• 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 ...
  • 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 ...
  • 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 ...