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Categorizing Students' Difficulties with Mathematical Proofs: Developing a Model of the Structure of Proof Construction
(2015-08-14)
Studies have shown that proof construction is a challenging task for students at all levels. The purposes of my study were to examine students' difficulties with proof construction and to explore a practical method to help ...
Totally Reflected Groups
(2016-05-13)
A group G is totally reflected if it has a generating set S such that each edge in the Cayley graph Gamma(G,S) is inverted by some color-preserving reflection on the graph. For example, we will show that Coxeter groups and ...
Webs for Type Q Lie Superalgebras
(2017-12-15)
In the first part of this dissertation, we construct a monoidal supercategory whose morphism spaces are spanned by equivalence classes of diagrams called oriented type Q webs, modulo certain relations. We then prove a ...
Some sharp inequalities related to Moser-Tridinger-Onofri inequality
(2014-05)
In this dissertation, we focus on the study of sharp inequalities of Moser-
Trudinger-Onofri type. We first establish the analog Bliss and Hardy inequal-
ities with sharp constant involving exponential weight function. ...
Some Types And Covers For Quaternionic Hermitian Groups
(2014-08-15)
In this dissertation we determine the reducibility of certain induced representations. We do this using Bushnell and Kutzko's method of types and covers. We consider certain quaternionic hermitian groups over a $p$-adic ...
Extensional Maps
(2014-05-09)
In a recent paper, Ziga Virk defined a type of continuous map which preserves extension properties. We generalize this notion and call such maps extensional maps. In this paper we will establish many of the basic properties ...
COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS
(2014-12)
From a geometric point of view, we use coordinates as the main tool to define the holomorphic gradient, the antiholomorphic gradient, and the complex gradient of a complex-valued function on Kahler manifolds. Then we define ...
Calculus Instructors' Resources, Orientations, and Goals in Teaching Low-Achieving Students
(2014-05-09)
Teaching and learning calculus has been the subject of mathematics education research for many years. Although the literature is mainly concerned with students’ difficulties with calculus, research on mathematicians’ day ...
Some Classes of Jacobi Matrices and Schrödinger Operators
(2014)
This dissertation addresses two classes of Jacobi matrices and Schrödinger operators. First, we consider Jacobi matrices and Schrödinger operators that are reflectionless on an interval. We give a systematic development ...
Complexity of Modules over Lie Superalgebras
(2014)
In this dissertation, a fair amount of work is dedicated to computing the complexity of modules over a classical Lie superalgebra $\fg=\fg_{\0}\oplus \fg_{\1}$ over the complex numbers $\C$. We will consider the category ...