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Back to Combinatorics and Probability

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806 ratings

Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following. If we need to count something, can we do anything better than just counting all objects one by one? Do we need to create a list of all phone numbers to ensure that there are enough phone numbers for everyone? Is there a way to tell that our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics.
In this online course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations.
One of the main â€˜consumersâ€™ of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop.
In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game.
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....

SP

Feb 26, 2021

Special thanks to Prof. Vladimir Podolskii and Prof. Alexander S. Kulikov for their amazing explanations and diligent visuals of the concepts as well as problem sets. You Rock!

KB

Dec 25, 2019

Great course, lots of good info, not too long. Some of the coding assignments and quizzes are challenging, but the staff respond very quickly to questions in the forums.

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By Alvee N A

â€¢Jun 1, 2020

I really loved this course. One suggestion would be to add some links to external resources for students to explore since learning from various sources is more likely to help them build a better intuition.

By Alexey S

â€¢Sep 21, 2019

Thank you for your course. The content was engaging, teachers were great. I was doing last exercise for long 5 hours to realize there was a simple mistake in my code, pure pleasure, excellent

By Joseph G N

â€¢Apr 28, 2019

This course is a nice introduction to probability and give good ideas to make proof of combinatorics (the week 2 was the best), all of this give it in a nice an intuitive way.

By Deleted A

â€¢Jun 23, 2020

Some of the concepts proved difficult on initial inspection but the videos made concepts clear and the quizzes ensure I understood the concept before moving on.

By Ziad B

â€¢Oct 13, 2018

I really enjoyed taking this course. The teaching was pretty good and some of the quiz questions will challenge you if you haven't done Combinatorics before.

By SUPAKORN S

â€¢Jul 17, 2020

Great lessons, great instructors, literacy slides, this course has everything. I'm so proud to complete two out of five courses in this specialization!

By Kaustubh F

â€¢May 29, 2020

Amazing course, gave me geometrical intuitions some times that made understanding a whole lot easier. The explanation was quite clear.

By James C

â€¢Sep 2, 2020

Difficult topics discussed in easy to understand ways and uses fun and interesting problems/exercises to test your understanding.

By Joseph D

â€¢Feb 11, 2018

informative material presented clearly and simply. I had studied bayes before and it was nice to get a concise review.

By Farhan F A

â€¢Apr 27, 2020

I am grateful to the teachers for such an amazing journey throughout the courses. Especially the puzzles designed.

By Peter N

â€¢Apr 6, 2019

Fantastic course! Really like Vladimir Podolskii's explanations and sense of humor. Great dice game at the end!

By ANIRUDH K

â€¢Aug 16, 2020

Great course, I really enjoyed it. Concepts becomes more clear if you have already studied combinatorics.

By Andrew M

â€¢Nov 11, 2017

A great course that is well organized. I love Professor Alexander Shen, because he makes me happy.

By Tyler E

â€¢Jul 11, 2020

I'm loving the discreet math in cs specialization and solving these problems is very rewarding!!!

By Harish K T

â€¢Sep 15, 2019

If you really want to have a greater grasp over mathematics, don't miss this course.

By Karan S

â€¢Sep 1, 2019

The explanations with examples and simulations make the concepts crystal clear.

By Aviral B

â€¢May 6, 2020

This course is aptly difficult as it should be

By M. A

â€¢Jul 27, 2020

The course is fine, but there are some problems. First, the instructors' explanations in the video sometimes inaudible. One should be careful when watching the lecture video. Second, there are some grammatical mistakes, particularly in the last week (Week 6). As far as I know, die is singular and dice is plural. There is no word "dices", yet one of the instructors uses this terminology. Third, there are some notational differences in this course to those normally used in probability theory. I don't know why the instructors use the lowercase variables f and g (instead of the standards X and Y) to denote random variables. And finally, some of the proofs are not rigorously explained. I advise whoever taking this class to refer to any standard textbook in combinatorics and probability theory. Nevertheless, despite all these problems, this course combines mathematical thinking and programming in an interesting setting. Perhaps, this is how mathematics is delivered in Russia, which is renown for its competitive programming achievements.

By Angelo A d M F

â€¢Dec 6, 2020

Some exercises are challenging, but I think the course is not well organized. If you're newbie to probability, it's not the course for you, because it's not comprehensive. If you had already studied probability, like me, this course allows you to review some concepts, but not all.

If I'd take a course of combinatorics and probability I'd rather choose the MIT Course from Edx, if it were available. I've watched some classes as an audit and it's far better.

By Luis M V F

â€¢Dec 29, 2019

This is course is informative, but the instructors in general are terrible. I do not like too much the approach the follow, and I cannot see a good mathematical background. In addition, some explanations are very vague. The contents of the course are great, but I strongly recommend reviewing materials by yourself if you really want to learn.

By Ghali L H

â€¢Sep 18, 2020

The final project's guide is not good.

More assistance should be required from the instructors.

By Shubham C

â€¢Jul 30, 2020

Teaching style may not suit to you. First take audit course for try.

By Konstantin K

â€¢Dec 4, 2017

It is better to read slides and do not watch the videos

By Jithin S

â€¢Oct 18, 2020

The french professor is not great at explaing

By Kunle O

â€¢Mar 3, 2022

Overall the course was fine, but there were MANY topics that they didn't bother explaining, yet the quized you on anyway. They need to do a better job of explaning the solutions to some of the problems. It was very frustrating at times to have no idea what they were talking about.

Separately, this wasn't a problem for me because I know Python, but the final quiz is all programming. That sucks for anyone who doesn't know Python and took this course for the math. I'm writing this because I'm sure there are many people who haven't been able to finish the course due to Python and haven't got a chance to express their frustration. The Week 6 discussion forum is full of people who are pissed off.

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