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....

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!

JC

Sep 8, 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

筛选依据：

创建者 Deleted A

•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.

创建者 Ziad B

•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.

创建者 SUPAKORN S

•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!

创建者 Kaustubh F

•May 29, 2020

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

创建者 James C

•Sep 2, 2020

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

创建者 Joseph D

•Feb 11, 2018

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

创建者 Farhan F A

•Apr 27, 2020

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

创建者 Peter N

•Apr 6, 2019

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

创建者 ANIRUDH K

•Aug 16, 2020

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

创建者 Andrew M

•Nov 11, 2017

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

创建者 Tyler E

•Jul 11, 2020

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

创建者 Harish K T

•Sep 15, 2019

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

创建者 Karan S

•Sep 1, 2019

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

创建者 Aviral B

•May 6, 2020

This course is aptly difficult as it should be

创建者 Arpan K D

•Feb 17, 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.

创建者 Guo F

•Dec 11, 2020

Pros: (1). Most of the quizzes are really well-designed and fun, sometimes challenging, but good for solidifying my understanding. (2) Lectures are generally of good quality.

Cons:(1) The material is not comprehensive, especially the probability part, expectation and stuff. But I guess this is a difficult balance when making an online course.

(2) The final project is very basic for anyone who knows programming well. Considering this course targets CS students (I guess?), I don't understand why people complain about the programming assignments. And I think it should be more challenging.

创建者 Muhammad Y A

•Nov 1, 2020

It was fantastic and awesome. This course is quite challenging but also interesting at the same time. You'll get assignments about combinatorics in the first half and about probabilities in the last half. In the end, you can practice what have you got from this course on the final project, a programming assignment about a dice game. Hope you can enjoy this course.

创建者 Yunsuk P

•Jan 4, 2020

This course does have some coding challenges which are at the same time very interesting. Actually, I did not think much about combinatorics in terms of coding but this was a very nice opportunity to learn more about mathematical thinking for programming and problem-solving.

创建者 Vishal M

•May 2, 2020

I like this course and it is puzzle oriented teaching methodology. Instructors were great and their way of teaching makes material easy to understand and stick in mind. This was a introductory course looking forward to more advanced courses.

创建者 Aryan R

•Aug 11, 2020

The Course is awesome if you know some basic maths. The instructors have a good way of teaching. The problems in middle of videos help in understanding better. The problems in tests are usually helpful in getting a better understanding

创建者 储忻

•May 2, 2021

very good content and inspirational material. I learned probability theory from multiple institutes but this one offers great insight into some formulae that we took for granted. e.g. Bayes Theorem

创建者 Siddhant P

•Feb 27, 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!

创建者 Jherson A M C

•Sep 9, 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

创建者 T K

•May 19, 2020

I lacked confidence in permutations and combinations since my high school, but now i am enjoying solving combinatorial problems. Thanks to professors

创建者 Chen Z

•Sep 11, 2018

The final project is hard for me cuz I don't have Python experience. and the logic is a little bit complicated. That's not for absolutely beginners!

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