Voltar para Combinatorics and Probability

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762 classificações

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168 avaliações

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....

SP

26 de Fev de 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!

JC

8 de Set de 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

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por Deleted A

•23 de Jun de 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.

por Ziad B

•13 de Out de 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.

por SUPAKORN S

•17 de Jul de 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!

por Kaustubh F

•29 de Mai de 2020

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

por James C

•2 de Set de 2020

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

por Joseph D

•11 de Fev de 2018

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

por Farhan F A

•27 de Abr de 2020

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

por Peter N

•6 de Abr de 2019

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

por ANIRUDH K

•16 de Ago de 2020

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

por Andrew M

•11 de Nov de 2017

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

por Tyler E

•11 de Jul de 2020

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

por Harish K T

•15 de Set de 2019

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

por Karan S

•1 de Set de 2019

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

por Aviral B

•6 de Mai de 2020

This course is aptly difficult as it should be

por M. A

•27 de Jul de 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.

por Angelo F

•6 de Dez de 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.

por Luis M V F

•29 de Dez de 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.

por Ghali L H

•18 de Set de 2020

The final project's guide is not good.

More assistance should be required from the instructors.

por Shubham C

•30 de Jul de 2020

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

por Konstantin K

•4 de Dez de 2017

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

por Jithin S

•18 de Out de 2020

The french professor is not great at explaing

por Suman S

•10 de Fev de 2020

I liked the course, but it should have a disclaimer of the pre-requisite of good python knowledge required. The last assignment is 23% of the total grades. Unfortunately, instructors don't even teach any basics of python to tackle the assignments. This is the most unprofessional thing about the course. The rest of the material in the course is fun. I am giving the course a 2-star rating because of my deep struggle with the last assignment.

por Abhishek M

•22 de Mai de 2021

You should provide more content materials and professors should describe more about the course or topics.

por Ryan B

•21 de Fev de 2020

Terrible instruction

por Arpan K D

•17 de Fev de 2021

A brilliant introduction to combinatorics and probability. The professors bring some method to the madness of combinatorics by drawing an extremely helpful quadrant (ordered or unordered vs with repetition or without repetition) to explain how to structurally approach combinatorics problems. The lessons on probability cover probability and random variables, with some well chosen problems to demonstrate why we need both concepts. Finally, the project in week 6 is extremely helpful for people who are rusty in programming, allowing them to implement a solution leveraging combinatorics and python programming.

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