课程信息
4.6
163 个评分
36 个审阅
100% 在线

100% 在线

立即开始,按照自己的计划学习。
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初级

初级

完成时间(小时)

完成时间大约为19 小时

建议:6 weeks, 3-5 hours/week ...
可选语言

英语(English)

字幕:英语(English)

您将获得的技能

Random VariableProbability InterpretationsProbabilityCombinatorics
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
初级

初级

完成时间(小时)

完成时间大约为19 小时

建议:6 weeks, 3-5 hours/week ...
可选语言

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 54 分钟), 4 个阅读材料, 9 个测验
Video12 个视频
Rule of Sum3分钟
How Not to Use the Rule of Sum3分钟
Convenient Language: Sets4分钟
Generalized Rule of Sum3分钟
Number of Paths4分钟
Rule of Product3分钟
Back to Recursive Counting3分钟
Number of Tuples5分钟
Licence Plates3分钟
Tuples with Restrictions5分钟
Permutations9分钟
Reading4 个阅读材料
Slides1分钟
Slides1分钟
Listing All Permutations5分钟
Slides1分钟
Quiz8 个练习
Rule of Sum in Programming4分钟
Numbers Divisible by 2 or 38分钟
Operations with Sets10分钟
Generalized Rule of Sum18分钟
Rule of Product in Programming10分钟
Applications of the Rule of Product12分钟
Tuples5分钟
Counting with Restrictions20分钟
2
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 76 分钟), 4 个阅读材料, 6 个测验
Video8 个视频
Number of Games in a Tournament10分钟
Combinations8分钟
Pascal's Triangle9分钟
Symmetries4分钟
Row Sums10分钟
Binomial Theorem12分钟
Practice Counting13分钟
Reading4 个阅读材料
Generating Combinatorial Objects: Code10分钟
Slides10分钟
Slides10分钟
Slides10分钟
Quiz6 个练习
Number of Segments and Diagonals20分钟
Forming Sport Teams15分钟
Number of Iterations of Nested For Loops4分钟
Sum of the First Six Rows of Pascal's Triangle2分钟
Expanding (3a-2b)^k20分钟
Practice Counting10分钟
3
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 36 分钟), 3 个阅读材料, 8 个测验
Video8 个视频
Review3分钟
Salad5分钟
Combinations with Repetitions7分钟
Distributing Assignments Among People3分钟
Distributing Candies Among Kids3分钟
Numbers with Fixed Sum of Digits4分钟
Numbers with Non-increasing Digits2分钟
Splitting into Working Groups4分钟
Reading3 个阅读材料
Salads10分钟
Slides1分钟
Slides1分钟
Quiz8 个练习
Salads10分钟
Combinations with Repetitions10分钟
Distributing Assignments Among People10分钟
Distributing Candies Among Kids15分钟
Numbers with Fixed Sum of Digits15分钟
Numbers with Non-increasing Digits7分钟
Splitting into Working Groups10分钟
Problems in Combinatorics45分钟
4
完成时间(小时)
完成时间为 5 小时

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 个视频 (总计 126 分钟), 4 个阅读材料, 11 个测验
Video17 个视频
Galton Board6分钟
Natural Sciences and Mathematics6分钟
Rolling Dice7分钟
More Probability Spaces10分钟
Not Equiprobable Outcomes4分钟
More About Finite Spaces6分钟
Mathematics for Prisoners7分钟
Not All Questions Make Sense10分钟
What Is Conditional Probability?7分钟
How Reliable Is The Test?8分钟
Bayes' Theorem8分钟
Conditional Probability: A Paradox7分钟
Past and Future8分钟
Independence8分钟
Monty Hall Paradox8分钟
`Our Position'6分钟
Reading4 个阅读材料
Slides0
Slides0
Slides0
Slides0
Quiz10 个练习
Concentration for Galton Board10分钟
Computing Probabilities for Two Dice12分钟
Computing Probabilities: More Examples12分钟
Fair Decisions and Imperfect Coins20分钟
Inclusion-Exclusion Formula10分钟
Computing Conditional Probabilities16分钟
Prisoner, King and Conditional Probabilities10分钟
More Conditional Probabilities8分钟
More About Independence20分钟
Monty Hall Gone Crazy20分钟
4.6
36 个审阅Chevron Right
工作福利

83%

通过此课程获得实实在在的工作福利

热门审阅

创建者 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.

创建者 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!

讲师

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
Avatar

Vladimir Podolskii

Associate Professor
Computer Science Department

关于 University of California San Diego

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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...

关于 Introduction to Discrete Mathematics for Computer Science 专项课程

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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