Senior Theses 2015-2016A collection of senior thesis papers from the Mathematics Department at Carthage Collegehttp://hdl.handle.net/123456789/26072019-06-16T12:51:39Z2019-06-16T12:51:39ZFundamental Groups of Simplicial ComplexesWheeler, Erlan IIIhttp://hdl.handle.net/123456789/26342017-03-10T21:18:33Z2016-01-01T00:00:00ZFundamental Groups of Simplicial Complexes
Wheeler, Erlan III
We define two different simplicial complexes, the common divisor simplicial complex and the prime divisor simplicial complex, from a set of
integers, and explore their similarities. We will show that if one is connected, then the other is connected. We will also show that for any given
set of integers, the fundamental groups of the resulting simplicial complexes are isomorphic.
2016-01-01T00:00:00ZWarValentine, Elizabethhttp://hdl.handle.net/123456789/26332017-03-10T21:26:49Z2016-01-01T00:00:00ZWar
Valentine, Elizabeth
The card game War is known for taking a long time to play. There are many different variations of the game of which could possibly make the game shorter. Using a program which we wrote in Java, we calculated the length of the card game War using 25 different “war lengths”. We found that, as the number of cards in a war increases, the number of tricks in a game decrease, meaning shorter games will need to have more cards in a war. We also found that games with bigger wars also have less variance in game length.
2016-01-01T00:00:00ZGeneralization of Riemann's Rearrangement TheoremWeber, Benjaminhttp://hdl.handle.net/123456789/26322017-03-10T16:19:08Z2016-01-01T00:00:00ZGeneralization of Riemann's Rearrangement Theorem
Weber, Benjamin
In this paper, we will examine Riemann's rearrangement theorem for sequences of real numbers. Continuing on, we will briefly discuss previous
generalizations of the theorem to the n dimensional case. Because of the
difficulty of that proof, we present a more approachable proof for the case
of complex numbers. Our proof is not significantly more difficuult than
the proof for real numbers. Furthermore, key aspects of the proof can
be applied to the n dimensional case. From there, we are able to prove
the n dimensional case using elementary techniques. We conclude by considering the possibility of an infinite dimensional generalization through
sequence or function spaces.
2016-01-01T00:00:00ZThe Mathematical Modeling of Forest FiresShaw, Claricehttp://hdl.handle.net/123456789/26312017-06-27T20:04:48Z2016-01-01T00:00:00ZThe Mathematical Modeling of Forest Fires
Shaw, Clarice
With worsening severity of forest fires in America, it has become a
necessity to understand the behavior of these phenomena. Not
only will this understanding assist land managers with preventing
the start and spread of fires, but they will also be better able to
protect the people living in areas experiencing forest fires. There
are many ways to model these fires, but one of the simplest is
through weather variables such as temperature, wind, and
humidity. Through the creation of a differential equation using
these parameters, one is able to determine many behavioral
patterns of wildfires. By implementing this equation in a C++
computer program, it was found that fires will burn more of a forest
if the wind is blowing in multiple directions, increasing the
probability of fire spread. Additionally, it was found that fires
which originate closer to the center of a forest will, in the end, burn
more trees than those originating near the outer edge. Many
other behaviors could be determined with the addition of fire-specific
weather parameters as well as fire-fighting measures to
the model. This type of information is vital for the prevention and
extinguishing of forest fires.
2016-01-01T00:00:00Z