Acerca de este Curso
4.6
19 calificaciones
3 revisiones
100 % en línea

100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.
Nivel intermedio

Nivel intermedio

Horas para completar

Aprox. 20 horas para completar

Sugerido: 4 hours/week...
Idiomas disponibles

Inglés (English)

Subtítulos: Inglés (English)...
100 % en línea

100 % en línea

Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles

Fechas límite flexibles

Restablece las fechas límite en función de tus horarios.
Nivel intermedio

Nivel intermedio

Horas para completar

Aprox. 20 horas para completar

Sugerido: 4 hours/week...
Idiomas disponibles

Inglés (English)

Subtítulos: Inglés (English)...

Programa - Qué aprenderás en este curso

Semana
1
Horas para completar
2 horas para completar

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 videos (Total: 73 min), 2 readings, 1 quiz
Video7 videos
Symbolic Method11m
Trees and Strings 14m
Powersets and Multisets 13m
Compositions and Partitions 15m
Substitution 6m
Exercises 3m
Reading2 lecturas
Getting Started10m
Exercises from Lecture 110m
Quiz1 ejercicio de práctica
Combinatorial Structures and OGFs4m
Semana
2
Horas para completar
2 horas para completar

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 videos (Total: 85 min), 1 reading, 1 quiz
Video7 videos
Symbolic Method for Labelled Classes 18m
Words and Strings 12m
Labelled trees 15m
Mappings 17m
Summary 4m
Exercises 2m
Reading1 lectura
Exercises from Lecture 210m
Quiz1 ejercicio de práctica
Labeled Structures and EGFs4m
Semana
3
Horas para completar
2 horas para completar

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 videos (Total: 84 min), 1 reading, 1 quiz
Video5 videos
Moment Calculations 24m
OBGF examples 17m
Labelled Classes 19m
Exercises 2m
Reading1 lectura
Exercises from Lecture 310m
Quiz1 ejercicio de práctica
Combinatorial Parameters and MGFs8m
Semana
4
Horas para completar
2 horas para completar

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 videos (Total: 109 min), 1 reading, 1 quiz
Video6 videos
Complex Functions 13m
Rational Functions 19m
Analytic Functions and Complex Integration 23m
Meromorphic Functions 34m
Exercises 3m
Reading1 lectura
Exercises from Lecture 410m
Quiz1 ejercicio de práctica
Complex Analysis, Rational and Meromorphic Asymptotics4m

Instructor

Avatar

Robert Sedgewick

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

Acerca de 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....

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