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.

本课程是 Introduction to Discrete Mathematics for Computer Science 专项课程 专项课程的一部分

# Combinatorics and Probability

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## 课程信息

### 学生职业成果

## 33%

## 50%

### 您将获得的技能

### 学生职业成果

## 33%

## 50%

#### 100% 在线

#### 可灵活调整截止日期

#### 初级

#### 完成时间大约为21 小时

#### 英语（English）

### 提供方

#### 加州大学圣地亚哥分校

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.

#### 国立高等经济大学

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 communicamathematics, engineering, and more.

## 教学大纲 - 您将从这门课程中学到什么

**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.

**完成时间为 3 小时**

**12 个视频**

**4 个阅读材料**

**8 个练习**

**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!

**完成时间为 3 小时**

**8 个视频**

**4 个阅读材料**

**6 个练习**

**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.

**完成时间为 3 小时**

**8 个视频**

**3 个阅读材料**

**8 个练习**

**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.

**完成时间为 5 小时**

**17 个视频**

**4 个阅读材料**

**10 个练习**

### 审阅

#### 4.6

##### 来自COMBINATORICS AND PROBABILITY的热门评论

This course provided me with new ways to confront the problems of combinatorics. I am very grateful to the faculty for their content and coursera for giving me financial aid.

Great course, lots of good info, not too long. Some of the coding assignments and quizzes are challenging, but the staff respond very quickly to questions in the forums.

Had loads of fun during most part of the course. Frequent quizzes keep the learner on toes. Thoroughly enjoyed the final programming quiz to implement a dice game.

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.

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!

Good first course in probability/combinatorics at the university level; last assignment had a lot more coding than other assignments, a lot more

I've covered these topics before but there were a lot of great problems and extensions of concepts in this course. Worth doing.

Awesome course, good topics. Easy to get help. Some topics weren't that clear at first, but you'll eventually understand.

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