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Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

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

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …

Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation considers an approximation strategy using a wavelet reconstruction scheme for solving elliptic problems. The foci of the work are on (1) the approximate solution of differential equations using multiresolution analysis based on wavelet transforms and (2) the homogenization process for solving one and two-dimensional problems, to understand the solutions of second order elliptic problems. We employed homogenization to compute the average formula for permeability in a porous medium. The structure of the associated multiresolution analysis allows for the reconstruction of the approximate solution of the primary variable in the elliptic equation. Using a one-dimensional wavelet reconstruction algorithm proposed …

Canonical Coordinates On Lie Groups And The Baker Campbell Hausdorff Formula, Nicholas Graner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Lie Groups occur in math and physics as representations of continuous symmetries and are often described in terms of their Lie Algebra. This thesis is concerned with finding a concrete description of a Lie group given its associated Lie algebra. Several calculations toward this end are developed and then implemented in the Maple Differential Geometry package. Examples of the calculations are given.

Brun's 1920 Theorem On Goldbach's Conjecture, James A. Farrugia

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One form of Goldbach’s Conjecture asserts that every even integer greater than 4is the sum of two odd primes. In 1920 Viggo Brun proved that every sufficiently large even number can be written as the sum of two numbers, each having at most nine prime factors. This thesis explains the overarching principles governing the intricate arguments Brun used to prove his result.

Though there do exist accounts of Brun’s methods, those accounts seem to miss the forest for the trees. In contrast, this thesis explains the relatively simple structure underlying Brun’s arguments, deliberately avoiding most of his elaborate machinery and …

Three Environmental Fluid Dynamics Papers, Eden Furtak-Cole

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Three papers are presented, applying computational fluid dynamics methods to fluid flows in the geosciences. In the first paper, a numerical method is developed for single phase potential flow in the subsurface. For a class of monotonically advancing flows, the method provides a computational savings as compared to classical methods and can be applied to problems such as forced groundwater recharge. The second paper investigates the shear stress reducing action of an erosion control roughness array. Incompressible Naiver-Stokes simulations are performed for multiple wind angles to understand the changing aerodynamics of individual and grouped roughness elements. In the third paper, …

A Series Of Papers On Detecting Examinees Who Used A Flawed Answer Key, Marcus W. Scott

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One way that examinees can gain an unfair advantage on a test is by having prior access to the test questions and their answers, known as preknowledge. Determining which examinees had preknowledge can be a difficult task. Sometimes, the compromised test content that examinees use to get preknowledge has mistakes in the answer key. Examinees who had preknowledge can be identified by determining whether they used this flawed answer key. This research consisted of three papers aimed at helping testing programs detect examinees who used a flawed answer key.

The first paper developed three methods for detecting examinees who used …

Learning Logic: A Mixed Methods Study To Examine The Effects Of Context Ordering On Reasoning About Conditionals, Christina W. Lommatsch

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Logical statements are prevalent in mathematics, the sciences, law, and many areas of everyday life. The most common logical statements are conditionals, which have the form “If H..., then C...,” where “H” is a hypothesis (or condition) to be satisfied and “C” is a conclusion to follow. Reasoning about conditionals is a skill that is only superficially understood by most individuals and depends on four main conditional contexts (e.g., intuitive, abstract, symbolic, or counterintuitive). The purpose of this study was to test a theory about the effects of context ordering on reasoning about conditionals. To test the theory, the researcher …

Modeling The Spread Of Alfalfa Stem Nematodes: Insights Into Their Dynamics And Control, Scott G. Jordan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Alfalfa is a major cash crop in the western United States, where fields that are infested with the alfalfa stem nematode (Ditylenchus dipsaci) can be found. With no nematicides available to control alfalfa stem nematode spread, growers can use nematode resistant varieties of alfalfa to manage nematode populations in a field. A deterministic, discrete-time, host-parasite model is presented that describes the spread of alfalfa stem nematodes on resistant hosts that was fit to experimental data obtained in Weber County, Utah. Numerical results obtained from simulations with the model are used to compare how varying levels of resistance can affect …

Mindset, Attitudes, And Success In Statistics, Matthew Isaac

Undergraduate Honors Capstone Projects

Students in many disciplines are required to take an introductory statistics course while pursuing a college education. Despite the utility of statistical methods in future research and career pursuits, many students have negative views of statistics. We are interested in how students' mindsets and attitudes towards statistics impact their performance in an undergraduate statistics course. We administered a survey to students in several undergraduate statistics courses at Utah State University. This survey included questions addressing mathematics experience, attitudes towards statistics, mindset, and course performance. We observed that the majority of students indicated the presence of a growth mindset and positive …

Relations Between Theta Functions Of Genus One And Two From Geometry, Thomas Hill

Undergraduate Honors Capstone Projects

Genus-two curves with special symmetries are related to pairs of genus-one curves by two and three-sheeted ramified coverings. This classical work dates back to early 20th century and is known as Jacobi and Hermite reduction. Jacobians of genus-two curves can be used to construct complex two-dimensional complex projective manifolds known as Kummer surfaces. On the other hand, the defining coordinates and parameters of both elliptic curves and Kummer surfaces can be related to Riemann Theta functions and Siegel Theta functions, respectively. This result goes back to the seminal work of Mumford in the 1980s. We use the geometric relation between …