Analytic combinatorics is the study of counting sequemces associated to combinatorial configurations and breaks up into two complementary components. First, we systematically encode and study counting problems through the use of power series (generating functions). Second, the analytic properties of these power series are used to understand the growth of counting sequences. Some examples are counting structured strings, functions, permutations, trees, and lattice paths. The principal analytic technique will be complex analysis and the course will include a user's self-contained introduction to complex analysis. Time permitting, we may study counting problems with parameters which naturally leads to multivariable generating functions and allows us to investigate statistical properties of counting sequences. Prerequisites: Math 310.
Course Attributes: AS NSM