課程信息
4.6
151 個評分
33 個審閱
專項課程
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
初級

初級

完成時間(小時)

完成時間大約為19 小時

建議:6 weeks, 3-5 hours/week ...
可選語言

英語(English)

字幕:英語(English)...

您將獲得的技能

Random VariableProbability InterpretationsProbabilityCombinatorics
專項課程
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
初級

初級

完成時間(小時)

完成時間大約為19 小時

建議:6 weeks, 3-5 hours/week ...
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 3 小時

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 個視頻(共 54 分鐘), 4 個閱讀材料, 9 個測驗
Video12 個視頻
Rule of Sum3分鐘
How Not to Use the Rule of Sum3分鐘
Convenient Language: Sets4分鐘
Generalized Rule of Sum3分鐘
Number of Paths4分鐘
Rule of Product3分鐘
Back to Recursive Counting3分鐘
Number of Tuples5分鐘
Licence Plates3分鐘
Tuples with Restrictions5分鐘
Permutations9分鐘
Reading4 個閱讀材料
Slides1分鐘
Slides1分鐘
Listing All Permutations5分鐘
Slides1分鐘
Quiz8 個練習
Rule of Sum in Programming4分鐘
Numbers Divisible by 2 or 38分鐘
Operations with Sets10分鐘
Generalized Rule of Sum18分鐘
Rule of Product in Programming10分鐘
Applications of the Rule of Product12分鐘
Tuples5分鐘
Counting with Restrictions20分鐘
2
完成時間(小時)
完成時間為 3 小時

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 個視頻(共 76 分鐘), 4 個閱讀材料, 6 個測驗
Video8 個視頻
Number of Games in a Tournament10分鐘
Combinations8分鐘
Pascal's Triangle9分鐘
Symmetries4分鐘
Row Sums10分鐘
Binomial Theorem12分鐘
Practice Counting13分鐘
Reading4 個閱讀材料
Generating Combinatorial Objects: Code10分鐘
Slides10分鐘
Slides10分鐘
Slides10分鐘
Quiz6 個練習
Number of Segments and Diagonals20分鐘
Forming Sport Teams15分鐘
Number of Iterations of Nested For Loops4分鐘
Sum of the First Six Rows of Pascal's Triangle2分鐘
Expanding (3a-2b)^k20分鐘
Practice Counting10分鐘
3
完成時間(小時)
完成時間為 3 小時

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 個視頻(共 36 分鐘), 3 個閱讀材料, 8 個測驗
Video8 個視頻
Review3分鐘
Salad5分鐘
Combinations with Repetitions7分鐘
Distributing Assignments Among People3分鐘
Distributing Candies Among Kids3分鐘
Numbers with Fixed Sum of Digits4分鐘
Numbers with Non-increasing Digits2分鐘
Splitting into Working Groups4分鐘
Reading3 個閱讀材料
Salads10分鐘
Slides1分鐘
Slides1分鐘
Quiz8 個練習
Salads10分鐘
Combinations with Repetitions10分鐘
Distributing Assignments Among People10分鐘
Distributing Candies Among Kids15分鐘
Numbers with Fixed Sum of Digits15分鐘
Numbers with Non-increasing Digits7分鐘
Splitting into Working Groups10分鐘
Problems in Combinatorics45分鐘
4
完成時間(小時)
完成時間為 5 小時

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 個視頻(共 126 分鐘), 4 個閱讀材料, 11 個測驗
Video17 個視頻
Galton Board6分鐘
Natural Sciences and Mathematics6分鐘
Rolling Dice7分鐘
More Probability Spaces10分鐘
Not Equiprobable Outcomes4分鐘
More About Finite Spaces6分鐘
Mathematics for Prisoners7分鐘
Not All Questions Make Sense10分鐘
What Is Conditional Probability?7分鐘
How Reliable Is The Test?8分鐘
Bayes' Theorem8分鐘
Conditional Probability: A Paradox7分鐘
Past and Future8分鐘
Independence8分鐘
Monty Hall Paradox8分鐘
`Our Position'6分鐘
Reading4 個閱讀材料
Slides分鐘
Slides分鐘
Slides分鐘
Slides分鐘
Quiz10 個練習
Concentration for Galton Board10分鐘
Computing Probabilities for Two Dice12分鐘
Computing Probabilities: More Examples12分鐘
Fair Decisions and Imperfect Coins20分鐘
Inclusion-Exclusion Formula10分鐘
Computing Conditional Probabilities16分鐘
Prisoner, King and Conditional Probabilities10分鐘
More Conditional Probabilities8分鐘
More About Independence20分鐘
Monty Hall Gone Crazy20分鐘
4.6
33 個審閱Chevron Right
工作福利

83%

通過此課程獲得實實在在的工作福利

熱門審閱

創建者 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.

創建者 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!

講師

Avatar

Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
Avatar

Vladimir Podolskii

Associate Professor
Computer Science Department

關於 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....

關於 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...

關於 Introduction to Discrete Mathematics for Computer Science 專項課程

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

常見問題

  • 注册以便获得证书后,您将有权访问所有视频、测验和编程作业(如果适用)。只有在您的班次开课之后,才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程,可能无法访问某些作业。

  • 您注册课程后,将有权访问专项课程中的所有课程,并且会在完成课程后获得证书。您的电子课程证书将添加到您的成就页中,您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容,可以免费旁听课程。

還有其他問題嗎?請訪問 學生幫助中心