15-359/659 Probability and Computing (SPRING 15), 12 Units


CLASS: Mon/Wed 1:30 p.m. - 2:50 p.m. in Scaife Hall 125

RECITATION A: Fri 1:30 p.m. - 2:20 p.m. in Scaife Hall 125

RECITATION B: Fri 2:30 p.m. - 3:20 p.m. in Scaife Hall 125

Class assignments and syllabus are here: HOMEWORKS & SYLLABUS

TEXT BOOK: Performance Modeling and Design of Computer Systems

You are expected to purchase a copy of this textbook for the class.

Probability theory has become indispensable in computer science. In areas such as artificial intelligence and computer science theory, probabilistic methods and ideas based on randomization are central. In areas such as networks and systems, probability is necessary to model variability in the arrival process and service requirements of jobs, so that we can understand how delay increases with increasing load, predict necessary buffer sizes, determine the appropriate number of servers in a data center, and so on. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context.

Material Covered Includes:

Part I : Probability on events. Everything about discrete random variables and continuous random variables, moments, conditioning, Bayes, Laplace transforms, z-transforms. Simulation of random variables. Also heavy-tailed distributions.

Part II : Concentration inequalities: Markov, Chebyshev, Chernoff Bounds. Introduction to Randomized algorithms (both Las Vegas and Monte Carlo).

Part III : Discrete-time Markov Chains (with ergodicity proofs) and Continuous-time Markov chains. Poisson process. Tons of applications. Elementary queueing theory with applications to modeling web server farms, routers, networking protocols, and capacity provisioning for data centers.

This class assumes NO PRIOR PROBABILITY/STATS classes, and will satisfy the Computer Science Probability/Statistics requirement. The course DOES assume that you have taken calculus (and still remember how to integrate and differentiate, as well as remembering Taylor-series expansions). The course also assumes that you can do simple double integrals and know some basic matrix algebra. The only real prereq is 15-251, where we expect that you learned how to sum basic arithmetic and geometric series and some basic combinatorics. This class is ideally taken BEFORE 15-451 and will help you a lot with that class. It will also be very helpful in any future machine learning classes. This is an HONORS class . The pace is fast and the homework level is high. However you will learn a ton.