Informações sobre o curso
4.6
19 classificações
3 avaliações
Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course 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....
Globe

cursos 100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Calendar

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Intermediate Level

Nível intermediário

Clock

Approx. 19 hours to complete

Sugerido: 4 hours/week...
Comment Dots

English

Legendas: English...
Globe

cursos 100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Calendar

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Intermediate Level

Nível intermediário

Clock

Approx. 19 hours to complete

Sugerido: 4 hours/week...
Comment Dots

English

Legendas: English...

Programa - O que você aprenderá com este curso

Week
1
Clock
2 horas para concluir

Combinatorial Structures and OGFs

Our first lecture is about the symbolic method, where we define combinatorial constructions that we can use to define classes of combinatorial objects. The constructions are integrated with transfer theorems that lead to equations that define generating functions whose coefficients enumerate the classes. We consider numerous examples from classical combinatorics. ...
Reading
7 vídeos (Total de 73 min), 2 leituras, 1 teste
Video7 videos
Symbolic Method11min
Trees and Strings 14min
Powersets and Multisets 13min
Compositions and Partitions 15min
Substitution 6min
Exercises 3min
Reading2 leituras
Getting Started10min
Exercises from Lecture 110min
Quiz1 exercício prático
Combinatorial Structures and OGFs4min
Week
2
Clock
2 horas para concluir

Labelled Structures and EGFs

This lecture introduces labelled objects, where the atoms that we use to build objects are distinguishable. We use exponential generating functions EGFs to study combinatorial classes built from labelled objects. As in Lecture 1, we define combinatorial constructions that lead to EGF equations, and consider numerous examples from classical combinatorics. ...
Reading
7 vídeos (Total de 85 min), 1 leitura, 1 teste
Video7 videos
Basics13min
Symbolic Method for Labelled Classes 18min
Words and Strings 12min
Labelled trees 15min
Mappings 17min
Summary 4min
Exercises 2min
Reading1 leituras
Exercises from Lecture 210min
Quiz1 exercício prático
Labeled Structures and EGFs4min
Week
3
Clock
2 horas para concluir

Combinatorial Parameters and MGFs

This lecture describes the process of adding variables to mark parameters and then using the constructions form Lectures 1 and 2 and natural extensions of the transfer theorems to define multivariate GFs that contain information about parameters. We concentrate on bivariate generating functions (BGFs), where one variable marks the size of an object and the other marks the value of a parameter. After studying ways of computing the mean, standard deviation and other moments from BGFs, we consider several examples in some detail. ...
Reading
5 vídeos (Total de 84 min), 1 leitura, 1 teste
Video5 videos
Basics19min
Moment Calculations 24min
OBGF examples 17min
Labelled Classes 19min
Exercises 2min
Reading1 leituras
Exercises from Lecture 310min
Quiz1 exercício prático
Combinatorial Parameters and MGFs8min
Week
4
Clock
2 horas para concluir

Complex Analysis, Rational and Meromorphic Asymptotics

This week we introduce the idea of viewing generating functions as analytic objects, which leads us to asymptotic estimates of coefficients. The approach is most fruitful when we consider GFs as complex functions, so we introduce and apply basic concepts in complex analysis. We start from basic principles, so prior knowledge of complex analysis is not required. ...
Reading
6 vídeos (Total de 109 min), 1 leitura, 1 teste
Video6 videos
Roadmap13min
Complex Functions 13min
Rational Functions 19min
Analytic Functions and Complex Integration 23min
Meromorphic Functions 34min
Exercises 3min
Reading1 leituras
Exercises from Lecture 410min
Quiz1 exercício prático
Complex Analysis, Rational and Meromorphic Asymptotics4min

Instrutores

Robert Sedgewick

William O. Baker *39 Professor of Computer Science
Computer Science

Sobre Princeton University

Princeton University is a private research university located in Princeton, New Jersey, United States. It is one of the eight universities of the Ivy League, and one of the nine Colonial Colleges founded before the American Revolution....

Perguntas Frequentes – FAQ

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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