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初級

完成時間大約為15 小時

建議:5 weeks, 3-5 hours/week ...

英語(English)

字幕:英語(English)

100% 在線

立即開始,按照自己的計劃學習。

可靈活調整截止日期

根據您的日程表重置截止日期。

初級

完成時間大約為15 小時

建議:5 weeks, 3-5 hours/week ...

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
完成時間為 3 小時

What is a Graph?

What are graphs? What do we need them for? This week we'll see that a graph is a simple pictorial way to represent almost any relations between objects. We'll see that we use graph applications daily! We'll learn what graphs are, when and how to use them, how to draw graphs, and we'll also see the most important graph classes. We start off with two interactive puzzles. While they may be hard, they demonstrate the power of graph theory very well! If you don't find these puzzles easy, please see the videos and reading materials after them.

...
14 個視頻 (總計 52 分鐘), 5 個閱讀材料, 5 個測驗
14 個視頻
Knight Transposition2分鐘
Seven Bridges of Königsberg4分鐘
What is a Graph?7分鐘
Graph Examples2分鐘
Graph Applications3分鐘
Vertex Degree3分鐘
Paths5分鐘
Connectivity2分鐘
Directed Graphs3分鐘
Weighted Graphs2分鐘
Paths, Cycles and Complete Graphs2分鐘
Trees6分鐘
Bipartite Graphs4分鐘
5 個閱讀材料
Slides1分鐘
Slides1分鐘
Slides1分鐘
Slides1分鐘
Glossary10分鐘
2 個練習
Definitions10分鐘
Graph Types10分鐘
2
完成時間為 5 小時

CYCLES

We’ll consider connected components of a graph and how they can be used to implement a simple program for solving the Guarini puzzle and for proving optimality of a certain protocol. We’ll see how to find a valid ordering of a to-do list or project dependency graph. Finally, we’ll figure out the dramatic difference between seemingly similar Eulerian cycles and Hamiltonian cycles, and we’ll see how they are used in genome assembly!

...
12 個視頻 (總計 89 分鐘), 4 個閱讀材料, 6 個測驗
12 個視頻
Total Degree5分鐘
Connected Components7分鐘
Guarini Puzzle: Code6分鐘
Lower Bound5分鐘
The Heaviest Stone6分鐘
Directed Acyclic Graphs10分鐘
Strongly Connected Components7分鐘
Eulerian Cycles4分鐘
Eulerian Cycles: Criteria11分鐘
Hamiltonian Cycles4分鐘
Genome Assembly12分鐘
4 個閱讀材料
Slides1分鐘
Slides1分鐘
Slides1分鐘
Glossary10分鐘
4 個練習
Computing the Number of Edges10分鐘
Number of Connected Components10分鐘
Number of Strongly Connected Components10分鐘
Eulerian Cycles2分鐘
3
完成時間為 4 小時

Graph Classes

This week we will study three main graph classes: trees, bipartite graphs, and planar graphs. We'll define minimum spanning trees, and then develop an algorithm which finds the cheapest way to connect arbitrary cities. We'll study matchings in bipartite graphs, and see when a set of jobs can be filled by applicants. We'll also learn what planar graphs are, and see when subway stations can be connected without intersections. Stay tuned for more interactive puzzles!

...
11 個視頻 (總計 55 分鐘), 4 個閱讀材料, 6 個測驗
11 個視頻
Trees8分鐘
Minimum Spanning Tree6分鐘
Job Assignment3分鐘
Bipartite Graphs5分鐘
Matchings3分鐘
Hall's Theorem7分鐘
Subway Lines1分鐘
Planar Graphs3分鐘
Euler's Formula4分鐘
Applications of Euler's Formula7分鐘
4 個閱讀材料
Slides1分鐘
Slides1分鐘
Slides1分鐘
Glossary10分鐘
3 個練習
Trees10分鐘
Bipartite Graphs10分鐘
Planar Graphs10分鐘
4
完成時間為 4 小時

Graph Parameters

We'll focus on the graph parameters and related problems. First, we'll define graph colorings, and see why political maps can be colored in just four colors. Then we will see how cliques and independent sets are related in graphs. Using these notions, we'll prove Ramsey Theorem which states that in a large system, complete disorder is impossible! Finally, we'll study vertex covers, and learn how to find the minimum number of computers which control all network connections.

...
14 個視頻 (總計 52 分鐘), 5 個閱讀材料, 8 個測驗
14 個視頻
Graph Coloring3分鐘
Bounds on the Chromatic Number3分鐘
Applications3分鐘
Graph Cliques3分鐘
Cliques and Independent Sets3分鐘
Connections to Coloring1分鐘
Mantel's Theorem5分鐘
Balanced Graphs2分鐘
Ramsey Numbers2分鐘
Existence of Ramsey Numbers5分鐘
Antivirus System2分鐘
Vertex Covers3分鐘
König's Theorem8分鐘
5 個閱讀材料
Slides1分鐘
Slides1分鐘
Slides1分鐘
Slides1分鐘
Glossary10分鐘
4 個練習
Graph Coloring10分鐘
Cliques and Independent Sets10分鐘
Ramsey Numbers10分鐘
Vertex Covers10分鐘
4.6
50 個審閱Chevron Right

33%

完成這些課程後已開始新的職業生涯

50%

通過此課程獲得實實在在的工作福利

33%

加薪或升職

來自Introduction to Graph Theory的熱門評論

創建者 SUFeb 28th 2019

Appreciate the structure and the explanations with examples. The practice tool before every lesson not makes it fun to learn but also sets the student in the context and can anticipate the concept.

創建者 RHNov 17th 2017

Was pretty fun and gave a good intro to graph theory. Definitely felt inspired to go deeper and understood the most basic proof ideas. The later lectures can spike in difficulty though. Very nice!

講師

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering

關於 加州大学圣地亚哥分校

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory....

關於 国立高等经济大学

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

關於 Introduction to Discrete Mathematics for Computer Science 專項課程

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses....
Introduction to Discrete Mathematics for Computer Science

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