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Full-Text Articles in Physical Sciences and Mathematics
The Statistics Of Lotteries, Matthew Thomas Bremer
The Statistics Of Lotteries, Matthew Thomas Bremer
Honors Theses, 1963-2015
This project begins with the analysis of several existing lotteries in the state of Minnesota. The raw data of these lotteries are used to calculate the expected values of certain random variables in an effort to describe and compare the lotteries mathematically. Next, the different criteria that contribute to a successful lottery are described and brought together. Finally, via mathematical modeling and computer simulation, a new lottery proposal is presented with the claim that it is superior to existing lotteries from an administrative standpoint.
An Investigation Of Iterated Function Systems And Fractals, David Wuolu
An Investigation Of Iterated Function Systems And Fractals, David Wuolu
Honors Theses, 1963-2015
This paper explores some of the fascinating ideas involved in the generation of fractals. A linear algebra and strong calculus background is sufficient to understand the main ideas, however many of the proofs require analysis. I examined metric spaces, and in particular, the metric space H(X), which consists of the compact subsets of the space X. The completeness of this space is proven, enabling the construction of fractals as fixed points of contractive transformations on H(X). I use the classical Cantor set and the Sierpinski triangle to illustrate the construction of fractals using iterated function systems (IFS's) which consist of …