Introduction to Enumerative Combinatorics に戻る

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Enumerative combinatorics deals with finite sets and their cardinalities. In other words, a typical problem of enumerative combinatorics is to find the number of ways a certain pattern can be formed.
In the first part of our course we will be dealing with elementary combinatorial objects and notions: permutations, combinations, compositions, Fibonacci and Catalan numbers etc. In the second part of the course we introduce the notion of generating functions and use it to study recurrence relations and partition numbers.
The course is mostly self-contained. However, some acquaintance with basic linear algebra and analysis (including Taylor series expansion) may be very helpful.
Do you have technical problems? Write to us: coursera@hse.ru...

Mar 30, 2018

Excellent selection of material and presentation; TAs were of great help as well. The techniques taught in this course will be a nice addition to my algorithms analysis toolbox.

Aug 22, 2017

Great lectures and content. I really enjoyed it. However, the solutions exercises could be clearer and in more detail. Thank you!

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by Tyler R

•Apr 12, 2017

This is a wonderful course. The lectures are engaging, clear, and intuitive, but from my perspective the best thing about this course is the depth of the problem sets; although not long (usually 3 - 4 problems), each problem requires genuine thought, understanding , and creativity. This has been especially refreshing in the world of online courses, where shallow and computational problem sets can sometimes be the norm. I highly recommend this course to anyone interested in an introduction to this beautiful subject.

by Shen-Fu T

•May 09, 2019

The course starts with basic enumerative combinatorics like counting sequences, permutation, etc. and gradually moves into generating function, which is a very powerful tool in combinatorics. It also gives interesting combinatorial proofs of several classical results. The quiz is helpful and final assignment a bit challenging and definitely fun!

by David A I T

•Aug 28, 2017

I enjoyed the course.

The lecturer was very good and the material quite interesting.

I feel that the assignments where sometimes very different compared to the material covered but I ended up doing extra research and learning more which is good!

Many thanks to the Coursera Staff as well as the Higher School of Economics.

by Harry A H

•Apr 29, 2020

This is a marvelous course, starting from absolutely basic things to quite advanced things. Extremely didactic. The problems sometimes seem frustrating, but after a few trials and review of the material one gets there. Thanks for this course,

by Enrico P

•Jun 14, 2019

Really great! Clear, concise, rich and stimulating, filled with many examples. Only the last part on q-world, although extremely interesting and very well introduced, is left almost without practical applications :-).

by R S K

•Feb 19, 2019

The professor is a little slow when he speaks but apart from that, he is a brilliant teacher. The course lets you get to the very roots of the topic by pushing you to do the derivations etc. Brilliant course!

by Ry A

•Mar 30, 2018

Excellent selection of material and presentation; TAs were of great help as well. The techniques taught in this course will be a nice addition to my algorithms analysis toolbox.

by Ritvik R

•Aug 22, 2017

Great lectures and content. I really enjoyed it. However, the solutions exercises could be clearer and in more detail. Thank you!

by DAVID P P

•Apr 21, 2017

Very good gourse, I persoally enjoyed the lectures in which the relatipnship with other areas of mathematics were discussed.

by Franck D

•May 07, 2017

This course is great! The instructor exposition is very clear and simple. Recommend to anyone considering this topic!

by sami

•Apr 11, 2020

i loved the course thanks to the

National Research University Higher School of Economics

by Herman Z

•Apr 10, 2017

Marvellous online course. High level and ultimate lessons.

Don't underestimate the level.

by Ze M

•Jun 20, 2017

Excelente course with real university level of concepts and exercises!

by Cong X

•Feb 12, 2018

by far the best math course I had (and I've taken many) on coursera

by Ajit C B

•Apr 11, 2017

Excellent course. I hope there are more courses by the same team.

by Cheung W C

•Jan 12, 2020

A detailed introduction to enumerative combinatorics.

by Francisco P

•May 07, 2018

Funny

Very good presentation

by Michael J F

•Jun 18, 2017

Great course!

by Dmitrii S

•Jun 07, 2018

Nice work!

by petya

•Dec 21, 2018

brilliant

by DAVID R M

•Jun 02, 2017

This was an engaging course and I welcomed the opportunity to try something a bit more advanced than the typical offerings on Coursera. Lectures are very well presented. Homework assignments were pretty good and the online forum was helpful. I recommend this course and I would be interested in further courses like this one. I found it helpful to have a couple of textbooks on hand for reference. For the earlier material I used Shaum's Outline of Combinatorics by Balakrishnan (free download on archive.org) and for the material on q-series I referred to Theory of Partitions by George Andrews.

Suggested improvements: add student interaction during lectures to test understanding and supplement with worked problems in videos. Also add lots more problems for students to work on.

(I have found that with nearly all online courses the number of problems provided is too few for me to learn a topic).

by Pierre m

•Mar 20, 2017

Good content, but way too slow. Please use pdf instead of writing everything.

by Stefan H

•May 19, 2017

Very mathematical, but cool and well done!

by Apurva D

•Jun 05, 2017

Great course

by zhen w

•Jul 28, 2017

The content is really interesting. but the presentation could be improved.

but thanks for such content