Physical Sciences and Mathematics Commons^™

A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating …

Leading Students To Investigate Diffusion As A Model Of Brine Shrimp Movement, Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell

Mathematics and Statistics Faculty Publications

Integrating experimental biology laboratory exercises with mathematical modeling can be an effective tool to enhance mathematical relevance for biologists and to emphasize biological realism for mathematicians. This paper describes a lab project de-signed for and tested in an undergraduate biomathematics course. In the lab, students follow and track the paths of individual brine shrimp confined in shallow salt water in a Petri dish. Students investigate the question, “Is the movement well characterized as a 2-dimensional random walk?” Through open, but directed discussions, students derive the corresponding partial differential equation, gain an understanding of the solution behavior, and model brine shrimp …

Random Motion And The Diffusion Of Brine Shrimp: A Project Based Learning Unit, Rebecca Atkins

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Over the years, there have been several trends, philosophies, and ideas about how mathematics should be taught. These have included progressive movements, essentialist movements, drill and practice, teacher-centered methodologies, student-centered methodologies, and others. However, despite these various instructional trends, research has found that mathematics teachers have basically taught the same way for years, with little or no variation with respect to the changing trends (Ward, 2001). For many students, the traditional teaching method employed in their mathematics classes is typically centered on the teacher and includes lecture in which the teacher provides the necessary definitions and notations and does several …

Teaching Probability Through Use Of An Applet, Melissa Gregory Jackson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The use of technology in the classroom is an ongoing debate by educators. Many teachers consider it to be a valuable teaching tool. Despite the many advantages, there are also drawbacks in using technology. A Java applet is a particular kind of multimedia technology proven to be useful in education. Because of students' struggles with learning basic probability in Statistics 1040, I have created a probability applet to reinforce the concept of probability. The applet was tested with two Statistics 1040 classes. The majority of students agreed that they learned more about probability from using the applet. Several of the …

Testing And Estimation For Functional Data With Applications To Magnetometer Records, Inga Maslova

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The functional linear model, Y_n = ψX_n + ε_n, with functional response and explanatory variables is considered. A simple test of the nullity of ψ based on the principal component decomposition is proposed. The test statistic has asymptotic chi-squared distribution, which is also an excellent approximation in finite samples. The methodology is applied to data from terrestrial magnetic observatories.

In recent years, the interaction of the auroral substorms with the equatorial and mid-latitude currents has been the subject of extensive research. We introduce a new statistical technique that allows us to test at a specified …

Modeling The Evolution Of Insect Phenology With Particular Reference To Mountain Pine Beetle, Brian P. Yurk

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Climate change is likely to disrupt the timing of developmental events (phenology) in insect populations in which development time is largely determined by temperature. Shifting phenology puts insects at risk of being exposed to seasonal weather extremes during sensitive life stages and losing synchrony with biotic resources. Additionally, warming may result in loss of developmental synchronization within a population, making it difficult to find mates or mount mass attacks against well-defended resources at low population densities. It is unknown whether genetic evolution of development time can occur rapidly enough to moderate these effects.

The work presented here is largely motivated …

Simulation, Kriging, And Visualization Of Circular-Spatial Data, William James Morphet

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The circular dataimage is defined by displaying direction as the color at the same direction in a color wheel composed of a sequence of two-color gradients with color continuity between gradients. The resulting image of circular-spatial data is continuous with high resolution. Examples include ocean wind direction, Earth's main magnetic field, and rocket nozzle internal combustion flow. The cosineogram is defined as the mean cosine of the angle between random components of direction as a function of distance between observation locations. It expresses the spatial correlation of circular-spatial data. A circular kriging solution is developed based on a model fitted …

Symmetry Analysis Of General Rank-3 Pfaffian Systems In Five Variables, Francesco Strazzullo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation we applied geometric methods to study underdetermined second order scalar ordinary differential equations (called general Monge equations), nonlinear involutive systems of two scalar partial differential equations in two independent variables and one unknown and non-Monge-Ampere Goursat parabolic scalar PDE in the plane. These particular kinds of differential equations are related to general rank-3 Pfaffian systems in five variables. Cartan studied these objects in his 1910 paper. In this work Cartan provided normal forms only for some general rank-3 Pfaffian systems with 14-, 7-, and 6-dimensional symmetry algebra.

In this dissertation we provided normal forms of all general …

Logistic Models With Missing Categorical Covariates, Jeremiah Rounds

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We present an EM based solution to missing categorical covariates in Binomial models with logit links using an assumption that experimental units are drawn from a Multinomial population of infinite size. We further address the problem of separation of points inducing large variances on parameter estimates by the use of a novel score-modification based on Firth's bias-reduction score-modification. We simulate to address questions about estimate bias, distribution, and appropriate parameter coverage by Wald intervals.

Superposition Formulas For Darboux Integrable Exterior Differential Sys-Tems, Ian M. Anderson, Mark E. Fels, Peter J. Vassiliou

Mathematics and Statistics Faculty Publications

In this article we solve an inverse problem in the theory of quotients for differential equations. We characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original. The fact that a system can be written as a quotient can be used to find the general solution to these equations. Some examples are given to demonstrate the theory.

An Investigation Of The Ends Of Finitely Generated Groups, Daniel T. Murphree

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Geometric group theory is a relatively new branch of mathematics, studied as a distinct area since the 1990's. It explores invariant properties of groups based on group actions defined on topological or geometrical spaces. One of the pioneering works in geometric group theory is the article "Topological Methods in Group Theory" by Peter Scott and Terry Wall, written in 1977. This article was an overview of revised notes from an advanced course give in Liverpool in the same year. This report is an attempt to make these notes more accessible to lower level graduate students in the fields of topology …

The Classification Of Simple Lie Algebras In Maple, D. Russell Sadler

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Lie algebras are invaluable tools in mathematics and physics as they enable us to study certain geometric objects such as Lie groups and differentiable manifolds. The computer algebra system Maple has several tools in its Lie Algebras package to work with Lie algebras and Lie groups. The purpose of this paper is to supplement the existing software with tools that are essential for the classification of simple Lie algebras over C.

In particular, we use a method to find a Cartan subalgebra of a Lie algebra in polynomial time. From the Cartan subalgebra we can compute the corresponding root system. …