SYLLABUS GENERAL: The textbook will be Probability and Random Processes by Geoffrey R. Grimmett and David R. Stirzaker (third edition). We will supplement this with many interesting problems from a variety of sources; an excellent read is Impossible?: Surprising Solutions to Counterintuitive Conundrums by Julian Havil (this is a suggested book for the class for those who want to see some additional fun problems; this book is not required for the course, and anything we use from the book will be explained completely in class). Please feel free to swing by my office or mention before, in or after class any questions or concerns you have about the course. If you have any suggestions for improvements, ranging from method of presentation to choice of examples, just let me know. If you would prefer to make these suggestions anonymously, you can send email from mathephs@gmail.com (the password is the first seven Fibonacci numbers, 11235813). Grading will be: 20% homework, 40% midterms (there will be at least two) and 40% final. You may also do a project involving probability, which would count for 10% of your grade (and the other categories would be reduced 10% each). All exams are cumulative, the lowest midterm grade will be dropped.

• More specific syllabus: As this is my first time teaching the course, I don't know exactly how long it will take to cover various topics. For the beginning of the semester we will follow the book closely except for combinatorics and probability, which will be more lecture notes and handouts. We will do chapters 3 and 4 simultaneously. We will diverge from the textbook again towards the end of the semester when we do the Central Limit Theorem. The rough ordering is as follows:
  • General overview of the course (mechanics, types of problems, ...): 1 day
  • Chapter 1: Events and their probabilities (not doing Section 1.6)
    • basic probability and set theory
    • combinatorics
    • conditional probability and independence
    • random walk
    • difference equations
  • Chapter 2: Random Variables and their Distributions (Section 2.2 optional):
    • Random variables (discrete and continuous)
    • cumulative distribution functions
    • several variables
  • Chapters 3 and 4 (Discrete and Continuous random variables):
    • mass and density functions
    • independence
    • expectation (LONG section!)
    • Chebyshev's theorem, Monte Carlo and the fall of Western Civilization
    • indicator random variables and matching
    • more examples of random variables
    • dependence
  • Chapter 5: Central Limit Theorem (will follow my handout instead)
    • generating functions
    • convolutions
    • warnings from real analysis
    • complex analysis results
    • central limit theorem