Browsing by Thesis Department "Mathematics"
Now showing items 18 of 8

Cohomology of Finite Modules over Short Gorenstein Rings
(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 SchwarzChristoffel transformation
(University of MissouriColumbia, 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 LowPerforming Mathematics Student
(2012)This study examined the effectiveness of the course, Math Recovery, on a group of ninthgrade students enrolled in the course Algebra/Geometry I measured by course grades and subsequent tenthgrade MAP scores. In addition, ... 
Exponential sums, character sums, sieve methods and distribution of prime numbers
(University of MissouriColumbia, 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 PiatetskiShapiro primes, Beatty sequences, almost primes and primes in arithmetic ... 
Generalized Koszul Properties of Commutative Local Rings
(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
(University of MissouriColumbia, 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 ModuleFinite Ring Extensions
(University of MissouriColumbia, 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 ffinite rings and their applications
(University of MissouriColumbia, 2017)This dissertation establishes uniform bounds in characteristic p rings which are either Ffinite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the HilbertKunz ...