Modeling Symmetries: An analysis on the interdisciplinary applications of Lie groups

Author

• Reece Humphreys

Date of Award

2021

Document Type

Dissertation/Thesis

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

McGovern, Warren

Abstract

Symmetries are a driving force in the universe and continue to reveal themselves the deeper we look. While many undergraduate mathematics students are introduced to symmetries with group theory, many practical applications are often overlooked. The application of symmetries provides deep insights into various problems and can frequently simplify complex mathematics. Applying symmetries typically requires high-level mathematics that can be prohibitive for people within other disciplines. As such, this paper explores how Lie groups, a mathematical structure for representing symmetries, can be utilized in computing, physics, and control theory to solve practical problems from within these elds. It also serves as an introduction to the mathematics necessary to utilize Lie groups.

Comments

Thesis (B.A.)--Florida Atlantic University, Harriet L. Wilkes Honors College, 2021

Recommended Citation

Humphreys, Reece, "Modeling Symmetries: An analysis on the interdisciplinary applications of Lie groups" (2021). Harriet L Wilkes Honors College Theses 2020 - Present. 111.
https://digitalcommons.fau.edu/etd_honors/111

Extent

57 p.

Identifier

FAUHT00146