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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Integer Compositions, Gray Code, And The Fibonacci Sequence, Linus Lindroos
Integer Compositions, Gray Code, And The Fibonacci Sequence, Linus Lindroos
Electronic Theses and Dissertations
In this thesis I show the relation of binary and Gray Code to integer compositions and the Fibonacci sequence through the use of analytic combinatorics, Zeckendorf's Theorem, and generating functions.
Global Domination Stable Graphs, Elizabeth Marie Harris
Global Domination Stable Graphs, Elizabeth Marie Harris
Electronic Theses and Dissertations
A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.
Improving Student Learning In Undergraduate Mathematics, Gabrielle Rejniak
Improving Student Learning In Undergraduate Mathematics, Gabrielle Rejniak
Electronic Theses and Dissertations
The goal of this study was to investigate ways of improving student learning, par- ticularly conceptual understanding, in undergraduate mathematics courses. This study focused on two areas: course design and animation. The methods of study were the following: Assessing the improvement of student conceptual understanding as a result of team project-based learning, individual inquiry-based learning and the modi ed empo- rium model; and Assessing the impact of animated videos on student learning with the emphasis on concepts. For the first part of our study (impact of course design on student conceptual understanding) we began by comparing the following three groups …
Cayley-Dickson Loops, Jenya Kirshtein
Cayley-Dickson Loops, Jenya Kirshtein
Electronic Theses and Dissertations
In this dissertation we study the Cayley-Dickson loops, multiplicative structures arising from the standard Cayley-Dickson doubling process. More precisely, the Cayley-Dickson loop Qn is the multiplicative closure of basic elements of the algebra constructed by n applications of the doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, sedenions). Starting at the octonions, Cayley-Dickson algebras and loops become nonassociative, which presents a significant challenge in their study.
We begin by describing basic properties of the Cayley–Dickson loops Qn. We establish or recall elementary facts about Qn, e.g., inverses, …