Spring 2016 Mathematical Sciences Honors Theses
Abstract: Carbon oset programs, such as that overseen by the California Air Resources Board (CA ARB), have emerged as a strategy for climate change mitigation. Oset projects sequestering carbon earn credits that can be traded on the Cap and Trade market to compensate for carbon emissions. The carbon stock embodied in harvested wood products can make up a substantial portion of the sequestered carbon in forest oset projects. In this paper, I investigate the sensitivity of the calculations for the number of credits allocated to a forest oset project. I also examine how alternative models for the decay of harvested wood products would change the amount of credits earned. The results show that the distribution of wood products produced has the greatest influence on the number of credits received, that it is important to include landll storage in the models, and that alternative models for the change in wood product stock may improve the accuracy of the calculations.
Abstract: Classical rings are rings in which every element is zero, a zero divisor, or a unit. In this study, we present properties which allow us to determine whether or not a ring is classical. We begin our search with nite rings and conclude that
all nite rings are classical. We study formal fractions both in commutative and noncommutative rings, determining that the total rings of quotients when they exist are classical. For more general cases in noncommutative rings, we nd that matrix rings are classical if and only if the corresponding ring from which the entries of the matrix originate was classical. We end our study with a look at chain conditions, concluding that Artinian rings are classical and, more generally, that rings of Krull dimension 0 are classical.
Abstract: This paper proposes an intuitive extension of positional weighted voting systems. A positional weighted voting system requires voters to submit fully ranked ballots and assigns point values to a voters preferences for each rank. The voters' rankings are sorted into the entries of a matrix called the preference matrix which when multiplied by a vector called the weights vector returns the number of points each candidate receives. Choosing dierent reasonable weights can lead to dierent outcomes in an election. The paper proposes a voting system in which the winner of an election is the candidate who would win over the greatest proportion of distinct reasonable weights vector choices. In the paper we conclude by applying the new method to the 2010 San Francisco district representative election.