4.6
170 ratings
39 reviews

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 15 hours to complete

Suggested: 5 weeks, 3-5 hours/week ...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 15 hours to complete

Suggested: 5 weeks, 3-5 hours/week ...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
3 hours to complete

## 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
14 videos
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
Slides1m
Slides1m
Slides1m
Slides1m
Glossary10m
2 practice exercises
Definitions10m
Graph Types10m
Week
2
5 hours to complete

## 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
12 videos
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
Slides1m
Slides1m
Slides1m
Glossary10m
4 practice exercises
Computing the Number of Edges10m
Number of Connected Components10m
Number of Strongly Connected Components10m
Eulerian Cycles2m
Week
3
3 hours to complete

## 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
11 videos
Trees8m
Minimum Spanning Tree6m
Job Assignment3m
Bipartite Graphs5m
Matchings3m
Hall's Theorem7m
Subway Lines1m
Planar Graphs3m
Euler's Formula4m
Applications of Euler's Formula7m
Slides1m
Slides1m
Slides1m
Glossary10m
3 practice exercises
Trees10m
Bipartite Graphs10m
Planar Graphs10m
Week
4
4 hours to complete

## 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
14 videos
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
Slides1m
Slides1m
Slides1m
Slides1m
Glossary10m
4 practice exercises
Graph Coloring10m
Cliques and Independent Sets10m
Ramsey Numbers10m
Vertex Covers10m
4.6
39 Reviews

## 33%

started a new career after completing these courses

## 50%

got a tangible career benefit from this course

## 33%

got a pay increase or promotion

### Top Reviews

By 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!

By PSFeb 2nd 2019

I wish to thank the professors for having brought this course to Coursera, this topic is absolutely fantastic, and very well presented. I highly recommend it.

## Instructor

### Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering

## About 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....

## About 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 communicamathematics, engineering, and more. Learn more on www.hse.ru...

## About the Introduction to Discrete Mathematics for Computer Science Specialization

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....