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.