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Full-Text Articles in Other 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. …
Set: The Probabilities And Possibilities, Tabitha K. Bollinger
Set: The Probabilities And Possibilities, Tabitha K. Bollinger
Undergraduate Theses and Capstone Projects
The card game SET involves finding groups o f three cards called SETs. Choices are based upon the individual card characteristics, including shape, pattern, number, and color. Previously, the maximum number o f cards that can be played without creating a SET has been determined as 20 cards by extensive computer work. This report further explored the probabilities and possibilities o f the game. Using discrete mathematics and probability, we explored how many SETs are possible and what strategies led to the most points. Additionally, this project exercised undergraduate logic and reasoning to generalize the results in order to be …
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.