The most basic question in mathematics is How many?. Counting problems arise in diverse areas including discrete probability and the analysis of the run time of algorithms.
In this course we present methods for answering enumeration questions exactly and approximately. Topics include fundamental counting problems (lists, sets, partitions, and so forth), combinatorial proof, inclusion-exclusion, ordinary and exponential generating functions, group-theory methods, and asymptotics. Examples are drawn from areas such as graph theory and block designs.
After completing this course students will be practiced in applying the fundamental functions (such as factorial, binomial coefficients, Stirling numbers) and techniques for solving a wide variety of exact enumeration problems as well as notation and methods for approximate counting (asymptotic equality, big-oh and little-oh notation, etc.).
This course is the same as 605.623 Introduction to Enumerative Combinatoricss.