返回到 Combinatorics and Probability

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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 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 `consumers’ 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.
Do you have technical problems? Write to us: coursera@hse.ru...

JC

Sep 09, 2020

It's a perfect introduction to combinatorics and probability, short, fun, and easy to understand. I would like to see more puzzles, those are extremely fun and interesting

KB

Dec 26, 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.

筛选依据：

创建者 Sudheera S

•Aug 29, 2018

Good introduction to combinations. I enjoyed the programming while learning mathematics. The audio of Prof. Alexander Shen is not clear in many instances. The way the checks are done in between the video lectures helps keep going with course. The tests and well designed. Good job Coursera.

创建者 Tomas R

•Jul 19, 2020

I took me some time to get used to the accent of lecturers, but otherwise the course was quite good. I liked that there also was a focus on intuitive understanding, and the difference between "normal" usage of some probabilistic term in language and exact mathematical meaning.

创建者 Gunjan B

•Jul 25, 2020

This course cover all important aspects of the probability. But the topics are explained in bit shorter time and without explaining the practical use of this in algorithm implementation. However it has explained where in the real world the fundamentals are used.

创建者 Jasvin M

•May 21, 2020

I've been taught Combinatorics & Probability before too in my college but this course helped iron out a lot of basic doubts and gave a lot of cool examples that will remember some basic concepts if in case you ever end up forgetting it.

创建者 Bryan W B

•Nov 27, 2018

Much stronger than the first course in this series. I very much enjoyed Vladimir and Alexander's lectures. The weakest part, unfortunately, were Alexander Shen's weeks. I must credit him, however, for being very responsive on the forum.

创建者 Alikhanov A

•Apr 04, 2020

Good course for people who forgot or never ever knew combinatorics and probability theory. A lot of applications and examples, but teachers pronounciation is not the best. I am russian but even for me it was difficult sometimes=)

创建者 Mark P T

•Aug 01, 2020

Great course. The final Project unclear had instructions on how to provide input. I spent a lot of time trying to troubleshoot it even though I already have a correct solution

创建者 Umakant V

•Jan 23, 2020

This course provided me with new ways to confront the problems of combinatorics. I am very grateful to the faculty for their content and coursera for giving me financial aid.

创建者 yk

•Apr 09, 2020

Everything except Week 4 was great. Alexander Shen the instructor for week 4 cannot explain a concept without adding more confusion to the subject.

创建者 Juan P Y

•Mar 02, 2018

Awesome course, good topics. Easy to get help. Some topics weren't that clear at first, but you'll eventually understand.

创建者 Malik T

•Feb 18, 2020

In this course, the use of language is a huge obstacle for students to understand the teachers clearly.

创建者 Rishabh A

•May 10, 2020

The course had amazing content and everything except the probability had a top-notch explanation.

创建者 Ajit C B

•Oct 19, 2017

I think the level could have been a bit more advanced. Overall a good course though.

创建者 Abhinav M

•Jun 04, 2020

Probability courses could have been more structured and more about definitions

创建者 Nikhil Y

•May 01, 2020

it was really amazing to work on this course!!

创建者 Jinqiang Z

•Dec 16, 2017

it's good in general. But slightly too simple.

创建者 Elton M

•May 05, 2018

The probability section could be more visual.

创建者 Saurabh P

•May 27, 2020

Great course with lots of exercises.

创建者 Michael K H E

•Jan 22, 2019

Prof Vlad has really great examples!

创建者 Ramesh

•Dec 09, 2017

Probability section was little weak

创建者 Lionel L R Q

•Jun 24, 2020

The last assignment is fun :)

创建者 MANOJ B B ( i C

•Jul 28, 2020

It was very good

创建者 M. A

•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.

创建者 Luis M V F

•Dec 30, 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.

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