À propos de ce cours
4.6
119 ratings
29 reviews
We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. In this course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students....
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Beginner Level

Niveau débutant

Clock

Recommandé : 5 weeks, 3-5 hours/week

Approx. 13 heures pour terminer
Comment Dots

English

Sous-titres : English
Globe

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Calendar

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.
Beginner Level

Niveau débutant

Clock

Recommandé : 5 weeks, 3-5 hours/week

Approx. 13 heures pour terminer
Comment Dots

English

Sous-titres : English

Programme du cours : ce que vous apprendrez dans ce cours

1

Section
Clock
3 heures pour terminer

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 vidéos (Total 52 min), 5 lectures, 5 quiz
Video14 vidéos
Knight Transposition2 min
Seven Bridges of Königsberg4 min
What is a Graph?7 min
Graph Examples2 min
Graph Applications3 min
Vertex Degree3 min
Paths5 min
Connectivity2 min
Directed Graphs3 min
Weighted Graphs2 min
Paths, Cycles and Complete Graphs2 min
Trees6 min
Bipartite Graphs4 min
Reading5 lectures
Slides1 min
Slides1 min
Slides1 min
Slides1 min
Glossary10 min
Quiz2 exercices pour s'entraîner
Definitions10 min
Graph Types10 min

2

Section
Clock
5 heures pour terminer

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 vidéos (Total 89 min), 4 lectures, 6 quiz
Video12 vidéos
Total Degree5 min
Connected Components7 min
Guarini Puzzle: Code6 min
Lower Bound5 min
The Heaviest Stone6 min
Directed Acyclic Graphs10 min
Strongly Connected Components7 min
Eulerian Cycles4 min
Eulerian Cycles: Criteria11 min
Hamiltonian Cycles4 min
Genome Assembly12 min
Reading4 lectures
Slides1 min
Slides1 min
Slides1 min
Glossary10 min
Quiz4 exercices pour s'entraîner
Computing the Number of Edges10 min
Number of Connected Components10 min
Number of Strongly Connected Components10 min
Eulerian Cycles2 min

3

Section
Clock
3 heures pour terminer

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 vidéos (Total 55 min), 4 lectures, 6 quiz
Video11 vidéos
Trees8 min
Minimum Spanning Tree6 min
Job Assignment3 min
Bipartite Graphs5 min
Matchings3 min
Hall's Theorem7 min
Subway Lines1 min
Planar Graphs3 min
Euler's Formula4 min
Applications of Euler's Formula7 min
Reading4 lectures
Slides1 min
Slides1 min
Slides1 min
Glossary10 min
Quiz3 exercices pour s'entraîner
Trees10 min
Bipartite Graphs10 min
Planar Graphs10 min

4

Section
Clock
4 heures pour terminer

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 vidéos (Total 52 min), 5 lectures, 8 quiz
Video14 vidéos
Graph Coloring3 min
Bounds on the Chromatic Number3 min
Applications3 min
Graph Cliques3 min
Cliques and Independent Sets3 min
Connections to Coloring1 min
Mantel's Theorem5 min
Balanced Graphs2 min
Ramsey Numbers2 min
Existence of Ramsey Numbers5 min
Antivirus System2 min
Vertex Covers3 min
König's Theorem8 min
Reading5 lectures
Slides1 min
Slides1 min
Slides1 min
Slides1 min
Glossary10 min
Quiz4 exercices pour s'entraîner
Graph Coloring10 min
Cliques and Independent Sets10 min
Ramsey Numbers10 min
Vertex Covers10 min
4.6

Meilleurs avis

par 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!

par 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.

Enseignant

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering

À propos de 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....

À propos de 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...

À propos de la Spécialisation 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

Foire Aux Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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