• Cohomology of Finite Modules over Short Gorenstein Rings 

    Menning, Melissa Christine (2016)
    We study two formal power series in the indeterminate t that generalize the Poincar´e series of a module. In the context of a Gorenstein local ring whose maximal ideal m satisfies m³ = 0, we prove that these two power ...
  • Conformal mappings and the Schwarz-Christoffel transformation 

    Heinen, Rebecca (University of Missouri--Columbia, 2017)
    Let ? be an open and connected set in the complex plane. A mapping f : ? ? C is said to be conformal at a point z0 if it preserves angles and orientation between curves intersecting at z0. We discuss tangent lines and their ...
  • The Effects of Math Recovery on the Low-Performing Mathematics Student 

    Rossiter, Robert F. (2012)
    This study examined the effectiveness of the course, Math Recovery, on a group of ninth-grade students enrolled in the course Algebra/Geometry I measured by course grades and subsequent tenth-grade MAP scores. In addition, ...
  • Exponential sums, character sums, sieve methods and distribution of prime numbers 

    Guo, Victor Zhenyu (University of Missouri--Columbia, 2017)
    This thesis is focus on the methods of exponential sums and sieve methods applying to distribution of primes numbers in several forms, such as Piatetski-Shapiro primes, Beatty sequences, almost primes and primes in arithmetic ...
  • Generalized Koszul Properties of Commutative Local Rings 

    Hoffmeier, Justin Cole (2014)
    We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers ...
  • Harmonic functions and the Dirichlet problem 

    Mayfield, Caleb James (University of Missouri--Columbia, 2017)
    Let ? be an open and connected subset of the complex plane. A real valued function u : ? ? R is said to be harmonic if it has continuous first and second partial derivatives and satisfies Laplaces equation ?u = ? 2u ?x2 + ...
  • Perinormality in Polynomial and Module-Finite Ring Extensions 

    McCrady, Andrew (University of Missouri--Columbia, 2017)
    In this dissertation we investigate some open questions posed by Epstein and Shapiro in [9] regarding perinormal domains. More specifically, we focus on the ascent/descent property of perinormality between "canonical" ...
  • Uniform bounds in f-finite rings and their applications 

    Polstra, Thomas Marion (University of Missouri--Columbia, 2017)
    This dissertation establishes uniform bounds in characteristic p rings which are either F-finite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the Hilbert-Kunz ...