15-359/659 Probability and Computing (FALL 16), 12 Units
CLASS: Mon/Wed 1:30 p.m. - 2:50 p.m. in GHC 4307
RECITATION A: Fri 1:30 p.m. - 2:20 p.m. in Wean Hall 5310
RECITATION B: Fri 2:30 p.m. - 3:20 p.m. in Wean Hall 5310
Class assignments and syllabus are here: HOMEWORKS & SYLLABUS
You are expected to purchase a copy of this textbook for the class.
Probability theory has become indispensable in computer science. It is central to machine learning theory. In computer science theory,
probabilistic methods and ideas based on randomization appear in many algorithms.
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.
15-359 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, including changing the order of integrals, and also know some basic matrix algebra (eigenvectors, solving equations, etc.). 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. Prior classes in 3-D Calculus and Linear Algebra are highly recommended, but are not absolute requirements, so long as you take full responsibility for knowing the needed material. 15-359 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.
- Instructor: Mor Harchol-Balter . Email: email@example.com. Office GHC 7207.
- Teaching Assistants: TBD
OFFICE HOURS: TBD
Your grade will be based on your percentage:
A = 90 - 100% ;
B = 80 - 89% ;
C = 70 - 79% ;
D = 60 - 69%
- Weekly homework -- worth 30% combined.
- Midterm 1 -- worth 25%.
- Midterm 2 -- worth 15%.
- Weekly Quizzes -- worth 10% combined. Lowest 2 quiz grades are dropped.
- Final -- worth 25%.
- Class Participation -- Can affect you if you're on the border.
TURNING IN HOMEWORK AND LATENESS POLICY:
Homework will be due each week on Friday at the start of recitation.
You are allowed a total of 4 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 4 late days, you cannot receive any more late days unless you have a note from 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.