RSS 1.0Theses and Dissertations-Mathematics
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Construction of a non-standard integral on AC [0, 1]
(1998-08)A review of the Riemann and Lebesgue integration leads into the development and proof of the Riesz Representation Theorem. After this a new function space and a new norm are presented. A dense subset is extracted and ...
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On the Axiomatization of Mathematical Understanding: Continuous Functions in the Transition to Topology
(2017-08)The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear ...
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Finding the “Best” n-die when Fixing the Sum
(2021-12)This paper discusses results found by systematically listing every possible 6-sided die with a fixed sum of 21 and running a round-robin tournament to find the “best” die. -
Metrization theorems
(2000-05)The goal of this study is to prove The Urysohn Metrization Theorem. This paper represents an introduction to topological spaces with the focus on metric spaces. We provide a background in set theory and function theory ... -
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An Alternative Solution Method for Trajectory Optimization for Martian Descent and Landing
(2021-05)No abstract prepared. -
Describing Students' Analogical Reasoning While Creating Structures in Abstract Algebra
(2021-05)Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning ...
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Applications of Hypergraphic Matrix Minors via Contributors
(2021-05)Hypergrahic matrix-minors via contributors can be utilized in a variety of ways. Specifically, this thesis illustrates that they are useful in extending Kirchhoff-type Laws to signed graphs and to reinterpret Hadamard's ...
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Power domination on permutation graphs
(2013-05)For the purposes of monitoring power networks, power companies use devices known as phase measurement units (PMUs); these monitor the waveform of the various nodes in a network. The cost of these units makes it worthwhile ... -
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Extremal Cayley Graphs
(2012-08)Let Γ be a finite group with m elements. Let A be a nonempty subset of Γ. The Cayley digraph of Γ generated by A, denoted by Cay (Γ, A), is the digraph with vertex set Γ and arc set {uv | u-1v ∈ A}. A simple ...
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A Proposal for Making a Decision from Sample Elements of any Distribution Function
(1971-08)No abstract prepared. -
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A Group-theoretic Characterization of M-groups
(2004-08)I. Martin Isaacs, among others, has posed the problem of finding a purely group-theoretic characterization of M-groups which traditionally are defined via character theory. This thesis seeks to understand and answer ...
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Exploring the Instructional Coherence of Introduction to Fractions in Chinese Classrooms
(2020-08)The study investigated the instructional coherence of Chinese teachers’ teaching in grade 3 mathematics classroom from Shandong, China. The study illustrates how the three Chinese teachers provide students with opportunity ...
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Transition Between Education and Profession: Experiences of Statisticians
(2020-08)The transition to the workplace is challenging across disciplines, but particularly decisive for statisticians since the demand for statistical skills is growing across many different fields and sectors. The employment ...
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Elementary Preservice Teachers' Conceptions of and Reflections on Student Autonomous Problem-Solving and Mathematical Practices
(2020-08)The findings of this dissertation study are from a single-site, qualitative, case study involving undergraduate elementary preservice teacher participants from a two-week summer mathematics camp for elementary and middle ...
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