课程信息
4.6
19 个评分
3 个审阅
100% 在线

100% 在线

立即开始,按照自己的计划学习。
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中级

中级

完成时间(小时)

完成时间大约为20 小时

建议:4 hours/week...
可选语言

英语(English)

字幕:英语(English)...
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
中级

中级

完成时间(小时)

完成时间大约为20 小时

建议:4 hours/week...
可选语言

英语(English)

字幕:英语(English)...

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 2 小时

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 个视频(共 73 分钟), 2 个阅读材料, 1 个测验
Video7 个视频
Symbolic Method11分钟
Trees and Strings 14分钟
Powersets and Multisets 13分钟
Compositions and Partitions 15分钟
Substitution 6分钟
Exercises 3分钟
Reading2 个阅读材料
Getting Started10分钟
Exercises from Lecture 110分钟
Quiz1 个练习
Combinatorial Structures and OGFs4分钟
2
完成时间(小时)
完成时间为 2 小时

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 个视频(共 85 分钟), 1 个阅读材料, 1 个测验
Video7 个视频
Basics13分钟
Symbolic Method for Labelled Classes 18分钟
Words and Strings 12分钟
Labelled trees 15分钟
Mappings 17分钟
Summary 4分钟
Exercises 2分钟
Reading1 个阅读材料
Exercises from Lecture 210分钟
Quiz1 个练习
Labeled Structures and EGFs4分钟
3
完成时间(小时)
完成时间为 2 小时

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 个视频(共 84 分钟), 1 个阅读材料, 1 个测验
Video5 个视频
Basics19分钟
Moment Calculations 24分钟
OBGF examples 17分钟
Labelled Classes 19分钟
Exercises 2分钟
Reading1 个阅读材料
Exercises from Lecture 310分钟
Quiz1 个练习
Combinatorial Parameters and MGFs8分钟
4
完成时间(小时)
完成时间为 2 小时

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 个视频(共 109 分钟), 1 个阅读材料, 1 个测验
Video6 个视频
Roadmap13分钟
Complex Functions 13分钟
Rational Functions 19分钟
Analytic Functions and Complex Integration 23分钟
Meromorphic Functions 34分钟
Exercises 3分钟
Reading1 个阅读材料
Exercises from Lecture 410分钟
Quiz1 个练习
Complex Analysis, Rational and Meromorphic Asymptotics4分钟

讲师

Avatar

Robert Sedgewick

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

关于 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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