# 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.

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
9 Mellin Transform Asymptotics311, 762-767

## Errata in Lecture slides

• Lecture 1, slide 9. $S_N$ should be $M^N$ not $N^M$

• Lecture 1, slide 16. Final expression for $G_N$ is incorrect (see Slide 15).

• Lecture 1, slide 42. GF for $C_M(z)$ is incorrect

• Lecture 1, slide 43. distinct powers of 2 in second question.

• Lecture 1, slide 47. Replace $z^{10}$ by $z^{20}$ in last two rows

• Lecture 1, slide 53. "z+" is missing from RHS of three equations at the bottom

• Lecture 1, slide 55. Missing right paren in eqn for $H(z)$