Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Partial Differential Equations (3)
- Dynamic Systems (2)
- Mathematics (2)
- Numerical Analysis and Computation (2)
- Other Applied Mathematics (2)
-
- Other Mathematics (2)
- Special Functions (2)
- Arts and Humanities (1)
- Composition (1)
- Discrete Mathematics and Combinatorics (1)
- Dynamical Systems (1)
- Fine Arts (1)
- Music (1)
- Music Theory (1)
- Musicology (1)
- Non-linear Dynamics (1)
- Number Theory (1)
- Ordinary Differential Equations and Applied Dynamics (1)
- Other Music (1)
- Other Physical Sciences and Mathematics (1)
- Set Theory (1)
- Keyword
- Publication Type
- File Type
Articles 1 - 4 of 4
Full-Text Articles in Applied Mathematics
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Undergraduate Theses and Capstone Projects
This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …
Mathematical Modeling: Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Mathematical Modeling: Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Student Scholar Showcase
Mathematical models are systems using mathematical concepts to explain various problems. Mathematical models examine realistic issues such as the different outcomes of wars and fictional problems such as the upcoming zombie apocalypse. The original predictor models of warfare were the Lanchester models, while the zombie apocalypse is a fictional expansion upon mathematical models for infectious diseases. In this paper, we examined and compared the basic versions of these dynamic models by analyzing each model’s set of variables, assumptions, and objectives. The basic versions of the Lanchester equations are the area aimed model and the aimed fire model. While the zombie …
The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates
The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates
Undergraduate Theses and Capstone Projects
We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.
Mathematical Methods In Composing Melodies, Thomas Brown
Mathematical Methods In Composing Melodies, Thomas Brown
Undergraduate Theses and Capstone Projects
This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …