Об этом курсе
4.6
Оценки: 166
Рецензии: 36
Специализация
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Часов на завершение

Прибл. 19 часа на выполнение

Предполагаемая нагрузка: 6 weeks, 3-5 hours/week ...
Доступные языки

Английский

Субтитры: Английский

Приобретаемые навыки

Random VariableProbability InterpretationsProbabilityCombinatorics
Специализация
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Гибкие сроки

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Начальный уровень

Начальный уровень

Часов на завершение

Прибл. 19 часа на выполнение

Предполагаемая нагрузка: 6 weeks, 3-5 hours/week ...
Доступные языки

Английский

Субтитры: Английский

Программа курса: что вы изучите

Неделя
1
Часов на завершение
3 ч. на завершение

Basic Counting

Suppose we need to count certain objects. Can we do anything better than just list all the objects? Do we need to create a list all phone numbers to check whether there are enough phone numbers for everyone? Is there a way to tell whether 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 module we will give an introduction to this field that will help us to answer basic versions of the above questions....
Reading
12 видео ((всего 54 мин.)), 4 материалов для самостоятельного изучения, 9 тестов
Video12 видео
Rule of Sum3мин
How Not to Use the Rule of Sum3мин
Convenient Language: Sets4мин
Generalized Rule of Sum3мин
Number of Paths4мин
Rule of Product3мин
Back to Recursive Counting3мин
Number of Tuples5мин
Licence Plates3мин
Tuples with Restrictions5мин
Permutations9мин
Reading4 материала для самостоятельного изучения
Slides1мин
Slides1мин
Listing All Permutations5мин
Slides1мин
Quiz8 практического упражнения
Rule of Sum in Programming4мин
Numbers Divisible by 2 or 38мин
Operations with Sets10мин
Generalized Rule of Sum18мин
Rule of Product in Programming10мин
Applications of the Rule of Product12мин
Tuples5мин
Counting with Restrictions20мин
Неделя
2
Часов на завершение
3 ч. на завершение

Binomial Coefficients

In how many ways one can select a team of five students out of ten students? What is the number of non-negative integers with at five digits whose digits are decreasing? In how many ways one can get from the bottom left cell to the top right cell of a 5x5 grid, each time going either up or to the right? And why all these three numbers are equal? We'll figure this out in this module!...
Reading
8 видео ((всего 76 мин.)), 4 материалов для самостоятельного изучения, 6 тестов
Video8 видео
Number of Games in a Tournament10мин
Combinations8мин
Pascal's Triangle9мин
Symmetries4мин
Row Sums10мин
Binomial Theorem12мин
Practice Counting13мин
Reading4 материала для самостоятельного изучения
Generating Combinatorial Objects: Code10мин
Slides10мин
Slides10мин
Slides10мин
Quiz6 практического упражнения
Number of Segments and Diagonals20мин
Forming Sport Teams15мин
Number of Iterations of Nested For Loops4мин
Sum of the First Six Rows of Pascal's Triangle2мин
Expanding (3a-2b)^k20мин
Practice Counting10мин
Неделя
3
Часов на завершение
3 ч. на завершение

Advanced Counting

We have already considered most of the most standard settings in Combinatorics, that allow us to address many counting problems. However, successful application of this knowledge on practice requires considerable experience in this kind of problems. In this module we will address the final standard setting in our course, combinations with repetitions, and then we will gain some experience by discussing various problems in Combinatorics....
Reading
8 видео ((всего 36 мин.)), 3 материалов для самостоятельного изучения, 8 тестов
Video8 видео
Review3мин
Salad5мин
Combinations with Repetitions7мин
Distributing Assignments Among People3мин
Distributing Candies Among Kids3мин
Numbers with Fixed Sum of Digits4мин
Numbers with Non-increasing Digits2мин
Splitting into Working Groups4мин
Reading3 материала для самостоятельного изучения
Salads10мин
Slides1мин
Slides1мин
Quiz8 практического упражнения
Salads10мин
Combinations with Repetitions10мин
Distributing Assignments Among People10мин
Distributing Candies Among Kids15мин
Numbers with Fixed Sum of Digits15мин
Numbers with Non-increasing Digits7мин
Splitting into Working Groups10мин
Problems in Combinatorics45мин
Неделя
4
Часов на завершение
5 ч. на завершение

Probability

The word "probability" is used quite often in the everyday life. However, not always we can speak about probability as some number: for that a mathematical model is needed. What is this mathematical model (probability space)? How to compute probabilities (if the model is given)? How to judge whether the model is adequate? What is conditional probability and Bayes' theorem? How our plausible reasoning can be interpreted in terms of Bayes' theorem? In this module we cover these questions using some simple examples of probability spaces and real life sutiations....
Reading
17 видео ((всего 126 мин.)), 4 материалов для самостоятельного изучения, 11 тестов
Video17 видео
Galton Board6мин
Natural Sciences and Mathematics6мин
Rolling Dice7мин
More Probability Spaces10мин
Not Equiprobable Outcomes4мин
More About Finite Spaces6мин
Mathematics for Prisoners7мин
Not All Questions Make Sense10мин
What Is Conditional Probability?7мин
How Reliable Is The Test?8мин
Bayes' Theorem8мин
Conditional Probability: A Paradox7мин
Past and Future8мин
Independence8мин
Monty Hall Paradox8мин
`Our Position'6мин
Reading4 материала для самостоятельного изучения
Slides
Slides
Slides
Slides
Quiz10 практического упражнения
Concentration for Galton Board10мин
Computing Probabilities for Two Dice12мин
Computing Probabilities: More Examples12мин
Fair Decisions and Imperfect Coins20мин
Inclusion-Exclusion Formula10мин
Computing Conditional Probabilities16мин
Prisoner, King and Conditional Probabilities10мин
More Conditional Probabilities8мин
More About Independence20мин
Monty Hall Gone Crazy20мин
4.6
Рецензии: 36Chevron Right
Карьерные преимущества

33%

получил значимые преимущества в карьере благодаря этому курсу

Лучшие рецензии

автор: ZBOct 13th 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.

автор: CZSep 11th 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!

Преподавателя

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Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
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Vladimir Podolskii

Associate Professor
Computer Science Department

О University of California San Diego

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory....

О National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

О специализации ''Introduction to Discrete Mathematics for Computer Science'

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses....
Introduction to Discrete Mathematics for Computer Science

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