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DEVELOPING MATHEMATICS FOR TEACHING THROUGH CONCEPT STUDY: A CASE OF PRE-SERVICE TEACHERS IN TANZANIA
DownloadSpring 2019
This descriptive qualitative case study investigates the question “In what ways does developing mathematics for teaching through concept study contribute to the professional knowledge and skills of pre-service teachers?” The concept studies were conducted in a classroom driven by five conditions:...
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Spring 2019
Let $G$ be a linear algebraic group defined over a ground field $k$, and let $\mu$ be a $\Gal(k^\sep/k)$-module.A \tb{cohomological invariant} is a morphism $a:H^1(-,G)\to H^n(-,\mu)$ of two functors from the category of field extensions over $k$ to the category of setswhere $H^1(-,G)$ is the...
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Spring 2019
Atkin and Swinnerton-Dyer conjectured a simple characterization of those Fuchsian groups whose modular forms have integral Fourier coefficient. It has a natural and far-reaching generalization, which we will call the vASD conjecture, to vector-valued modular forms. We confirm vASD conjecture for...
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Fall 2020
The kinetic chemotaxis equations have long been used to model biological processes. We will analyze a volume filling variant of the kinetic chemotaxis equations on the torus. Since the kinetic chemotaxis systems have well known blow-up solutions, we spend a considerable amount of time showing...
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2021-04-01
A large portion of mathematics education research focuses on elementary and middle year’s content with professional development about how to teach mathematics often focused using specific tasks to teach certain topics. This kind of professional development makes it difficult for teachers to...
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Characterizing Population Heterogeneity of Salmonella Motion in Mucosal Environments Using Stochastic Modeling and the EM Algorithm
DownloadFall 2022
Salmonella are pathogenic bacteria that infect many species including humans. This pathogen thrives in the gastrointestinal track of their hosts and propel themselves in mucus with motion structures called flagella. Each cell has multiple flagella that can rotate either synchronously, resulting...
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Writing Research Articles in Discrete Mathematics: A Rhetorical, Multimodal Genre Analysis and Pedagogy
DownloadSpring 2022
This dissertation reports my rhetorical, multimodal genre analysis of research articles (RAs) in discrete mathematics and its pedagogical applications. The increasing demand on graduate students to publish their research in English and the need of these students to write in the key genres of...
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Fall 2023
The affine vertex superalgebra A=L^1(D(2,1;-v/w)) plays a key role as the geometric Langlands kernel VOA for SVOAs associated to so(3), osp(1|2) and other rank one Lie superalgbras. Since D(2,1;a) is an extension of the direct sum of 3 copies of sl(2), A can be naturally realized as an...
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Fall 2023
The aim of this thesis is to provide an exposition to Mochizuki and Hoshi's approach to birational anabelian geometry of mixed characteristic local fields. In the introductory chapter, we begin by recalling the relevant backgrounds on the Grothendieck conjectures on the étale fundamental groups...
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2023-02-01
SSHRC IDG awarded 2023: Mathematics is typically conceived as a cerebral, solitary activity. Tasks are ubiquitous in the mathematics classroom. From traditional textbook questions and worksheets to collaborative, inquirybased problems, tasks are the stage on which mathematical knowing and doing...