This volume is based on classes in probability for advanced undergraduates held at the IAS/Park City Mathematics Institute (Utah). It is derived from both lectures (Chapters 1–10) and computer simulations (Chapters 11–13) that were held during the program. The material is coordinated so that some of the major computer simulations relate to topics covered in the first ten chapters. The goal is to present topics that are accessible to advanced undergraduates, yet are areas of current research in probability. The combination of the lucid yet informal style of the lectures and the hands-on nature of the simulations allows readers to become familiar with some interesting and active areas of probability.

The volume concludes with a number of problems ranging from routine to very difficult. Of particular note are problems that are typical of simulation problems given to students by the authors when teaching undergraduate probability.

Gregory F. Lawler: Duke University, Durham, NC;

Lester N. Coyle: Loyola College, Baltimore, MD

1. Chapter 1. Simple random walk and Stirling’s formula
2. Chapter 2. Simple random walk in many dimensions
3. Chapter 3. Self-avoiding walk
4. Chapter 4. Brownian motion
5. Chapter 5. Shuffling and random permutations
6. Chapter 6. Seven shuffles are enough (sort of)
7. Chapter 7. Markov chains on finite sets
8. Chapter 8. Markov chain Monte Carlo
9. Chapter 9. Random walks and electrical networks
10. Chapter 10. Uniform spanning trees
11. Chapter 11. Random walk simulations
12. Chapter 12. Other simulations
13. Chapter 13. Simulations in finance