ORC Course Description: This course is a more theoretical introduction to probability theory than Math 20. In addition to the basic content of Math 20, the course will include other topics such as continuous probability distributions and their applications.
Textbook: Introduction to Probability (2nd Rev Ed), Charles M. Grinstead & J. Laurie Snell, American Mathematical Society (1997). By courtesy of the authors, this book is freely available on the internet (here).
Grading Formula: Participation & in-class quizzes (10%) + Weekly homework problem sets (20%) + Midterm (30%) + Final Project + 15 min Presentation (40%).
Tentative lecture plan which may be subject to further changes.
|Week 1||Course Overview & Basic Concepts of Discrete Probability; Continuous Probability Densities; Permutations|
|Week 2||Combinations; Discrete Conditional Probability; Continuous Conditional Probability|
|Week 3||Important Distributions & Densities; Expected Value & Variance; Expected Value & Variance of Continuous Random Variables|
|Week 4||Sums of Independent Random Variables; Review of Functions of Random Variables; Weak Law of Large Numbers|
|Week 5||Generating Functions for Discrete Random Variables; Generating Functions for Continuous Densities; Central Limit Theorem|
|Week 6||Theory of Branching Processes; Markov Chains|
|Week 7||Fundamental Limit Theorem; Mean First Passage Time; Markov Process in Continuous Time (Poisson Process)|
|Week 8||Random Walks; Gambler’s Ruin; Diffusion Limit of Random Walks|
|Week 9||Reserved final paper presentations|
Course projects are listed in the alphabetical order of student names, and will be updated once more progresses are made by the students.