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. In this course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations. One of the main `consumers’ of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop. In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students. Do you have technical problems? Write to us: coursera@hse.ru

이 강좌는 Introduction to Discrete Mathematics for Computer Science 전문 분야의 일부입니다.

# Combinatorics and Probability

제공자:

## About this Course

### Learner Career Outcomes

## 33%

## 50%

### 귀하가 습득할 기술

### Learner Career Outcomes

## 33%

## 50%

#### 100% 온라인

#### 다음 전문 분야의 5개 강좌 중 2번째 강좌:

#### 유동적 마감일

#### 초급 단계

#### 완료하는 데 약 21시간 필요

#### 영어

### 제공자:

#### 캘리포니아 샌디에고 대학교

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.

#### 국립 연구 고등 경제 대학

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. Learn more on www.hse.ru

## 강의 계획 - 이 강좌에서 배울 내용

**완료하는 데 3시간 필요**

## 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.

**완료하는 데 3시간 필요**

**12개의 동영상**

**4개의 읽기 자료**

**8개 연습문제**

**완료하는 데 3시간 필요**

## 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!

**완료하는 데 3시간 필요**

**8개의 동영상**

**4개의 읽기 자료**

**6개 연습문제**

**완료하는 데 3시간 필요**

## 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.

**완료하는 데 3시간 필요**

**8개의 동영상**

**3개의 읽기 자료**

**8개 연습문제**

**완료하는 데 5시간 필요**

## 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.

**완료하는 데 5시간 필요**

**17개의 동영상**

**4개의 읽기 자료**

**10개 연습문제**

### Combinatorics and Probability의 최상위 리뷰

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.

## Introduction to Discrete Mathematics for Computer Science 전문 분야 정보

## 자주 묻는 질문

Coursera Plus란 무엇이고 환불 규정은 어떻게 되나요?

강의 및 과제를 언제 이용할 수 있게 되나요?

강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

이 전문 분야를 구독하면 무엇을 이용할 수 있나요?

강좌를 등록하면 전문 분야의 모든 강좌에 접근할 수 있고 강좌를 완료하면 수료증을 취득할 수 있습니다. 전자 수료증이 성취도 페이지에 추가되며 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 내용만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

환불 규정은 어떻게 되나요?

재정 지원을 받을 수 있나요?

궁금한 점이 더 있으신가요? 학습자 도움말 센터를 방문해 보세요.