Voltar para Combinatorics and Probability

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743 classificações

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163 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 Akash K y

•14 de Jun de 2019

it is a nice course

por Zhe Y

•23 de Jul de 2018

pure math course...

por SHIVENDU P

•23 de Jul de 2020

VERY COOL TO LEARN

por Serhat G

•22 de Dez de 2018

Excellent, thanks.

por Ivan Y C M

•15 de Jul de 2020

very good course

por André U

•17 de Ago de 2020

great course!!!

por danish m

•25 de Set de 2019

taught me a lot

por Karn T

•10 de Jul de 2020

Nice course...

por Ana G

•8 de Fev de 2021

Great course!

por Arka M

•8 de Jul de 2018

Great Course.

por haozhen

•22 de Fev de 2020

Good Course!

por Afnan A

•15 de Ago de 2020

Fantastic!

por Deleted A

•6 de Set de 2019

Excellent!

por Ahmed A

•11 de Ago de 2020

Thank you

por Thành N K

•11 de Set de 2019

so useful

por Stefan D

•18 de Nov de 2017

Loved it

por Md H R

•5 de Mai de 2020

AWESOME

por Anna S

•22 de Nov de 2017

Great!)

por HaotianWang

•15 de Jul de 2018

useful

por Cheng-Ying W

•30 de Jul de 2020

Good!

por GERALD M F B B

•29 de Set de 2020

good

por JY M

•4 de Abr de 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.

por Keagan P R

•28 de Jul de 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.

por Vicky L

•6 de Mar de 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.

por Vincent L

•12 de Set de 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!

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