Analytic Combinatorics, Part II

开始时间: 04/22/2022 持续时间: 6 weeks

所在平台: CourseraArchive

课程类别: 数学

大学或机构: Princeton University（普林斯顿大学）

授课老师： Robert Sedgewick

课程主页: https://www.coursera.org/course/introACpartII

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课程详情

Analytic Combinatorics is based on formal methods for deriving functional relationships on generating functions and asymptotic analysis treating those functions as functions in the complex plane. Part II covers the symbolic method for defining generating functions immediately from combinatorial constructions, then develops methods for directly deriving asymptotic results from those generating functions, using complex asymptotics, singularity analysis, saddle-point asymptotics, and limit laws. The course teaches the precept "if you can specify it, you can analyze it".

课程大纲

Lecture 1 Combinatorial Structures and OGFs

Lecture 2 Labelled Structures and EGFs

Lecture 3 Combinatorial Parameters and MGFs

Lecture 4 Complex Analysis, Rational and Meromorphic Asymptotics

Lecture 5 Applications of Rational and Meromorphic Asymptotics

Lecture 6 Singularity Analysis of Generating Functions

Lecture 7 Applications of Singularity Analysis

Lecture 8 Saddle-Point Asymptotics

Lecture 9 Multivariate Asymptotics and Limit Laws

Lecture 10 Mellin Transform Asymptotics

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课程简介

This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. Part II introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations.