Browsing by Thesis Department "Mathematics"
Now showing items 16 of 6

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 ... 
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, ... 
Frames and applications: distribution of frame coeficients, integer frames and phase retrieval
(2015)The present dissertation is divided into two main areas: frame theoretic results and applications of frames. In particular, the beginning half develops the first detailed theory of the distribution of frame coefficients. ... 
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 ... 
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type
(2015). The present dissertation consists of three main parts. One theme underscoring the work carried out in this dissertation concerns the relationship between analysis and geometry. As a first illustration of the interplay ... 
Trace/extension operators in rough domains and applications to partial differential equations
(2015)Trace and extension theory lay the foundation for solving a plethora of boundary value problems. In developing this theory, one typically needs wellbehaved extension operators from a specified domain to the entire Euclidean ...