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初級レベル

英語

字幕:英語, ギリシャ語, 中国語(簡体)

習得するスキル

Random VariableProbability InterpretationsProbabilityCombinatorics

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自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

初級レベル

英語

字幕:英語, ギリシャ語, 中国語(簡体)

シラバス - 本コースの学習内容

1
3時間で修了

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.

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12件のビデオ (合計54分), 4 readings, 9 quizzes
12件のビデオ
Rule of Sum3 分
How Not to Use the Rule of Sum3 分
Convenient Language: Sets4 分
Generalized Rule of Sum3 分
Number of Paths4 分
Rule of Product3 分
Back to Recursive Counting3 分
Number of Tuples5 分
Licence Plates3 分
Tuples with Restrictions5 分
Permutations9 分
4件の学習用教材
Slides1 分
Slides1 分
Listing All Permutations5 分
Slides1 分
8の練習問題
Rule of Sum in Programming4 分
Numbers Divisible by 2 or 38 分
Operations with Sets10 分
Generalized Rule of Sum18 分
Rule of Product in Programming10 分
Applications of the Rule of Product12 分
Tuples5 分
Counting with Restrictions20 分
2
3時間で修了

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!

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8件のビデオ (合計76分), 4 readings, 6 quizzes
8件のビデオ
Number of Games in a Tournament10 分
Combinations8 分
Pascal's Triangle9 分
Symmetries4 分
Row Sums10 分
Binomial Theorem12 分
Practice Counting13 分
4件の学習用教材
Generating Combinatorial Objects: Code10 分
Slides10 分
Slides10 分
Slides10 分
6の練習問題
Number of Segments and Diagonals20 分
Forming Sport Teams15 分
Number of Iterations of Nested For Loops4 分
Sum of the First Six Rows of Pascal's Triangle2 分
Expanding (3a-2b)^k20 分
Practice Counting10 分
3
3時間で修了

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.

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8件のビデオ (合計36分), 3 readings, 8 quizzes
8件のビデオ
Review3 分
Salad5 分
Combinations with Repetitions7 分
Distributing Assignments Among People3 分
Distributing Candies Among Kids3 分
Numbers with Fixed Sum of Digits4 分
Numbers with Non-increasing Digits2 分
Splitting into Working Groups4 分
3件の学習用教材
Salads10 分
Slides1 分
Slides1 分
8の練習問題
Salads10 分
Combinations with Repetitions10 分
Distributing Assignments Among People10 分
Distributing Candies Among Kids15 分
Numbers with Fixed Sum of Digits15 分
Numbers with Non-increasing Digits7 分
Splitting into Working Groups10 分
Problems in Combinatorics45 分
4
5時間で修了

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.

...
17件のビデオ (合計126分), 4 readings, 11 quizzes
17件のビデオ
Galton Board6 分
Natural Sciences and Mathematics6 分
Rolling Dice7 分
More Probability Spaces10 分
Not Equiprobable Outcomes4 分
More About Finite Spaces6 分
Mathematics for Prisoners7 分
Not All Questions Make Sense10 分
What Is Conditional Probability?7 分
How Reliable Is The Test?8 分
Bayes' Theorem8 分
Conditional Probability: A Paradox7 分
Past and Future8 分
Independence8 分
Monty Hall Paradox8 分
`Our Position'6 分
4件の学習用教材
Slides
Slides
Slides
Slides
10の練習問題
Concentration for Galton Board10 分
Computing Probabilities for Two Dice12 分
Computing Probabilities: More Examples12 分
Fair Decisions and Imperfect Coins20 分
Inclusion-Exclusion Formula10 分
Computing Conditional Probabilities16 分
Prisoner, King and Conditional Probabilities10 分
More Conditional Probabilities8 分
More About Independence20 分
Monty Hall Gone Crazy20 分
4.6
48件のレビューChevron Right

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Combinatorics and Probability からの人気レビュー

by 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.

by 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!

講師

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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

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