Physical Sciences and Mathematics Commons^™

The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre

Presentations and Publications

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …

Students Rise To The Challenge Of Modeling Yeast Growth Despite Sour Hiccups From Imperfect Data, Alicia Caldwell

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

Students rarely receive the opportunity to experience a learning activity involving mathematical modeling. This paper describes a lab in which students in an Applied Mathematics in Biology course observe the growth of Saccharomyces cerevisiae, a yeast strain, in differing sugar concentrations for use in learning modeling. They parameterized the logistic equation and an alternate model, which they themselves constructed, based on the data they collected. I participated in this lab as a student in 2012 then observed and reviewed the work of other students involved. I found that students gained a deeper understanding of limiting factors and the role of …

Tournament Directed Graphs, Sarah Camille Mousley

Undergraduate Honors Capstone Projects

Paired comparison is the process of comparing objects two at a time. A tournament in Graph Theory is a representation of such paired comparison data. Formally, an n-tournament is an oriented complete graph on n vertices; that is, it is the representation of a paired comparison, where the winner of the comparison between objects x and y (x and y are called vertices) is depicted with an arrow or arc from the winner to the other.

In this thesis, we shall prove several results on tournaments. In Chapter 2, we will prove that the maximum number of vertices …

Processing And Manipulation Of Data Collected From The Educational On-Line Game Refraction, Xiaotian Dai

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

A team of students, artists, and researchers at the Center for Game Science at the

University of Washington are trying to create video games that can discover optimal

pathways for learning. They have focused so far on early mathematics education,

including topics such as fractions and algebra, which are some of the main bottlenecks

preventing students from pursuing a career in science. As a result, the educational

on-line game \Refraction" was created, which is aimed at students who start learning

fraction computations. When the students are playing the game online, all the data

and information, such as mouse movements and …

Dot Product Graphs And Their Applications To Ecology, Sean Bailey

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We will introduce a new tool to visualize the comparison between different birds. This tool will allow users to use any number of measurable traits to see relationships between different birds, both individually and collectively.

Particle Dynamics And Resistivity Characteristics In Bifurcated Current Sheets, Tushar Andriyas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Charged particle chaos and its collective effects in different magnetic geometries are investigated in a sequence of various numerical experiments. The fields generated by the particles as a result of interaction with the background electric and magnetic fields is not accounted for in the simulation. An X-line is first used to describe the geometry of the magnetotail prior to magnetic reconnection and a study of the behavior of charged particles is done from a microscopic viewpoint. Another important geometry in the magnetotail prior to substorm onset is Bifurcated Current Sheet. The same analysis is done for this configuration. The existence …

Concurrent Neurological And Behavioral Assessment Of Number Line Estimation Performance In Children And Adults, Joseph Michael Baker

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Understanding the brain’s response to common math-learning activities may help improve math education. For example, by imaging the brains of typically developing children and adults throughout a number line estimation task, it is possible to establish a baseline of what “typical” brains do in such situations. Thus, comparisons may be made to determine the degree to which brain functioning differs between typical and atypical math learners. Moreover, by identifying methods that may increase the brain’s response to real-world math activities, it may be possible to improve the math learning process for typical and atypical learners alike.

Brain imaging devices such …

Spock, Euler, And Madison: Graph Theory In The Classroom, Michael Buhler

Undergraduate Honors Capstone Projects

This work is an attempt to accomplish two main objectives. First is to encourage secondary students to engage in the kinds of mathematical reasoning skills that will be necessary to them when they move to college math classes. My experience in college, along with that of many others is that "school math," with its obsession with calculations and memorization, is dreadfully insufficient in preparing students for the proof and reasoning-based classes they will face in high school. This is an attempt to integrate some of those reasoning skills into high school courses using graph theory as a vehicle.

The second …