Lecture Slides

Here are lecture slides that accompany Analytic Combinatorics., under development and schedule for completion in April 2012.

These slides are for the first half of an undergraduate course taught at Princeton, developed to provide an overview of An Introduction to the Analysis of Algorithms and Analytic Combinatorics.

The course format is "introduce-read-discuss". We introduce a set of topics in lecture; students read about the topics and work selected exercises between lectures, and we discuss any questions about the reading and the exercises at the beginning of the next lecture. Each lecture ends with a slide or two giving assignments to be completed before the next lecture and to be discussed at the beginning of the next lecture. Some lectures contain in-class exercises.

While much of the reading material may be difficult for a typical undergraduate to master on such a quick pass through, a substantial fraction of the coverage is elementary. One purpose of the discussion format is to help students learn to master the elementary material so as to make the book content more accessible.

Lecture slides are available both in 1-up format (accessible by clicking the lecture name when it is activated as a link) and in “4-up” format (accesible by editing the extension -2x2 to the filename in your browser). Example: Lecture 1 slides are in the file AC01-OGFs.pdf, accessible by clicking “Combinatorial Structures and OGFs” in the “Topic” column. The 4-up version is in the file AC01-OGFs-2x2.pdf.

CHAPTER	TOPIC	READING
1	Combinatorial Structures and OGFs	15-94
2	Labelled Structures and EGFs	95-149
3	Combinatorial Parameters and MGFs	151-219
4	Complex Analysis, Rational and Meromorphic Asymptotics	223-288
5	Applications of Rational and Meromorphic Asymptotics	289-374
6	Singularity Analysis of Generating Functions	375-438
7	Applications of Singularity Analysis	439-540
8	Saddle-Point Asymptotics	541-608
9	Mellin Transform Asymptotics	311, 762-767