References Richard Stanley; Enumerative Combinatorics, Vol. 1, Chapters 1,4.

Basic enumeration: recurrence relations, inclusion-exclusion principle, permutation statistics, Stirling numbers, Bell numbers, calculus of nite dif-ferences. Generating functions: formal power series, formal exponential gener-ating functions, Dirichlet series, moments of distributions, cycle index of the symmetric group, snake oil method, Mobius inversion, Lagrange inversion. The ve basic algorithms for hypergeometric identities: Mary Celine Fasenmyer's algorithm, Gosper's algorithm, Zeilberger's algorithm, Petkovsek's algorithm, the WZ phenomena, dual and companion identities. Rational generating functions: rational power series in one variable, transfer-matrix method, factorization in free monoids. Computer algebra: Maple programming