Calculus, Linear algebra and some exposure to proofs and abstract mathematics.
Programming in Sage will be a part of every lecture. Students will need to bring a laptop with access to the IISc WLAN.
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.
Suggested books and references:
Herbert Wilf, Generatingfunctionology, ISBN-13 - 978-1568812793; Freely downloadable from http://www.math.upenn.edu/~wilf/DownldGF.html.
Richard P. Stanley, Enumerative Combinatorics: Volume 1 (Second Edition), ISBN-13 - 978-1107602625 Older version freely downloadable from http://www-math.mit.edu/~rstan/ec/ec1/.