Combinatorics, Probability & Statistics

Course Syllabus:

Combinatorics: Basic combinatorial numbers, Selection with repetition, Pigeon Hole principle, Inclusion–Exclusion principle, Double counting, Recurrence relations, Generating functions, Special combinatorial numbers : Sterling numbers (of 1^st & 2^nd kind), Catalan numbers, Partition numbers, Introduction to Ramsey theory, Combinatorial designs, Latin Squares, Introduction to Probabilistic methods, Introduction to Linear Algebra methods.

Probability & Statistics: Probability spaces and continuity of probability measures, Random variables and Expectation, Moment inequalities, Multivariate random variables, Sequence of random variables & different modes of convergence, Law of large numbers, Markov chains, Statistical hypothesis testing, Exponential methods, Introduction to large deviations

Reference Books:

R. P. Grimaldi, B. V. Ramana, “Discrete and Combinatorial Mathematics : An Applied Introduction”, Pearson Education, 2007.

Richard A Brualdi, “Introductory Combinatorics”, Pearson Education Inc, 2004.

Miklos Bona, “Introduction to Enumerative Combinatorics”, McGraw Hill, 2007.

Vijay K Rohatgi, AKMD, Ehsanes Saleh, “An Introduction to Probability & Statistics”, Wiley, 2^nd Edition, 2000.

Allen Gut, “An Intermediate Course in Probability”, Springer, 2008.

Recurrence Relations

Generating Functions