Mathematics Commons^™

Group Rings, Christopher Wrenn

Masters Essays

No abstract provided.

Mathematical Curves In The High School Classroom, Magdalena Zook

Masters Essays

No abstract provided.

Advanced Enrichment Topics In An Honors Geometry Course, Kayla Woods

Masters Essays

No abstract provided.

The Development Of Secondary Mathematics Teachers’ Pedagogical Identities In The Social Context Of Classroom Interactions, Hyung Won Kim

School of Mathematical & Statistical Sciences Faculty Publications

Research demonstrates a disjuncture between the practices encouraged by teacher education programs and what teachers actually do in the classroom. It also informs us that the cognitive and social characteristics of individual teachers such as their attitudes, beliefs and knowledge contribute to their classroom practices. This qualitative study investigates how the teacher identity of mathematics teachers – the person’s sense of who he/she is as a mathematics teacher – is related to the disjuncture between encouraged and actual classroom practices. Specifically, the study looks into how mathematics teachers form their teaching practices in the social context of their classroom interactions, …

Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

Here we investigate the effect of the vertical rate of change in thermal diffusivity due to a hydrothermal convective flow in a horizontal porous medium. The continuity equation, the heat equation and the momentum-Darcy equation constitute the governing system for the flow in a porous medium. Assuming a vertically varying basic state, we derive the linear system and from this linear system, we compute the critical Rayleigh and wave numbers. Using fourth-order Runge-Kutta and shooting methods, we obtain the marginal stability curves and linear solutions to analyze the solution pattern for different diffusivity parameters.

Exchanging Deficit For Affordance: Developing Preservice Teachers’ Capacity To See Emergent Bilingual Students’ Resources, Aaron T. Wilson, Hyung Won Kim, M. Alejandra Sorto

School of Mathematical & Statistical Sciences Faculty Publications

We present a Scholarship of Teaching and Learning (SoTL) research project aimed at helping pre-service teachers to grasp the importance of their emergent bilingual students' bilingualism and cultural backgrounds as resources to serve them in apprehending mathematics instruction and explaining their mathematics to others.

Oer Women In Math Course, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

This Women in Math course takes a look at 11 notable women mathematicians through readings, quizzes, discussion boards, and activities related to the mathematical contributions of the women. Several of the activities are original and can be found separately at Pittsburg State University Digital Commons (https://digitalcommons.pittstate.edu/ - search by author for Huffman, Cynthia).

Course URL

The OER Women in Math course can be accessed at https://pittstate.instructure.com/courses/1081791 .

Active Calculus Multivariable: 2018 Edition, Steven Schlicker, David Austin, Matthew Boelkins

Open Textbooks

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are freely readable online in HTML format (new in this version of Active Calculus Multivariable) and are also available for in PDF; in the electronic format, graphics are in full color; the texts are open source, and interested instructors can gain access to the original source files on GitHub; the style of the texts requires students to be active learners — there are very few worked examples in the …

Preceding-Jump Simplex Method, Natdanai Kafakthong

Chulalongkorn University Theses and Dissertations (Chula ETD)

A practical linear programming solver uses the simplex method to identify the optimal solution by iteratively searching among adjacent feasible vertices. It may visit numerous vertices before finding the optimal one for a large linear programming problem taking a long time to succeed. This research proposes a heuristic method to alleviate this issue by jumping to a new vertex close to the optimal one before performing the simplex method. The new vertex is identified by first jumping from the initial vertex along the gradient vector of the objective function or alternative direction if the objective direction points out of the …

Closed-Form Formula For Pricing Discretely-Sampled Moment Swaps On One-Dimensional Ito Process, Kittisak Chumpong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Moment swaps are essentially forward contracts on realized higher moments of log-returns of a specified underlying asset, which play an important role in protection against different kinds of market shocks. Variance, skewness, and kurtosis swaps are examples of moment swaps currently traded in markets. To facilitate market practitioners, this work provides a simple and easy-to-use pricing formula of moment swaps on discrete sampling under the Ito process, extended Black-Scholes model for stock prices and Schwartz model for commodity prices. Furthermore, the interesting topics of the fair prices are also investigated. Finally, Monte Carlo simulations are performed to support the accuracy …

Covering Of Objects Related To Rupert Property, Pongbunthit Tonpho

Chulalongkorn University Theses and Dissertations (Chula ETD)

One problem related to covering problem is whether one object has Rupert property. An object K in R³ has the Rupert property if a hole could be cut through one copy of K with the same size to permit another copy to pass through it. There are objects in R³ which have Rupert property, such as a cube. But not all of objects in R³ has Rupert property, such as a sphere. It is interesting to check that a given object has Rupert property. In this work, we construct useful lemmas for studying this problem. Furthermore, we apply these lemmas …

Noncommutative Reality-Based Algebras Of Rank 6, Allen Herman, Mikhael Muzychuk, Bangteng Xu

EKU Faculty and Staff Scholarship

We show that noncommutative standard reality-based algebras (RBAs) of dimension 6 are determined up to exact isomorphism by their character tables. We show that the possible character tables of these RBAs are determined by seven real numbers, the first four of which are positive and the remaining three real numbers can be arbitrarily chosen up to a single exception. We show how to obtain a concrete matrix realization of the elements of the RBA-basis from the character table. Using a computer implementation, we give a list of all noncommutative integral table algebras of rank 6 with orders up to 150. …

Onsager Reciprocal Relations: Microscopic (Onsager) Or Macroscopic (Sliepcevich), R. E. "Buddy" Babcock

Chemical Engineering Faculty Publications and Presentations

This paper is a combination of the discussion of two nineteenth century theoretical giants Lars Onsager and C. M. Sliepcevich, their works in general, and specifically the famous reciprocal relations of Onsager with respect to irreversible thermodynamics. Emphasis is placed on their penetrating depth and breadth of analysis so inherently necessary in their problem-solving endeavors. The landscape of their work will be laid out for the reader by a comparison of Onsager’s microscopic statistical mechanics derivation of the famous reciprocal relationships and a macroscopic thermodynamic derivation published by C. M. Sliepsevich that led to considerable discussion in the literature in …

Linear Algebra Applications In 3d Computer Graphics, Albert A. Antero, Chris Choung, Chris Goff

Math 365 Class Projects

Linear Transformations, Homogenous Coordinates, World Matrix, Project Matrices, Normalized Device Coordinates, View Matrix

Quasi-Gorenstein Modules, Alexander York

Electronic Theses and Dissertations

This thesis will study the various roles that quasi-Gorenstein modules and their properties play in the study of homological dimensions and linkage of modules. To that effect we begin by studying these modules in their own right. An R-module M of grade g will be quasi-Gorenstein if ExtiR(M, R) = 0 for i 6= g and there is an isomorphism M ∼= ExtgR(M, R). Such modules have many nice properties which we will explore throughout this thesis. We will show they help extend a characterization of diagonalizable matrices over principal ideal domains to more general rings. We will use their …

Weierstrass Vertices And Divisor Theory Of Graphs, Ajani Ruwandhika Chulangi De Vas Gunasekara

Electronic Theses and Dissertations

Chip-firing games and divisor theory on finite, connected, undirected and unweighted graphs have been studied as analogs of divisor theory on Riemann Surfaces. As part of this theory, a version of the one-dimensional Riemann-Roch theorem was introduced for graphs by Matt Baker in 2007. Properties of algebraic curves that have been studied can be applied to study graphs by means of the divisor theory of graphs. In this research, we investigate the property of a vertex of a graph having the Weierstrass property in analogy to the theory of Weierstrass points on algebraic curves. The weight of the Weierstrass vertices …

3d Printing Of 2d N = (0, 2) Gauge Theories, Sebastían Franco, Azeem Hasan

Publications and Research

We introduce 3d printing, a new algorithm for generating 2d N = (0, 2) gauge theories on D1-branes probing singular toric Calabi-Yau 4-folds using 4d N = 1 gauge theories on D3-branes probing toric Calabi-Yau 3-folds as starting points. Equivalently, this method produces brane brick models starting from brane tilings. 3d printing represents a significant improvement with respect to previously available tools, allowing a straightforward determination of gauge theories for geometries that until now could only be tackled using partial resolution. We investigate the interplay between triality, an IR equivalence between different 2d N = …

Course Portfolio For Math 407 Mathematics For High School Teaching: Refining Conceptual Understanding In A Mathematics Course For Pre-Service Teachers, Alexandra Seceleanu

UNL Faculty Course Portfolios

My intention in this portfolio is to present my approach to teaching an upper-level mathematics course for pre-service secondary level mathematics teachers. Several teaching strategies are discussed in the context of designing a coherent approach to this course, which emphasizes the need for conceptual reasoning above all other goals. These strategies are evaluated and assessed in connection to the learning outcomes using samples of student work from the course.

Also presented are samples of course materials that were used to lead students through an organized discussion of the relevant concepts. These materials convey some basic mathematical knowledge and therefore may …

Restriction Of A Quadratic Form Over A Finite Field To A Nondegenerate Affine Quadric Hypersurface, Edoardo Ballico

Turkish Journal of Mathematics

Let $h, h_M: \mathbb {F} _q^n\to \mathbb {F} _q$ be quadratic forms with $h$ not degenerate. Fix $k\in \mathbb {F} _q$ and set $C_n(k,h)_{\mathbb {F} _q}:= \{h(x_1,\dots ,x_n)=k\}\subset \mathbb {F}_q^n$. We compute (in many cases) the image of $h_{M C_n(k,h)_{\mathbb {F} _q}}$. This question is related to a question on the numerical range of matrices over a finite field.

A Coanalytic Menger Group That Is Not $\Sigma$-Compact, Seçi̇l Tokgöz

Turkish Journal of Mathematics

Under $V=L$ we construct coanalytic topological subgroups of reals, demonstrating that even for definable groups of reals, selection principles may differ.