Combinatorics and Probability
Introduction to Discrete Mathematics for Computer Science,
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.
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| Rating | 4.4★ based on 71 ratings |
|---|---|
| Length | 7 weeks |
| Effort | 6 weeks, 3-5 hours/week |
| Starts | Jul 3 (42 weeks ago) |
| Cost | $79 |
| From | University of California San Diego, National Research University Higher School of Economics, HSE University via Coursera |
| Instructors | Alexander S. Kulikov, Vladimir Podolskii, Владимир Подольский |
| Download Videos | On all desktop and mobile devices |
| Language | English |
| Subjects | Programming Mathematics |
| Tags | Computer Science Algorithms Math And Logic |
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What people are saying
probability and combinatorics
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.
I completely recommend it Probability section was little weak It is better to read slides and do not watch the videos A very nice introduction to probability and combinatorics.
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alexander shen
I love Professor Alexander Shen, because he makes me happy.
The weakest part, unfortunately, were Alexander Shen's weeks.
The audio of Prof. Alexander Shen is not clear in many instances.
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bit more
However, I felt some of the videos could do with a bit more editing (with the typos and etc.).
However, I felt that the instructors could have been a bit more responsive on the forums to help us clear our doubts.
dice game
Great dice game at the end!
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.
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final project
Challenging final project but worth trying!
The final project is hard for me cuz I don't have Python experience.
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nice introduction
Hard to understand lecturer This course is a nice introduction to probability and give good ideas to make proof of combinatorics (the week 2 was the best), all of this give it in a nice an intuitive way.
Really nice introduction to discrete math and basic algorithms.
probability theory
although I have learnt probability theory both in undergraduate and postgraduate level, it still gives me some inspiration toward probability theory.
Some paradoxes examples help me to understand the probability theory better and clearer.
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.
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more advanced
This one is a bit more 'mathy' than the first one, it has a good pace and the exercises are really cool I think the level could have been a bit more advanced.
last assignment
Good first course in probability/combinatorics at the university level; last assignment had a lot more coding than other assignments, a lot more overall great course and it was exactly what I was looking for.
The last assignment is 23% of the total grades.
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| Rating | 4.4★ based on 71 ratings |
|---|---|
| Length | 7 weeks |
| Effort | 6 weeks, 3-5 hours/week |
| Starts | Jul 3 (42 weeks ago) |
| Cost | $79 |
| From | University of California San Diego, National Research University Higher School of Economics, HSE University via Coursera |
| Instructors | Alexander S. Kulikov, Vladimir Podolskii, Владимир Подольский |
| Download Videos | On all desktop and mobile devices |
| Language | English |
| Subjects | Programming Mathematics |
| Tags | Computer Science Algorithms Math And Logic |
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