Mathematics Senior Theses 2012-2013
http://hdl.handle.net/123456789/187
Selected Mathematics Senior Theses submitted for the 2012-2013 Academic Year2019-05-24T08:22:40ZSymbolic Dynamics over Free Groups
http://hdl.handle.net/123456789/434
Symbolic Dynamics over Free Groups
Pekoske, Abby
Symbolic dynamics is used to model functions acting on complex topological
spaces. This work explores the symbolic dynamics over a non-Abelian
group, the free group on two generators. We begin by introducing the
fundamentals of symbolic dynamics and Cayley graph coloring. We then
explain the relationship between these fields and characterize classes
of periodic points of the full shift over the free group.
2013-10-24T00:00:00ZThe Ultimate Lineup
http://hdl.handle.net/123456789/433
The Ultimate Lineup
Kelterborn, Chad
We explore the optimization of a youth baseball teams batting order, considering each players individual
statistics. Specifically, we wanted to see if an alternating batting order of walkers and hitters (e.g. Highest
Walk Average, Highest Batting Average, Second Highest Walk Average) would be a better lineup than the
conventional batting order by descending batting average. For our calculations, we take into account each
individual's Hit Average, On-base Percentage, Walk Average and Strike-out Average. From our simulations,
we found that an alternating lineup produces fewer runs at 7.7913 runs per game than a descending lineup
which produces 7.9716 runs per game. Although the descending lineup was found to be better than 99% of
all possible lineups, our simulation found that the lineups that scored more runs per game on average than
the descending lineup shared certain characteristics in the ordering of the lineup.
2013-10-24T00:00:00ZA Typed Lambda Calculus for Input Sanitation
http://hdl.handle.net/123456789/432
A Typed Lambda Calculus for Input Sanitation
Fulton, Nathan
Programmers often wish to validate or sanitize user input. One common approach to this problem is the use of regular expressions. Unvalidated or insufficiently sanitized user input can cause security problems. Therefore, a compile-time guarantee that input sanitation algorithms are implemented and used correctly could ensure the absence of certain sorts of vulnerabilities. This thesis presents $\lcs$, a typed lambda calculus which captures the essential properties necessary to achieve such a guarantee.
2013-10-24T00:00:00ZSurviving the End of the World: A Mathematical Model of the Zombie Apocalypse
http://hdl.handle.net/123456789/431
Surviving the End of the World: A Mathematical Model of the Zombie Apocalypse
Sorrell, Emma
We develop differential equations models for a zombie invasion based on a variety of assumptions about zombies and humans.
2013-10-24T00:00:00Z