Probability and Stochastic Processes (M. Tech. CS I year, 2017)
Probability and Stochastic Processes (M. Tech. CS I year, 2017)
Instructor Arijit Ghosh
Teaching assistant Gopinath Mishra
Description To study the basics of probability theory and stochastic processes, and their applications to computer science and combinatorics.
Prerequisites Mathematical maturity of a finishing undergraduate student in engineering sciences or mathematical sciences.
Class timings Monday and Wednesday 14:15 - 16:15 hrs and Friday 16:15 - 18:15 hrs.
Syllabus
Sample space and Probability theory
Discrete random variables
Continuous random variables
Functions of random variables
Limit theorems
Chernoff bounds
Balls and bins framework
Martingale
Markov chains
Branching processes
References
[BT08] Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd Edition, 2008.
[F68] William Feller, An Introduction to Probability and its Applications: Volume I, 3rd Edition, John Wiley & Sons, 1968.
[F71] William Feller, An Introduction to Probability and its Applications: Volume II, 2nd Edition, John Wiley & Sons, 1971.
[R13] Sheldon Ross, A First Course in Probability, 9th Edition, Pearson, 2013.
[AS16] Noga Alon and Joel Spencer, The Probabilistic Method, 4th Edition, Wiley, 2016.
[MU05] Michael Mitzenmacher and Eli Upfal, Probability and Computing, Cambridge University Press, 2005.