Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.
" ""Wilf's writing is clear and friendly; his exorcises are instructive and plentiful... This book is valuable reading for even the best of specialists..."" -E. Rodney Canfield, The Mathematical Intelligencer , March 1993
""This is a first rate, carefully planned and executed book written by a 'black belt gereratingfunctionologist.' I'll be using it the next time I teach..."" -George Andrews, SIAM News, October 1994
""Wilf's book is very well-written and easy to read by any serious mathematics student. Scientists in other disciplines often encounter the need to study sequences that naturally arise in their own discipline. The book is well-suited fo them, too."" -Short Book Reviews, January 2006"