- Pierre Nicodème, Université Paris 13
- "Introduction to Analytic Combinatorics"
- The course is a short introduction to Analytic Combinatorics (AC), a relatively recent and powerful branch of mathematics that draws upon combinatorial and analytic techniques to investigate the properties of (large) discrete combinatorial structures. The course will focus on two fundamental and representative tools: the symbolic method (combinatorial techniques) and singularity analysis (analytical techniques), although we will briefly touch upon some other important techniques, methods and tools from AC like the saddle point method. Along the course, we will illustrate with numerous examples the basics of AC using applications coming from Computer Science, more specifically from the analysis of algorithms and data structures. Some background on data structures and algorithms (to follow the examples and understand the applications of AC), and on elementary probability, combinatorics and complex analysis (to understand the principles of AC) is necessary. First-year undergraduate level must be enough to follow the course, but for students who would like to delve into more advanced material on their own, a stronger background in mathematics and Computer science is necessary. The fundamental bibliographic reference is the book by Flajolet and Sedgewick "Analytic Combinatorics", Cambridge U. Press (2009), which is freely available in the web.