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Creation Of A College Math Club For High School Students, Lilian N. Chavez
Creation Of A College Math Club For High School Students, Lilian N. Chavez
Theses and Dissertations
This study aimed to investigate the variables that contribute to high school students' desire to join a math club, specifically the FMiM VIP Club, which is an extension of UTRGV's Follow Me into Math research project. The research utilized multiple questionnaire s to examine the combination of factors that contribute to the students' attitudes toward the math club. The participants were high school Algebra 2 students from two different schools, and the study was conducted in two stages. The first stage was conducted in the Spring of 2022, focusing on girls' math identity and their interactions with the FMiM VIP …
The Gini Index In Algebraic Combinatorics And Representation Theory, Grant Joseph Kopitzke
The Gini Index In Algebraic Combinatorics And Representation Theory, Grant Joseph Kopitzke
Theses and Dissertations
The Gini index is a number that attempts to measure how equitably a resource is distributed throughout a population, and is commonly used in economics as a measurement of inequality of wealth or income. The Gini index is often defined as the area between the "Lorenz curve" of a distribution and the line of equality, normalized to be between zero and one. In this fashion, we will define a Gini index on the set of integer partitions and prove some combinatorial results related to it; culminating in the proof of an identity for the expected value of the Gini index. …
States And The Numerical Range In The Regular Algebra, James Patrick Sweeney
States And The Numerical Range In The Regular Algebra, James Patrick Sweeney
Theses and Dissertations
In this dissertation we investigate the algebra numerical range defined by the Banach algebra of regular operators on a Dedekind complete complex Banach lattice, i.e., V (Lr(E), T) = {Φ(T) : Φ ∈ Lr(E)∗, ||Φ|| = 1 = Φ(I)}. For T in the center Z(E) of E we prove that V (Lr(E), T) = co(σ(T)). For T ⊥ I we prove that V (Lr(E), T) is a disk centered at the origin. We then consider the part of V (Lr(E), T) obtained by restricting ourselves to positive states Φ ∈ Lr(E)∗. In this case we show that we get a …
Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik
Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik
Theses and Dissertations
Teaching students with Intellectual Disability (ID) is a relatively new endeavor. Beginning in 2001 with the passage of the No Child Left Behind Act, the general education curriculum integrated algebra across the K-12 curriculum (Kendall, 2011; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010), and expansion of the curriculum included five intertwined skills (productive disposition, procedural fluency, strategic competence, adaptive reasoning, and conceptual understanding) (Kilpatrick, Swafford, & Findell, 2001). Researchers are just beginning to explore the potential of students with ID with algebra (Browder, Spooner, Ahlgrim-Delzell, Harris & Wakeman, 2008; Creech-Galloway, Collins, Knight, …
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
Theses and Dissertations
An n-dimensional halved cube is a graph whose vertices are the binary strings of length n, where two vertices are adjacent if and only if they differ in exactly two positions. It can be regarded as the graph whose vertex set is one partite set of the n-dimensional hypercube, with an edge joining vertices at hamming distance two. In this thesis we compute the automorphism groups of the halved cubes by embedding them in R n and realizing the automorphism group as a subgroup of GLn(R). As an application we show that a halved cube is a circulant graph if …
Infinitely Generated Clifford Algebras And Wedge Representations Of Gl∞|∞, Bradford J. Schleben
Infinitely Generated Clifford Algebras And Wedge Representations Of Gl∞|∞, Bradford J. Schleben
Theses and Dissertations
The goal of this dissertation is to explore representations of $\mathfrak{gl}_{\infty|\infty}$ and associated Clifford superalgebras. The machinery utilized is motivated by developing an alternate superalgebra analogue to the Lie algebra theory developed by Kac. In an effort to establish a natural mathematical analogue, we construct a theory distinct from the super analogue developed by Kac and van de Leur. We first construct an irreducible representation of a Lie superalgebra on an infinite-dimensional wedge space that permits the presence of infinitely many odd parity vectors. We then develop a new Clifford superalgebra, whose structure is also examined. From here, we extend …
Infinite Product Group, Keith G. Penrod
Infinite Product Group, Keith G. Penrod
Theses and Dissertations
The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.