Back to Combinatorics and Probability

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786 ratings

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174 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 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 ‘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

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By JY M

•Apr 4, 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 Keagan R

•Jul 28, 2020

I felt this course lacking compared to the last (Mathematical Thinking in Computer Science). Also, I felt like some explanations were a little bit poorly done. I often found myself being confused by the language used (which I am not even sure was correct use of language in some cases) only to find out that the concept was pretty straightforward when learned from other resources. My favourite thing about the first course was the puzzles. I enjoyed struggling and learning myself. There is not much of that here. Most of the discovery will be done by pausing videos before the instructor gives things away. It's funny that I am complaining about the instruction merely being present, but I guess that goes to show how rewarding it is to learn from self-discovery. I hope the next course in the specialisation: graph theory, makes use of the interactive puzzle method more. Still probably a far superior education in Discrete Math than I would otherwise be able to get.

By Vicky L

•Mar 6, 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.

By Vincent L

•Sep 12, 2018

overall great course and it was exactly what I was looking for. I deducted one star because there were multiple mistakes in the video which were caught immediately by the yellow bar notification, but still was somewhat disappointed because the mistakes were simple, which mean it was as instructors were blindly reading the script rather than thinking and doing the problem on the spot. With that being said though, I really really liked the course and would recommend this to anyone who is looking to have a primer on combinatorics!

By Anton M P

•Dec 17, 2017

This course is indeed a very well taught introduction to combinatorics and probability theory, and it can positively ground the student in all the foundational aspects of the discipline with both intuitive-geometric explanations and more advanced formal definitions.

It has helped me consolidate various concepts of probability and combinatorics thanks to the different points of view and examples through which these mathematical objects are presented. Highly recommended.

By Trần C L

•Nov 5, 2019

Quite hard to fully understand Combinatorics and Probability since it's a complicated aspect. The russian teachers have standard skill with ok English, sometimes I lost my focus and didn't pay enough attention because they lacks of appealing approaches. I am sure this course has brought me many very interesting topics and quizzes. Pretty average teaching quality but with excellent choices of content. This course deserves 8/10, good!

By Ahmad A

•Jul 10, 2021

** (( Notice that u need to know how to program to succeed in the final project ))**
Great course but I get to be honest with two point that made me give this rating
**#1** Instructor poor preparations for the videos and poor explanations for some topics
**#2** Some Assignment were "Over powered" for our current knowledge so u must be prepared that you will need to google some stuff coz you will get stuck many times.

By Ethan H

•Sep 14, 2020

Good course overall. Sometimes, lectures felt like they were not taking the shortest path to reach student understanding. It would also be nice to see the solution for the final problem written by the instructor; it would be great to see alternative (and likely better) solutions than the one I wrote!

By Jonathan M

•Feb 6, 2021

Last assignment was a test of programming intuition and python usage not covered in course. It wasn't overly difficult, but I could see how it would annoy people considering there was little guidance about the implementation (programming) of the material covered in lectures. Otherwise, good course.

By 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.

By 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.

By 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.

By Tobin H

•Apr 10, 2021

Excellent content, Russian lecturers face some language barriers but for the content and style of learning it is well worth overcoming these minor language things. Language in math is hard anyways so thinking a bit extra does not hurt. Useful course.

By 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.

By 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.

By Alikhanov A

•Apr 4, 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=)

By Paolo T

•Aug 1, 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

By 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.

By yk

•Apr 9, 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.

By Juan P Y

•Mar 1, 2018

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

By Abhishek K

•May 31, 2021

I really liked the course. Most of the concepts were explained lucidly. The final assignment was enjoyable.

By Malik T

•Feb 18, 2020

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

By giannisvasilakopoulos

•Jan 31, 2021

Very good course. I learned a lot of things although I think it would be better to have more examples.

By Rishabh A

•May 10, 2020

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

By John W

•Jul 30, 2021

Make sure to refresh and resubmit final project to judge whether program is working correctly

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