Physical Sciences and Mathematics Commons^™

Algebraic Properties Of Killing Vectors For Lorentz Metrics In Four Dimensions, Jesse W. Hicks

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

Four-dimensional space-times with symmetry play a central role in the theory of general relativity. In 1961, in the book Einstein Spaces, A.Z. Petrov gave a complete local classification of four-dimensional space-times based upon their local isometry group, that is, their Lie algebra of Killing vector fields. In this report we discuss algebraic and geometric properties of these Lie algebras. A database of these properties has been computed for the five-dimensional Lie algebras of Killing vectors found in Petrov. As an application of our work, we present dieomorphisms between a few pairs of these Lie algebras of Killing vectors.

Modeling Phloem Temperatures Relative To Mountain Pine Beetle Phenology, Matthew Jared Lewis

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

We explore a variety of methods to estimate phloem temperatures from ambient air temperatures suitable for the mountain pine beetle, Dendroctonus ponderosae. A model's ability to induce the same phenology generated from observed phloem temperatures measures its effectiveness rather than a simple reconstruction of phloem temperatures. From a model's phenology results we are able to ascertain whether the model produces a similar amount of developmental energy exhibited by observed phloem temperatures.

Three models performed best: Newton, Newton South and Matching. The Newton model uses Newton's Law of Cooling to effectively estimate northern aspect phloem temperatures. The Newton South model …

Darboux Integrability - A Brief Historial Survey, Ian M. Anderson

Mathematics and Statistics Faculty Presentations

No abstract provided.

Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, Florence Funmilayo Obielodan

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

Despite the significance and the emphasis placed on mathematics as a subject and field of study, achieving the right attitude to improve students‟ understanding and performance is still a challenge. Previous studies have shown that the problem cuts across nations around the world, both developing countries and developed alike. Teachers and educators of the subject have responsibilities to continuously develop innovative pedagogical approaches that will enhance students‟ interests and performance. Teaching approaches that emphasize real life applications of the subject have become imperative. It is believed that this will stimulate learners‟ interest in the subject as they will be able …

Solving Equations Applet Project, Kimberly Thatcher

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

The purpose of this paper is to summarize a Masters Project for the MMath Degree. The purpose of the project was to create and evaluate an applet that maintains the advantages of the existent manipulatives (Hands-On Equations® and the NLVM applet) while also overcoming the limitations of each. Another product of this project is accompanying lesson plans for teachers.

Mathematical Justification Of Introductory Hypothesis Tests And Development Of Reference Materials, Jennifer L. Loveland

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

This purpose of this project was to create a set of reference material for an introductory level statistics course. The focus was on the Neyman-Pearson approach to hypothesis testing. A brief historical development of the Neyman-Pearson approach is followed by mathematical proofs of each of the hypothesis tests covered in the reference material. The reference material includes the basic hypothesis tests taught in an introductory statistics course, the accompanying distributions, and prerequisite information.

Estimation Of Beta In A Simple Functional Capital Asset Pricing Model For High Frequency Us Stock Data, Yan Zhang

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

This project applies the methods of functional data analysis (FDA) to intra-daily returns of US corporations. It focuses on an extension of the Capital Asset Pricing Model (CAPM) to such returns. The CAPM is essentially a linear regression with the slope coefficient β. Returns of an asset are regressed on index return. We compare the estimates of β obtained for the daily and intra-daily returns. The variability of these estimates is assessed by two bootstrap methods. All computations are performed using statistical software R. Customized functions are developed to process the raw data, estimate the parameters and assess their variability. …

Ranking Score Vectors Of Tournaments, Sebrina Ruth Cropper

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

Given , a tournament on vertices, Landau derived a method to determine how close is to being transitive or regular. This comparison is based on the tournament’s hierarchy number, ̅, a value derived from its score vector ̅ ( ). Let be the set of all score vectors of tournaments on vertices with the entries listed in non-decreasing order. A partial order, poset, exists on the set using the following binary relation. Given ̅ ̅ such that ̅ ̅, let ̅ ̅ if Σ Σ for and Σ Σ . Let this poset be represented as ( ) ( ) …

Controlling Error Rates With Multiple Positively-Dependent Tests, Abdullah Al Masud

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

It is a typical feature of high dimensional data analysis, for example a microarray study, that a researcher allows thousands of statistical tests at a time. All inferences for the tests are determined using the p-values; a smaller p-value than the α-level of the test signifies a statistically significant test. As the number of tests increases, the chance of observing some small p-values is very high even when all null hypotheses are true. Consequently, we make wrong conclusions on the hypotheses. This type of potential problem frequently happens when we test several hypotheses simultaneously, i.e., the multiple testing problem. …

Graphshop: An Interactive Software Environment For Graph Theory Research And Applications, Aaron Andersen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Graph Theory is the mathematical study of the structure of abstract relationships between objects. Although these constructions (graphs) are themselves purely theoretical, their ability to model pair-wise relationships in systems of arbitrary complexity yields abundant direct correspondence with numerous important physical and societal systems in the real world. Additionally, the simple discrete nature of fundamental graph structures allows for easy pseudo-geometric visualization of graphs in a wide variety of ways. Taken together, these two properties suggest that graph theory teaching, research, and applications would benefit greatly from the use of a unified software environment for graph construction, interaction, and visualization. …

Critical Issues In Middle And Secondary Mathematics Placement: A Case Study, Morgan E. Summers

Undergraduate Honors Capstone Projects

This qualitative research project focuses on the issues facing middle and secondary mathematics placement through an extensive literature review as well as a case study of a local school district. As students move from elementary school to middle and secondary schools, they are placed into classes that appear to be based on ability. One of the driving questions of this project is how is this ability level determined? Through an in-­‐depth look at one school district, it is found that a primary source of information is both norm-­‐referenced and criterion-­‐referenced assessments given to students in fifth and eighth grades. In …

B ̈Acklund Transformations For Darboux Integrable Equations, Ian M. Anderson

Mathematics and Statistics Faculty Presentations

Lie symmetry reduction is typically viewed as an integration method for differential systems of finite type, that is, systems of ordinary differential equations.

In this talk I shall present two new, recent applications of Lie symmetry reduction to the study of partial differential equations.

The first gives a remarkably simple method for constructing B ̈acklund transformations.

The second also gives a simple, very general method for constructing Darboux integrable equations.

The combination of these result in a new method for constructing B ̈acklund transformations for Darboux integrable equations.

The utility of this group theoretic approach will be illustrated by a …

On The Use Of Log-Transformation Vs. Nonlinear Regression For Analyzing Biological Power-Laws, Xiao Xiao

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

Power-law relationships are among the most well-studied functional relationships in biology . Recently the common practice of fitting power-laws using linear regression on log-transformed data (LR) has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations we demonstrate that the error distribution determines which method performs better, with LR better characterizing data with multiplicative lognormal error and NLR better characterizing data with additive normal error. Analysis of 471 biological power-laws shows that both …

Rank 2 Distributions Of Monge Equations: Symmetries, Equivalences, Ex-Tensions, Ian M. Anderson, B. Kruglikov

Mathematics and Statistics Faculty Publications

By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the corresponding Tanaka algebras leads to a new Lie-Backlund theorem. We prove that all flat Monge equations are successive integrable extensions of the Hilbert-Cartan equation. Many new examples are provided.

An Ethnographic Study Of In-Service And Pre-Service Teacher Collaboration In The Development And Execution Of Mathematics Lessons, Jessica Munns

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

While much is known about effective strategies for teaching mathematics, less is understood about how to lead new teachers to employ research-based practices in their work. To address this issue we followed a Methods of Teaching Secondary and Middle School Mathematics course at Utah State University where collaboration between inservice and pre-service teachers was emphasized. This report documents examples of the implementation of research-based teaching practices by collaborative groups during the course. The structure of collaboration followed a lesson study model involving research and planning, execution and observation, and reflection and revision of lessons. Preservice and in-service teachers met twice …