Back to Combinatorics and Probability

4.6

stars

491 ratings

•

103 reviews

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...

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.

Aug 03, 2019

Had loads of fun during most part of the course. Frequent quizzes keep the learner on toes. Thoroughly enjoyed the final programming quiz to implement a dice game.

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By Javier O

•Dec 15, 2017

Excellent and complete course. I completely recommend it

By Nick S

•Jun 12, 2020

Python knowledge is a must for the final projects!

By Ziqi Y

•Dec 31, 2018

Great! Challenging final project but worth trying!

By Miguel A D A

•Nov 26, 2018

Super interesting the topic about combinatorics

By Shubham K P

•Apr 19, 2019

Especially the probability part was very good.

By Orkun Ö

•Oct 15, 2019

Great course! Many thanks to the instructors!

By Steven W

•Dec 01, 2017

This course will fill your head with numbers.

By Zhen X

•Jul 08, 2020

very solid course, very helpful course

By Kartish J

•Sep 05, 2019

I Love It while learning this course:)

By Parthasaradhi T

•Jul 16, 2019

Best Course for beginners

By Akash y

•Jun 14, 2019

it is a nice course

By Zhe Y

•Jul 23, 2018

pure math course...

By Serhat G

•Dec 22, 2018

Excellent, thanks.

By DANISH M

•Sep 25, 2019

taught me a lot

By Karn T

•Jul 10, 2020

Nice course...

By Arka M

•Jul 08, 2018

Great Course.

By haozhen

•Feb 22, 2020

Good Course!

By Deleted A

•Sep 06, 2019

Excellent!

By Nguyen K T

•Sep 11, 2019

so useful

By Stefan D

•Nov 18, 2017

Loved it

By Md H R

•May 05, 2020

AWESOME

By Ganna S

•Nov 22, 2017

Great!)

By HaotianWang

•Jul 15, 2018

useful

By Jing-Yeu M

•Apr 04, 2020

In general an enjoyable tour of picking up what I used to know and something new. The first two weeks might seem a bit light if you have a solid fundamental of high school math, but into the third week you are going to see the beef of combinatorics.

Week 4 is probably the trickiest one but indeed the materials are also probably the most difficult to be explained. I think Prof. Shen has tried his best although it was not always very easy to digest. After all, I think if you do go through the quiz sections you should be able to learn something.

Week 5 is the most interesting part to me personally, as I was not very familiar with linearity of expectation and Markov's inequality before. If you are like me, this part will be really brilliant, brain-storming, and lots of fun. I appreciate the effort the staff put in and the proof is easy to follow and the exercises are adequate.

If only thing I'd say I was hoping there could be more touches on continuous probability as well as cdf/pdf. Overall, I really like what I've learnt from this course and I'd like to take the chance here to express my appreciation.

By Vicky L

•Mar 06, 2019

The course is structured reasonably well. I especially liked how the quizzes were setup, there were lots of them testing my understanding from different angles.

However, I felt some of the videos could do with a bit more editing (with the typos and etc.). While these errors were pointed out as quizzes inside the video, it gets a bit distracting. Furthermore, for some of the weeks (week 4 say), there were a lot more material comparing to others (week 6 say). It felt a bit strange with such a huge change in workload to me personally and would have been nice to be slightly more consistent.

Overall, I enjoyed the course and felt like I have learnt the basics for what I wanted. Thanks.

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