Informações sobre o curso
4.6
141 classificações
32 avaliações
100% online

100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Nível iniciante

Nível iniciante

Horas para completar

Aprox. 14 horas para completar

Sugerido: 5 weeks, 3-5 hours/week ...
Idiomas disponíveis

Inglês

Legendas: Inglês
100% online

100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Nível iniciante

Nível iniciante

Horas para completar

Aprox. 14 horas para completar

Sugerido: 5 weeks, 3-5 hours/week ...
Idiomas disponíveis

Inglês

Legendas: Inglês

Programa - O que você aprenderá com este curso

Semana
1
Horas para completar
3 horas para concluir

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....
Reading
14 vídeos (total de (Total 52 mín.) min), 5 leituras, 5 testes
Video14 videos
Knight Transposition2min
Seven Bridges of Königsberg4min
What is a Graph?7min
Graph Examples2min
Graph Applications3min
Vertex Degree3min
Paths5min
Connectivity2min
Directed Graphs3min
Weighted Graphs2min
Paths, Cycles and Complete Graphs2min
Trees6min
Bipartite Graphs4min
Reading5 leituras
Slides1min
Slides1min
Slides1min
Slides1min
Glossary10min
Quiz2 exercícios práticos
Definitions10min
Graph Types10min
Semana
2
Horas para completar
5 horas para concluir

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! ...
Reading
12 vídeos (total de (Total 89 mín.) min), 4 leituras, 6 testes
Video12 videos
Total Degree5min
Connected Components7min
Guarini Puzzle: Code6min
Lower Bound5min
The Heaviest Stone6min
Directed Acyclic Graphs10min
Strongly Connected Components7min
Eulerian Cycles4min
Eulerian Cycles: Criteria11min
Hamiltonian Cycles4min
Genome Assembly12min
Reading4 leituras
Slides1min
Slides1min
Slides1min
Glossary10min
Quiz4 exercícios práticos
Computing the Number of Edges10min
Number of Connected Components10min
Number of Strongly Connected Components10min
Eulerian Cycles2min
Semana
3
Horas para completar
3 horas para concluir

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!...
Reading
11 vídeos (total de (Total 55 mín.) min), 4 leituras, 6 testes
Video11 videos
Trees8min
Minimum Spanning Tree6min
Job Assignment3min
Bipartite Graphs5min
Matchings3min
Hall's Theorem7min
Subway Lines1min
Planar Graphs3min
Euler's Formula4min
Applications of Euler's Formula7min
Reading4 leituras
Slides1min
Slides1min
Slides1min
Glossary10min
Quiz3 exercícios práticos
Trees10min
Bipartite Graphs10min
Planar Graphs10min
Semana
4
Horas para completar
4 horas para concluir

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....
Reading
14 vídeos (total de (Total 52 mín.) min), 5 leituras, 8 testes
Video14 videos
Graph Coloring3min
Bounds on the Chromatic Number3min
Applications3min
Graph Cliques3min
Cliques and Independent Sets3min
Connections to Coloring1min
Mantel's Theorem5min
Balanced Graphs2min
Ramsey Numbers2min
Existence of Ramsey Numbers5min
Antivirus System2min
Vertex Covers3min
König's Theorem8min
Reading5 leituras
Slides1min
Slides1min
Slides1min
Slides1min
Glossary10min
Quiz4 exercícios práticos
Graph Coloring10min
Cliques and Independent Sets10min
Ramsey Numbers10min
Vertex Covers10min
4.6
32 avaliaçõesChevron Right

Melhores avaliações

por 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!

por DNNov 12th 2017

I like this course. Very basic, but teachers are really great and explanations are perfect! Highly recommended for all who wants to begin with Graph Theory.

Instrutores

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering

Sobre University of California San Diego

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....

Sobre National Research University Higher School of Economics

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 communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

Sobre o Programa de cursos integrados Introduction to Discrete Mathematics for Computer Science

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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