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Filtering by: Contributor advisor sim Dray, Tevian Remove constraint Contributor advisor sim: Dray, Tevian

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The Geometry of the Penrose Diagram for Minkowski Spacetime

Creator:

Siebersma, Maxwell

Abstract:

Culture of Writing Award in Mathematics (2022)

Resource Type:

Technical Report
Orienting the Cube in Minkowski Space and Orienting Myself in Mathematics

Creator:

O'Harrow, Josie

Abstract:

This is a two-part thesis. The first part is a generalization of vector calculus tools to Minkowski Space, a non-Euclidean 3-dimensional geometry that has a distance function that is not positive definite. We orient a cube in Minkowski Space using the generalized Stokes' Theorem to relate a divergence integral to...

Resource Type:

Honors College Thesis
Using Euclidean Geometry to Construct Objects in the Elliptic Klein Disk

Creator:

Connolly, Genevieve

Abstract:

Constructions using only a straightedge and compass are basic tools in any geometer's toolbox. We show how to construct an elliptic straightedge and compass in the Klein Disk model of (single) elliptic geometry, using only a Euclidean compass and straightedge.

Resource Type:

Research Paper
Describing Particles with Lie and Clifford Algebras

Creator:

Johnson, Isabella G.

Abstract:

I construct and examine the properties of Lie and Clifford algebras which are used to describe certain types of particles. These algebras are then related to the traditional theory of division algebras. Quaternions are applied to these algebras and their properties are exploited to model physical properties of particles. The...

Resource Type:

Undergraduate Thesis
Student Thoughts on Derivatives of Vector Fields

Creator:

Walker, Mesa E.

Abstract:

Junior level physics students are familiar with a few types of vector ﬁeld derivatives, such as divergence and curl, but are typically unfamiliar with how to take a general derivative of a vector ﬁeld. Three junior-level physics students were interviewed with the open-ended prompt, “How would you think about taking...

Resource Type:

Capstone Project
Subalgebras of the Split Octonions

Creator:

Bentz, Lida

Abstract:

We classify the subalgebras of the split octonions, paying particular attention to the null subalgebras and their extensions.

Resource Type:

Capstone Project
Classifying Octonionic-Linear Operators

Creator:

Putnam, Alexander

Abstract:

The goal of this paper is to classify linear operators with octonionic coefficients and octonionic variables. While building up to the octonions we also classify linear operators over the quaternions and show how to relate the linear operators over the quaternions and octonions to matrices. We also construct a basis...

Resource Type:

Capstone Project
The geometry of the octonionic multiplication table

Creator:

Killgore, Peter Lloyd

Abstract:

We analyze some symmetries of the octonionic multiplication table, expressed in terms of the Fano plane. In particular, we count how many ways the Fano plane can be labeled as the octonionic multiplication table, all corresponding to a specified octonion algebra. We show that only 28 of these labelings of...

Resource Type:

Honors College Thesis
The local conservation laws of the nonlinear Schrödinger equation

Creator:

Barrett, Johnner

Abstract:

The nonlinear Schrödinger equation is a well-known partial differential equation that provides a successful model in nonlinear optic theory, as well as other applications. In this dissertation, following a survey of mathematical literature, the geometric theory of differential equations is applied to the nonlinear Schrödinger equation. The main result of...

Resource Type:

Dissertation
Division algebra representations of SO(4,2)

Creator:

Kincaid, Joshua James

Abstract:

Representations of SO(4,2;R) are constructed using 4 x 4 and 2 x 2 matrices with elements in H' ⊗ C . Using 2 x 2 matrix representations of C and H', the 4 x 4 representation is interpreted in terms of 16 x 16 real matrices. Finally, the known isomorphism...

Resource Type:

Masters Thesis

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Academic Affiliation

Mathematics13
Physics1

Advisor

Dray, Tevian16

Commencement Year

Commencement Year range begin – Commencement Year range end

Current results range from 1995 to 2022

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Unknown 2

Committee Member

Manogue, Corinne A.4
Dick, Thomas2
Petsche, Clayton2
Barofsky, Douglas F.1
Escher, Christine1
more Committee Members »

Creator

Agnew, Alfonso F.1
Barrett, Johnner1
Bentz, Lida1
Boersma, Stuart F.1
Connolly, Genevieve1
more Creators »

Date

Date range begin – Date range end

Current results range from 1994 to 2022

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Decade

2020-20294
2010-20197
2000-20092
1990-19993

Degree Field

Mathematics14
Physics2

Degree Level

Doctoral7
Bachelor's5
Master's4

Degree Name

Doctor of Philosophy (Ph.D.)7
Master of Science (M.S.)4
Bachelor of Science (B.S.)2
Honors Bachelor of Science (H.B.S.)2

File Format

application/pdf1

Language

English [eng]16

License

All rights reserved6
Attribution 4.0 (CC BY 4.0)2
Attribution 3.0 United States1
Attribution-NonCommercial-NoDerivatives 4.0 (CC BY-NC-ND 4.0)1
Attribution-ShareAlike 3.0 United States1

Non-Academic Affiliation

Oregon State University. Graduate School8
Oregon State University. Honors College2
Oregon State University. Writing Intensive Curriculum2

Peer Reviewed

No14

Resource Type

Dissertation7
Capstone Project3
Honors College Thesis2
Masters Thesis1
Research Paper1
more Resource Types »

Rights Statement

In Copyright13
Copyright Not Evaluated3

Subject

Space and time2
Cayley numbers (Algebra)1
Conservation laws (Mathematics)1
Division algebras1
Exceptional Lie algebras1
more Subjects »

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