Back to 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 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....

LL

Sep 20, 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

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!

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By Charalambos P

â€¢Oct 9, 2018

Most of the courses of this specialisation (not only on prob) are VERY hard to follow. Instructors lack of passion while teaching and they just reading the script from the slides. Whatever I passed and learned was from random sources at the internet.

To the instructors: Take a blackboard and start solving the problems by hand. By reading a long queue of numbers from slides for 10min, the student can't follow at all. This is not a simple presentation, this is math topics. You can't just pass a slide full of numbers and some sentences thinking that the student can comprehend all that stuff.

On the other hand, on the 3rd party quizzes has been made a magnificent job.

By Vijay R

â€¢Nov 24, 2018

While I imagine Alexander Shen to be a great person and a math genius, he seems entirely unprepared for the lectures. He speaks well, I can understand his accent, but his lack of preparation and poor slides make a difficult situation terrible. The other instructors do a much better job, but I also wish there were more tests of our knowledge.

By Mike P

â€¢Mar 3, 2019

Quite enjoyable, however Alex is not the strongest presenter though his passion is evident :)

By Mallori H

â€¢Oct 5, 2017

Hard to understand lecturer

By AJ A

â€¢Sep 25, 2018

Good first course in probability/combinatorics at the university level; last assignment had a lot more coding than other assignments, a lot more

By Keenan B

â€¢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.

By PLN R

â€¢Aug 3, 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.

By Howoo J

â€¢May 4, 2020

Final Project will be difficult if you don't have any python background

By Suman S

â€¢Feb 10, 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.

By Abhishek M

â€¢May 22, 2021

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

By Ryan B

â€¢Feb 21, 2020

Terrible instruction

By Bappaditya D

â€¢Dec 3, 2019

This course offers very detailed concepts of probability theory and helps students to think over real world scenarios where we can apply the magic of probability theory. One needs continuous study of the provided resources and notes to grasp the intuition of probability theory. As per what I have learned from this course is that probability theory is not only abstract mathematics with equations and formulas with tips and tricks rather how we interpret every single problem. Its really random in nature. Thanks to the teachers of these course for interpreting these complex concepts in a much easier and acceptable way.

By Christopher W

â€¢Mar 7, 2020

What a great class. I picked up tons of great insights about permutations, combinations, and probability in ways that I will actually be able to remember and apply, not the usual block of formulas to memorize. Somehow it just seems right learning maths from slightly scary looking dudes with Russian accents. LOL, just kidding, but the instructors were amazing. Incredibly brilliant and gifted in explaining things such that a dullard like me can even understand them. Bravo!

By Saptarshi M

â€¢Oct 10, 2018

Concepts are presented in such a way that a novice can understand easily. For an advanced learner, there are concepts that are lit from a different perspective. Not all the instructors are equally competent. Sometimes you have to watch the videos twice to get the full understanding. But that's worth of your time. Overall enjoyable. Programming practices are also good and of intermediate quality.

By Blanca H M

â€¢Nov 28, 2019

One of the best MOOCs I have ever taken! Very engaging instructors and good material. My only objection would be some more advanced lectures, as I really enjoyed the last one and the dice game, but still very valuable, especially if you want to brush up on combinatorics and probability or want to improve these abilities for programming, as the quizzes are challenging and well thought.

By Jedediah S

â€¢May 19, 2019

This course was really challenging. I feel like the final project was more difficult to program than to calculate so make sure you have a solid foundation in python. Also itertools is very helpful. The instructors were clear in the lectures and I felt like there was a good progression of exercises. I was really challenged by this course but highly recommend it.

By Liang T

â€¢Jan 6, 2018

It is a pretty good course. although I have learnt probability theory both in undergraduate and postgraduate level, it still gives me some inspiration toward probability theory. I love the examples given in the lecture, which are classical and typical enough. Some paradoxes examples help me to understand the probability theory better and clearer.

By Alex C

â€¢Jun 27, 2020

Great course which reminds me how totally counter intuitive this stuff is! I suspect i was doing harder stuff in my final year maths at school and never really did any of this stuff in my maths degree...but i really struggled getting some of these answers! No fault of the instructors, i am just hopeless at probability!

By aparna s

â€¢Sep 1, 2020

The course is really interesting and is very useful. The only problem is that we need to know python programming to do the final project. So, if you are not familiar with python programming, it is advisable to learn python prior to this course for smooth completion of the project.

By LordTejas

â€¢Feb 23, 2020

One of the best courses I ever seen. I learned so much about combinatorics and probability that I never got to learn from my college. Also, how to apply these knowledge in real life and solve problems efficiently. I am gonna tell my friends to check out these course.

By Aditya K P

â€¢Jan 27, 2018

Clear and concise lectures, mixed with examples rooted in daily life makes this offering of the course one of the best courses for probability for the general audience. The instructors easily manage to convey and teach non-intuitive facts with ease. A must have.

By Chukwudi O

â€¢Jan 25, 2020

Combinatorics and Probability course has helped me know probability and combinatorics better than what was taught in school. This course is unique and well-taught for beginner and I can't wait to finish the remaining courses under this Specialization.

By Olivio A C J

â€¢May 8, 2020

A good course with good teachers. The explanations are well presented and the exercises are interesting. It was a good revision of the main concepts in probability wich I had already seen some years ago. It is a valuable course.

By Pedro H

â€¢Jun 17, 2018

Really nice introduction to discrete math and basic algorithms. The content is quite basic, but as mentioned in the syllabus is for beginners. Still, for those of you who are at that level is worth taking this specialization.

By Devansh H

â€¢Jul 11, 2020

The Combinatorics section was brilliant !! I would have loved to study more about Independence of events in a probability space. A more clear and detailed explanation could have been given. Great course !!