課程信息
4.6
19 個評分
3 個審閱
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中級

中級

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完成時間大約為20 小時

建議:4 hours/week...
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英語(English)

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100% online

100% online

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
中級

中級

完成時間(小時)

完成時間大約為20 小時

建議:4 hours/week...
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 2 小時

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 個視頻(共 73 分鐘), 2 個閱讀材料, 1 個測驗
Video7 個視頻
Symbolic Method11分鐘
Trees and Strings 14分鐘
Powersets and Multisets 13分鐘
Compositions and Partitions 15分鐘
Substitution 6分鐘
Exercises 3分鐘
Reading2 個閱讀材料
Getting Started10分鐘
Exercises from Lecture 110分鐘
Quiz1 個練習
Combinatorial Structures and OGFs4分鐘
2
完成時間(小時)
完成時間為 2 小時

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 個視頻(共 85 分鐘), 1 個閱讀材料, 1 個測驗
Video7 個視頻
Basics13分鐘
Symbolic Method for Labelled Classes 18分鐘
Words and Strings 12分鐘
Labelled trees 15分鐘
Mappings 17分鐘
Summary 4分鐘
Exercises 2分鐘
Reading1 個閱讀材料
Exercises from Lecture 210分鐘
Quiz1 個練習
Labeled Structures and EGFs4分鐘
3
完成時間(小時)
完成時間為 2 小時

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 個視頻(共 84 分鐘), 1 個閱讀材料, 1 個測驗
Video5 個視頻
Basics19分鐘
Moment Calculations 24分鐘
OBGF examples 17分鐘
Labelled Classes 19分鐘
Exercises 2分鐘
Reading1 個閱讀材料
Exercises from Lecture 310分鐘
Quiz1 個練習
Combinatorial Parameters and MGFs8分鐘
4
完成時間(小時)
完成時間為 2 小時

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 個視頻(共 109 分鐘), 1 個閱讀材料, 1 個測驗
Video6 個視頻
Roadmap13分鐘
Complex Functions 13分鐘
Rational Functions 19分鐘
Analytic Functions and Complex Integration 23分鐘
Meromorphic Functions 34分鐘
Exercises 3分鐘
Reading1 個閱讀材料
Exercises from Lecture 410分鐘
Quiz1 個練習
Complex Analysis, Rational and Meromorphic Asymptotics4分鐘

講師

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Robert Sedgewick

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

關於 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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