(The lectures from 2007
are still available on-line, although there will be
many differences between the 2007 and 2008 versions
of the course.)
Most of my lecture notes are embedded in Mathematica notebooks, along with Mathematica code that implements the algorithms under discussion. If you can't open the notebooks, or can't run the code, on account of not having Mathematica, fear not! Wolfram Research has just announced a new service that makes it possible to share Mathematica notebooks with anyone, whether or not they have Mathematica: "Using the new Publish for Player site, you can now convert your interactive notebooks for use with the free Mathematica Player." I haven't taken the time to do this, but if any of you want me to, let me know!
To view a section of a a Mathematica notebook, double-click on the bracket to the right of the caption. To close the section, select the appropriate bracket and double-click on it.
Lecture #1: Random and Quasirandom Simulation. [Mathematica notebook Lec01.nb] [PDF file Lec01.pdf]
Lecture #2: Random and Quasirandom Simulation, continued. Random Variables (Review). Quasirandomness demo. [Mathematica notebook Lec02.nb] [PDF file Lec02.pdf] [Rotor-router applet]
Lecture #3: Absorbing Markov chains. Ergodic Markov chains. [Mathematica notebook Lec03.nb] [PDF file Lec03.pdf]
Lecture #4: The first half of the 9/29/08 lecture was the second half of Lecture 3 from 2007 ("Monday Sept. 24"), on the subject of stationary distribution and the law of large numbers, and the second half of the lecture was the first half of Lecture 4 from 2007 ("Monday Oct. 1"), with more about ergodic Markov chains. (You'll note that the first half of Lecture 3 from 2007 is a review of discrete probability theory; I moved this material into Lecture 2 for 2008.) The relevant files are Lec03-2007.nb, Lec03-2007.doc, and Lec04-2007.nb. (Note that the second half of Lecture 4 from 2007 deals with chip-firing; you should skip this part.)
Lecture #5: The 10/6/08 lecture consisted of the topics "Random walks in one dimension" and "Examples of Markov chains" from Lec06-2007.nb.
Lecture #6: The 10/15/08 lecture consisted of the topic "More examples of Markov chains" from Lec07-2007.nb.
Lecture #7: Sampling from a specified distribution. Knowing when to stop. [Mathematica notebook Lec07.nb] [PDF file Lec07.pdf]
Lecture #8: Exact sampling. Chip-firing for absorbing Markov chains. Chip-firing for ergodic Markov chains. [Mathematica notebook Lec08.nb] [PDF file Lec08.pdf]
Lecture #9: From chip-firing to rotor-routing. Final projects. Pseudorandom vs. quasirandom simulation for ergodic Markov chains Chip-firing for ergodic Markov chains. [Mathematica notebook Lec09.nb] [PDF file Lec09.pdf]
Lecture #10: Extending rotor-routing. The Goldbug walk. Rotor-routing on infinite graphs. [Mathematica notebook Lec10.nb] [PDF file Lec10.pdf]
Lecture #11: Electrical networks and random walk. Importance sampling. Recurrence and transience. [Mathematica notebook Lec11.nb] [PDF file Lec11.pdf]
Lecture #12: Poisson processes. [Mathematica notebook Lec12.nb] [PDF file Lec12.pdf]
Lecture #14: Poisson processes and Brownian motion. [Mathematica notebook Lec14.nb] [PDF file Lec14.pdf]