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• ### Writing Research Articles in Discrete Mathematics: A Rhetorical, Multimodal Genre Analysis and Pedagogy

Spring 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...

• ### Characterizing Population Heterogeneity of Salmonella Motion in Mucosal Environments Using Stochastic Modeling and the EM Algorithm

Fall 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...

• ### Theories that Inform the Use of Variation in Mathematics Pedagogy

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...

• ### Analysis of scaling limits of the Kinetic Chemotaxis Equations

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...

• ### Cohomological Invariants of Simple Linear Algebraic Groups Arising via the Killing Form

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...

• ### DEVELOPING MATHEMATICS FOR TEACHING THROUGH CONCEPT STUDY: A CASE OF PRE-SERVICE TEACHERS IN TANZANIA

Spring 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:...

• ### Unbounded Denominators for Hypergeometric Functions and Modular Forms

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...

• ### Evaluation of Assistive Technology Resources for Access to Hands-On Activities by Students with Disabilities, and Assistive Technology Teams

2018-03-15

SSHRC PEG Awarded 2018: Two in-depth case studies will evaluate use of Lego Mindstorm robots and teaching materials developed specifically for these as math aids, by students with hand-based disabilities, their teachers, and Assistive Technology team. Quantitative data collected will include 1)...

• ### Geometric and Graphical Study of 1-Dimensional N-Extended Supersymmetry Algebras

Fall 2018

In this thesis, we explore the relationship between graphical representations of the 1-dimensional N-extended supersymmetry algebra called Adinkras, compact Riemann surfaces, and quivers. An Adinkra is a graph which was originated in physics to study off-shell representations of the supersymmetry...

• ### The influence of contextual factors on assistive technology strategies for mathematics learning in students with physical impairments

Fall 2018

Performance of students with physical impairments in mathematics are often limited because of the use of hands-on strategies using manipulatives (e.g., blocks or Cuisenaire rods) to learn early concepts. Two assistive technology (AT) strategies have been used by students to handle manipulatives,...

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