About this Course
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100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

탄력적인 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

완료하는 데 약 15시간 필요

권장: 5 weeks, 3-5 hours/week ...

영어

자막: 영어

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

탄력적인 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

완료하는 데 약 15시간 필요

권장: 5 weeks, 3-5 hours/week ...

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 3시간 필요

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 videos (Total 52 min), 5 readings, 5 quizzes
14개의 동영상
Knight Transposition2m
Seven Bridges of Königsberg4m
What is a Graph?7m
Graph Examples2m
Graph Applications3m
Vertex Degree3m
Paths5m
Connectivity2m
Directed Graphs3m
Weighted Graphs2m
Paths, Cycles and Complete Graphs2m
Trees6m
Bipartite Graphs4m
5개의 읽기 자료
Slides1m
Slides1m
Slides1m
Slides1m
Glossary10m
2개 연습문제
Definitions10m
Graph Types10m
2
완료하는 데 5시간 필요

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 videos (Total 89 min), 4 readings, 6 quizzes
12개의 동영상
Total Degree5m
Connected Components7m
Guarini Puzzle: Code6m
Lower Bound5m
The Heaviest Stone6m
Directed Acyclic Graphs10m
Strongly Connected Components7m
Eulerian Cycles4m
Eulerian Cycles: Criteria11m
Hamiltonian Cycles4m
Genome Assembly12m
4개의 읽기 자료
Slides1m
Slides1m
Slides1m
Glossary10m
4개 연습문제
Computing the Number of Edges10m
Number of Connected Components10m
Number of Strongly Connected Components10m
Eulerian Cycles2m
3
완료하는 데 3시간 필요

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 videos (Total 55 min), 4 readings, 6 quizzes
11개의 동영상
Trees8m
Minimum Spanning Tree6m
Job Assignment3m
Bipartite Graphs5m
Matchings3m
Hall's Theorem7m
Subway Lines1m
Planar Graphs3m
Euler's Formula4m
Applications of Euler's Formula7m
4개의 읽기 자료
Slides1m
Slides1m
Slides1m
Glossary10m
3개 연습문제
Trees10m
Bipartite Graphs10m
Planar Graphs10m
4
완료하는 데 4시간 필요

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 videos (Total 52 min), 5 readings, 8 quizzes
14개의 동영상
Graph Coloring3m
Bounds on the Chromatic Number3m
Applications3m
Graph Cliques3m
Cliques and Independent Sets3m
Connections to Coloring1m
Mantel's Theorem5m
Balanced Graphs2m
Ramsey Numbers2m
Existence of Ramsey Numbers5m
Antivirus System2m
Vertex Covers3m
König's Theorem8m
5개의 읽기 자료
Slides1m
Slides1m
Slides1m
Slides1m
Glossary10m
4개 연습문제
Graph Coloring10m
Cliques and Independent Sets10m
Ramsey Numbers10m
Vertex Covers10m
5
완료하는 데 4시간 필요

Flows and Matchings

This week we'll develop an algorithm that finds the maximum amount of water which can be routed in a given water supply network. This algorithm is also used in practice for optimization of road traffic and airline scheduling. We'll see how flows in networks are related to matchings in bipartite graphs. We'll then develop an algorithm which finds stable matchings in bipartite graphs. This algorithm solves the problem of matching students with schools, doctors with hospitals, and organ donors with patients. By the end of this week, we'll implement an algorithm which won the Nobel Prize in Economics!...
13 videos (Total 99 min), 6 readings, 4 quizzes
13개의 동영상
The Framework8m
Ford and Fulkerson: Proof11m
Hall's theorem10m
What Else?8m
Why Stable Matchings?6m
Mathematics and Real Life4m
Basic Examples6m
Looking For a Stable Matching6m
Gale-Shapley Algorithm6m
Correctness Proof6m
Why The Algorithm Is Unfair7m
Why the Algorithm is Very Unfair9m
6개의 읽기 자료
Slides1m
Slides1m
The algorithm and its properties (alternative exposition)10m
Gale-Shapley Algorithm2m
Project Description10m
Glossary10m
4개 연습문제
Choose an Augmenting Path Carefully20m
Constant Degree Bipartite Graphs30m
Base Cases10m
Algorithm
4.6
49개의 리뷰Chevron Right

33%

이 강좌를 수료한 후 새로운 경력 시작하기

50%

이 강좌를 통해 확실한 경력상 이점 얻기

33%

급여 인상 또는 승진하기

최상위 리뷰

대학: 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.

대학: 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!

강사

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering

캘리포니아 샌디에고 대학교 정보

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....

국립 연구 고등 경제 대학 정보

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...

Introduction to Discrete Mathematics for Computer Science 전문 분야 정보

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

자주 묻는 질문

  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

  • 강좌를 등록하면 전문 분야의 모든 강좌에 접근할 수 있고 강좌를 완료하면 수료증을 취득할 수 있습니다. 전자 수료증이 성취도 페이지에 추가되며 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 내용만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

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