Theses and DissertationsMathematics
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Application of the LefschetzHopf Fixed Point Theorem to Closed Orientable Surfaces
(200712)No abstract prepared. 
Quasicontinuous Functions and Functions of Bounded Variation
(196508)The purpose of this investigation is threefold. First, since quasicontinuous functions are a generalization of continuous functions, properties of quasicontinuous functions similar to the properties of continuous functions ... 
Stokes' Theorem: Calculus of Differential Forms
(200412)This thesis connects a number of fields of mathematics in relation to Euclidean nspace. It defines the meanings of differentiation for functions between these spaces and gives an exposition of the inverse function theorem. ... 


Exploring Prospective Elementary Teacher's PeerInterviewer Verbal Interactions in a Mathematics Content Course
(202005)Responsive teaching interactions, an effective teaching practice, are difficult to develop. To train prospective elementary teachers of mathematics to interact responsively with students completing mathematics tasks, we ... 
Necklaces and Slimes
(202005)It was asked if one can find a bijective map between the following two objects: binary necklaces with n black beads and k white beads and certain (n, k)codes whose weighted sum is 0 modulo n (Brauner et al.,2019 [9]; ...

Finding an Upper Bound to the Order of Permutation Groups Using the Size of the Largest Conjugacy Class
(202005)No abstract prepared. 

On the Pebbling Numbers of Graphs
(200505)Graph pebbling is an application which has evolved from the study of graph theory. The goal of pebbling m a graph is to use pebbling steps to move one pebble onto a designated root vertex. A pebbling step is produced ...

On Depth of Powers of Ideals
(201104)The paper “The depth of powers of an ideal," by Herzog and Hibi is expanded to include background information and proof details. The numerical function f(k)=depth(S/Ik] is discussed where S is Noetherian local or standard ... 

A Fast Solver for the Expanded Mixed Finite Element Method
(20180416)We present a fast solver for expanded mixed finite element method with a discontinuous coefficient. Our result is based on the auxiliary space preconditioning method and the CrouzeixRaviart Finite Element Method. 
Evolving Mathematical Identity for PostSecondary Students
(201805)Mathematics encompasses more than formulas, theorems and proofs. For many, mathematics can be a way of life or even a culture and like within any culture, an individual who associates with that culture has an identity: a ... 
Assessing ITP Students' Validating Ability: Framing, Developing and Validating a Pilot Assessment
(20190712)In this paper I discuss the process of creating a closedform multiplechoice assessment of students’ ability to validate mathematical proofs at the introduction to proof (ITP) level. This process involved: (1) creating ... 

Chinese middle school mathematics teachers' pedagogical content knowledge and cultural beliefs towards teaching
(20190426)This study investigated the pedagogical content knowledge and cultural beliefs towards teaching of middle school mathematics teachers in Shandong, China. The study illustrates how four middle school mathematics teachers ...

A new 5step perturbationbased multicollinearity diagnostic package
(20190416)The ordinary least squares method, for estimating unknown parameters of a multiple linear regression (MLR) model, produces an idealistic solution if the column vectors (regressors) of the design matrix X are linearly ...