Office: 238 Bell Hall
Office Hours: Mon & Wed 3pm-4pm
Phone: 645-3180 x 160
Email: hungngo (at) cse (dot) buffalo (dot) edu

Probabilistic analysis and randomized algorithms have become an indispensible tool in virtually all areas of Computer Science, ranging from combinatorial optimization, machine learning, approximation algorithms analysis and designs, complexity theory, coding theory, to communication networks and secure protocols. This course has two major objectives: (a) it introduces key concepts, tools and techniques from probability theory which are often employed in the development of probabilistic algorithms and analyses and in the constructions of combinatorial objects, and (b) it gives a glance of how these concepts and techniques are used in algorithm analysis and design and combinatorial constructions, among other usages.

In addition to the probabilistic paradigm, students are expected to gain substantial discrete mathematics problem solving skills essential for computer engineers.

• Have fun learning!
• Grasp the essential ideas of probabilistic thinking in computer science
  • randomized and derandomized algorithms
  • the probabilistic method
  • discrete time Markov chain and random walks
  • approximate counting and the Monte Carlo method
• Gain substantial problem solving skills in designing randomized algorithms and discrete mathematics

Prerequisites:

Basic Algorithm course (CSE 531), a good sense of discrete mathematics thinking, and rudimentary knowledge of probability theory.
The desire and ability to learn new ideas quickly.

At the end of this course, each student should be able to:

• Have a good overall picture of the probabilistic paradigm as applied in many areas of computer science
• Be able to "think" probabilistically, i.e. to formulate problems probabilistically and have a sense of how to solve problems with probabilistic thinking

References:

• Required Textbook:
  • Michael Mitzenmacher and Eli Upfal, Probability and Computing, Cambridge University Press, 2005.
• Other references: (Helpful but not required)
  • Rajeev Motwani and Prabhakar Raghavan, Randomized Algorithms, 492 pages, Cambridge University Press (August 25, 1995), ISBN: 0521474655
  • Alon, Noga; Spencer, Joel H. The probabilistic method. Second edition. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons, New York, 2000. xviii+301 pp. ISBN: 0-471-37046-0
  • Bella Bolobas, Random Graphs (2nd ed.), Cambridge University Press, Studies in Advanced Mathematics, #73, September 2001.
  • Molloy, Michael; Reed, Bruce Graph colouring and the probabilistic method. Algorithms and Combinatorics, 23. Springer-Verlag, Berlin, 2002. xiv+326 pp. ISBN: 3-540-42139-4
  • Gamerman, D. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Boca Raton, FL: CRC Press, 1997.
  • W. R. Gilks, D. J. Spiegelhalter, Sylvia Richardson, Markov Chain Monte Carlo in Practice, CRC Press, Feb 1996.
• Plus other reading material specified on the course homepage

Course homepage:

http://www.cse.buffalo.edu/~hungngo/classes/2007/694/

Work load:

• Approx. 30 pages of fairly dense reading per week
• 5 written homework assignments (to be done individually)
• 1 final presentation and a report on a topic relating to randomized algorithms and the probabilistic method. The topic will be suggested by the instructor but the student can choose her/his own paper/topic with the consent of the instructor.

Grading policy:

• 5 written assignments: 16% each (I reserve my right to add or reduce the number of assignments)
• Final presentation and report : 20%
• Assignments due at the end of the lecture on the due date
  • 1 day (up to 24 hours) late: 20% reduction
  • Each extra (24 hours) day late: 40% reduction (which means you don't have to bother submit your assignment if it's more than 2 days late)
• Incomplete/make-up exams: NOT GIVEN, except in provably extraordinary cases

Academic Honesty:

• Please do the assignments on your own.
• No tolerance on plagiarism:
  • 0 on the particular assignment/exam for first attempt
  • Fail the course on the second
  • Consult the University Code of Conduct for details on consequences of academic misconduct
  • See also Prof. Shapiro's page on Academic Integrity of the CSE department: http://www.cse.buffalo.edu/~shapiro/Courses/integrity.html
• I will take cheating VERY VERY seriously. Don't waste your time begging !!

Misc. Items:

• Absolutely no lame excuses please, such as "I have to go home early, allow me to take the test on Dec 1", or "I had a fight with my girlfriend, which effects my performance", blah blah blah. Even when they are true, they are still lame.
• No extra work in the next semester given to improve your grade.