Counting problems in sets, multisets, permutations, partitions, trees, tableaux;
ordinary and exponential generating functions;
posets and principle of inclusion-exclusion, the transfer matrix method;
the exponential formula, Polya theory;
bijections, combinatorial identities and the WZ method.
Course webpage: http://www.math.iisc.ac.in/~arvind/ma318/
Basic notions of probability, conditional probability and independence, Bayes' theorem, random variables and distributions, expectation and variance, conditional expectation, moment generating functions, limit theorems. Samples and sampling distributions, estimations of parameters, testing of hypotheses, regression, correlation and analysis of variance.
Representation theory: Representation of finite groups, irreducible representations, complete reducibility, Schur's lemma, characters, orthogonality, class functions, regular representations and induced representation, the group algebra.
Linear groups: Representations of the group SU2
Books
Aritin, M., Algebra, Prentice Hall of India, 1994.
Fulton W., and Harris, J., Representation Theory, Spinger-Verlag, 1991.
Serre, J. P., Linear Representations of Finite Groups, Springer-Verlag, 1977.
This site hosts some courses of the Department of Mathematics at IISc.
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