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


CLASS: M/W 1:30 p.m. - 2:50 p.m. in Scaife Hall 125

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

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. We will cover basic probability including discrete and continuous random variables, expectations, higher moments, Laplace and z-transforms, and joint distributions. We will also cover many advanced topics including combinatorial probability and random graphs, heavy tail distributions, concentration inequalities, randomized algorithms, sampling random variables and computer simulation, discrete Markov chains and continuous-time Markov chains and their many applications, elementary queueing theory and a look at its use in modeling the web, routers, data centers, and networking protocols.

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. 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.





Homework will be due each week on Friday at the start of recitation. You are allowed a total of 5 late days. No more than 2 late days can be used for each homework. Saturdays and Sundays count as late days. It is your responsibility to deliver the late homework to the TA. Once you have used up your 5 late days, you cannot receive any more late days unless you were in the hospital, so please save these up for illnesses and interviews.


I love to teach, and I expect your full participation. Classes will be interactive! No cell phones in class. Laptops are only permitted for taking notes. Internet must be turned off. If you use your laptop for anything other than taking notes, I reserve the right to take your laptop.


If you use an outside source (web site, book, person, etc.), you *must* cite that source. It is fine to discuss problems with others, but you need to write up the actual homework alone. At the top of your homework sheet, you must list all the people with whom you discussed any problem. Crediting help from other others will not take away any credit from you, and will prevent us from assuming cheating if your answers look similar to those of someone else. Note that the person providing answers is just as guilty as the person receiving answers. The above is the standard policy in all of academia.