Back to Introduction to Graph Theory

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We invite you to a fascinating journey into Graph Theory â€” 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 online 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....

SU

Feb 27, 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.

RH

Nov 16, 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!

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By Bryan W B

â€¢Dec 3, 2018

This course was very weak compared to the previous two courses in this series. The concepts are challenging but not very well presented. The quizzes are too easy and do not require you to master the material. The final algorithm problem is laughably easy. However, Dr. Alexander Shen was very responsive to all my questions.

By Justus G

â€¢Nov 6, 2017

Instructors' language was extremely difficult to understand. The potential applications of many of these theoretical concepts was not addressed algorithmically; it was very difficult to put any of this into practice.

By Eugenio L C

â€¢Jan 6, 2019

The course gives a good overview to understand graphs and the math behind them. However, I expected more and I'm not satisfied with several parts of the course, poorly explained or with vague exercises. Specially the last week. This does not worth 70â‚¬ a month

By Ahmed F

â€¢May 30, 2018

it is excellent but it may need to have a small 3, 4 videos tutorial on python which is powerful language to brush on the basics but over the all it is well suited with the puzzles and quiz on each topic and learning a lot about graph which represent a lot of our life and how things are connected one of the best I enjoyed.

By Robert Y H

â€¢Nov 17, 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 Saptarshi M

â€¢Nov 15, 2018

Liked in depth discussion of graph theory. Being an CS student, I have read graph theory from couple of books. But this course has provided a comprehensive understanding and many real life problems that can be solved using graph theory. Keep up your good work.

By Sivakrishna U

â€¢Feb 28, 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.

By patrizio s

â€¢Feb 2, 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.

By Edward P v

â€¢Feb 21, 2018

I have been reading and buying books on Graph Theory in the hopes of finding some interesting insights I could bring to my after school students. None of them had Guarini's Puzzle which really is a beautiful and succinct example of Graph Theory in action. Hoping we can use what I am learning here to develop some rigorous graph methods for finding the solutions to tiling polyominoes and packing the SOMA cube. We like to make build physical objects as a starting off point for study. (leonardosbasement.org).

I am enjoying the "try this" before "we explain everything" approach also. Solving problems in python notebook is also great.

By Christopher W

â€¢Apr 8, 2020

I loved this course so much. Some very difficult topics were made understandable to even a dunderhead like me. These professors are great. They have such a good command of the subject and they use humor, copious examples, and a very relatable style to explain it thoroughly and in a way that makes sense. The exercises and puzzles were really thought-provoking and left me primed and wanting to learn more. Very good stuff. I can't wait for the next course!

By Arthur T R

â€¢Dec 20, 2018

This course is an excellent introduction to Graph Theory. It gives an overview of important topics and have a intuitive approach to the main problems. Also, the exercises are very helpful on memorizing the main concepts and training what you have learned. I strongly recommend this course for a first contact with Graph Theory.

By Pedro H

â€¢Jun 17, 2018

Really nice introduction to discrete math and basic algorithms. The content is quite basic, but as mentioned in the syllabus is for beginners. Still, for those of you who are at that level is worth taking this specialization.

By Jure Å½

â€¢May 17, 2020

This course is very efficient in teaching you about graph theory in computer science. I had to check other youtube videos on one occasion but otherwise, I always managed to pass the tests just with the course material.

By Dmytro N

â€¢Nov 12, 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.

By kartikey g

â€¢Apr 9, 2019

It was really good experiencing the different way of learning everything explained so properly all doubt are clear and the quiz and puzzle really helpfull

By Liang T

â€¢Dec 12, 2017

A good course with proper explanation. The mathematical proof of this course is generally easy to understand although a small part of them are vague

By Steven W

â€¢Dec 9, 2017

This course provides a great overview to graph theory. I especially liked the special attention that was paid to trees and bipartite graphs.

By Ayush T

â€¢Nov 25, 2017

This course is really good. If someone has interest in graph theory or he wants to learn it, then this course is definitely a good start.

By Pengcheng X

â€¢Nov 6, 2017

I just audit this course and it's very good. It gives basic ideas about graph theory and this is a super interesting subject!

By afaq a

â€¢May 3, 2019

Very friendly and applied course.

A well-balanced approach, even layman can understand the concept with exceptional ease.

By Praveen K R

â€¢Jan 23, 2019

The course content is good. All exercises and problems are very nice for learning and understanding any concept.

By RLee

â€¢Oct 8, 2018

A follow up course about Flows, Cuts and Networks should well be considered in a more Mathematical perspective.

By Joe L

â€¢Nov 17, 2018

I really love this course, it can help me to solve problems in life with Graph, stongly recommend this course!

By Greg M

â€¢Apr 21, 2019

very good course. made me curious to learn more graph theory. (in spite of years working on networking.)

By Aren T

â€¢Nov 19, 2019

Highly enjoyable and very clear introduction to a wide range of graph problems.