Physical Sciences and Mathematics Commons^™

Book Review: What’S Luck Got To Do With It? The History, Mathematics, And Psychology Of The Gambler’S Illusion By Joseph Mazur, Michael Lugo

Journal of Humanistic Mathematics

This review of Joseph Mazur's book on the history of gambling, for a general audience, is in three parts, paralleling the structure of the book. The first part briefly outlines Mazur's coverage of the history of probability from prehistory to the present day, with a focus on gambling. The second part examines the relationship between the mathematics of gambling and probability theory, and summarizes classical problems in probability arising from gambling such as Galileo's dice and the Pascal-Fermat problem of points. The third part, on psychology, discusses the gambler's illusion and psychological motivations for gambling.

Rumors Of Our Rarity Are Greatly Exaggerated: Bad Statistics About Women In Science, Cathy Kessel

Journal of Humanistic Mathematics

During the past few years, three bad statistics have been persistently used in discussions of women in science, technology, engineering, and mathematics (STEM). The first was questionable when it was published in 1983 and has since been widely used. The second came to prominence in 2006 – and now leads an international and perhaps eternal life on the Web. The third may have made its debut in 2007. Its variants occur in popular and academic books and journals, including the 2011 Proceedings of the National Academy of Sciences.

This report presents case histories of the three bad statistics, suggests writing …

The Quantum Dialectic, Logan Kelley

Pitzer Senior Theses

A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …

Markov Bases For Noncommutative Harmonic Analysis Of Partially Ranked Data, Ann Johnston

HMC Senior Theses

Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool …

Martingale Couplings And Bounds On Tails Of Probability Distributions, Kyle Luh

HMC Senior Theses

Wassily Hoeffding, in his 1963 paper, introduces a procedure to derive inequalities between distributions. This method relies on finding a martingale coupling between the two random variables. I have developed a construction that establishes such couplings in various urn models. I use this construction to prove the inequality between the hypergeometric and binomial random variables that appears in Hoeffding's paper. I have then used and extended my urn construction to create new inequalities.

How Other Drivers’ Vehicle Characteristics Influence Your Driving Speed, Russell Brockett

CMC Senior Theses

An analysis of the effect of passing vehicles’ characteristics and their impact on other drivers’ velocities was investigated. Three experimental studies were proposed and likely outcomes were discussed. Experiment 1 focused on the effect of passing vehicle type (SUV, sedan or truck) on driver speed. Drivers were hypothesized as going faster when the same vehicle type as they were driving passed them versus when no vehicle or a different vehicle passed them. Experiment 2 focused on the effect of passing SUV age on driver’s speed. Evidence suggests passing older SUVs will increase the driver’s speed more than new SUVs. Experiment …

Applying Localized Realized Volatility Modeling To Futures Indices, Luella Fu

CMC Senior Theses

This thesis extends the application of the localized realized volatility model created by Ying Chen, Wolfgang Karl Härdle, and Uta Pigorsch to other futures markets, particularly the CAC 40 and the NI 225. The research attempted to replicate results though ultimately, those results were invalidated by procedural difficulties.