FRS 002D - Sec. 001 - (2 units) - CRN 92784 - T 10:00 – 11:50 am - 25 Wellman
Chance and Randomness: From Probability Theory to Games
Instructor: Jane-Ling Wang, Department of Statistics, College of Letters and Science
Description: We encounter randomness in our daily life and are taking chances constantly. What exactly is randomness and how should one take chances? Is uncertainty really a myth, and is there a logical way to understand and encounter them? In this seminar, we will explore these topics and show that Probability Theory is a systematical and logical way to quantify uncertainty and to gather information. We will learn to calculate the chance, or formally the probability, of an event; the law of probability and the concept of mathematical expectations. The seminar aims to unveil the mathematics behind Probability Theory in an accessible way. We will use games, such as Blackjack, Poker, Roulette, Craps and Keno to illustrate the derivation of probability laws and conditional probability. Through these games students will learn the rigorous theory and concepts behind probability and the philosophy of chance and randomness. Also through individual reading assignments and oral and written presentations in class, students will learn how to search scientific information, communicating/disseminating knowledge, and making formal presentations. The primary goal of the seminar is to train students' critical thinking skills through the topic of probability active learning process, and students will be guided through the course to learn the research process and how to report their findings in written projects and in a final report.
Format: The seminar will meet for two hours each week for eight weeks. The first three weeks will be devoted to the concept of randomness, basic rules of counting and probability theory. The next two weeks will be devoted to mathematical expectations and conditional probability. Game theory and optimal strategy will be the focus of the last three weeks. Class time will be divided between informal brief lectures, student presentations and discussions. Students are required to do reading assignments based on discussions with the instructors, and will search for some of the reading material on their own. They will present some of their readings to the class and prepare the necessary handouts. A written report on a self-selected topic approved by the instructor is due at the end of the course. There is no text for the course, and several references are listed below:
The Mathematics of Games and Gambling, by Edward Packel, Mathematical Assoc. of America (1996)
What Are the Odds?: Chance in Everyday Life, by Michael Orkin, Henry Holt and Company (1999).
Randomness by Deborah Bennett, Harvard University Press (1998).
The Theory of Blackjack, by Peter Griffin, Huntington Press (1999, 6th edition). The Theory of Poker, by David Sklansky, Two plus Two Publishing LLC (1999, 3rd edition).
Grading: The course grade will be based on the quality of student participation, both orally in class and submitted work in writing. The breakdown is: Oral presentation and class discussion (50%), Written presentations and final report (50%).
About the Instructor: Jane-Ling Wang is a Professor of Statistics at UC Davis. Her research interest ranges from theoretical statistics to multi-disciplinary collaborative research. She has taught the topic of probability at various levels.