the solution sets of certain linear equations. In particular, the goal is to determine all irreducible elements ...
  • Existence and Boundedness of Solutions for Systems of First Order Nonlinear Differential Equations 

    Mubarak, Abdulrahman A. M. A. (2017-02-22)
    In this thesis we discuss the classification, continuablity, existence, and boundedness of monotonic solutions for the system of first order nonlinear differential equations in the form x'(t) = p(t)f(y(t)), y'(t) = ...
  • Factorization in rings of upper triangular Toeplitz matrices 

    McQueen, Ashlee (2014-07-25)
    Let D be a principal ideal domain and let Rm(D) be the ring of (m + 1) × (m + 1) upper triangular Toeplitz matrices with entries in D. Then Rm(D) is a commutative, Noetherian ring with identity, and hence is atomic. We ...
  • Factorizations of Upper Triangular Matrices with Non-Commutative Entries 

    Jeffries, Joel (2017-02-01)
    The study of factorization theory concerns writing elements of various algebraic structures as products of other unfactorable elements. Factorization in commutative semigroups has been well studied, but far less work has ...
  • Irreducible divisor simplicial complexes 

    Hobson, Jake (2012-06-07)
    Recently there has been much research on irreducible divisor graphs | visual representations of the factorizations of elements in commutative rings. In this thesis we expand on this concept by introducing the irreducible ...
  • The Monotone Catenary Degree of Block Monoids 

    Card, Alexander (2015-07-27)
    The block monoid B(G) of a finite abelian group G is the set of zero-sum sequences g1 · · · gn such that !n i=1 gi = 0 with operation given by concatenation. A factorization z = α1 · · · · · αn of length |z| = n of α ...
  • Variations on a Putnam Problem 

    Luther, Loren (2017-02-01)
    The following problem appeared in the afternoon session of the Fiftieth William Lowell Putnam Mathematical Competition in 1989. A dart, thrown at random, hits a square target. Assuming that any two parts of the target ...