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.

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## 이 전문 분야 정보

### 귀하가 습득할 기술

#### 100% 온라인 강좌

#### 유동적 일정

#### 초급 단계

#### 완료하는 데 약 3개월 필요

#### 영어

### 전문분야 이용 방법

### 강좌 수강

Coursera 특화 과정은 한 가지 기술을 완벽하게 습득하는 데 도움이 되는 일련의 강좌입니다. 시작하려면 특화 과정에 직접 등록하거나 강좌를 둘러보고 원하는 강좌를 선택하세요. 특화 과정에 속하는 강좌에 등록하면 해당 특화 과정 전체에 자동으로 등록됩니다. 단 하나의 강좌만 수료할 수도 있으며, 학습을 일시 중지하거나 언제든 구독을 종료할 수 있습니다. 학습자 대시보드를 방문하여 강좌 등록 상태와 진도를 추적해 보세요.

### 실습 프로젝트

모든 특화 과정에는 실습 프로젝트가 포함되어 있습니다. 특화 과정을 완료하고 수료증을 받으려면 프로젝트를 성공적으로 마쳐야 합니다. 특화 과정에 별도의 실습 프로젝트 강좌가 포함되어 있는 경우, 다른 모든 강좌를 완료해야 프로젝트 강좌를 시작할 수 있습니다.

### 수료증 취득

모든 강좌를 마치고 실습 프로젝트를 완료하면 취업할 때나 전문가 네트워크에 진입할 때 제시할 수 있는 수료증을 취득할 수 있습니다.

### 이 전문 분야에는 5개의 강좌가 있습니다.

### Mathematical Thinking in Computer Science

Mathematical thinking is crucial in all areas of computer science: algorithms, bioinformatics, computer graphics, data science, machine learning, etc. In this course, we will learn the most important tools used in discrete mathematics: induction, recursion, logic, invariants, examples, optimality. We will use these tools to answer typical programming questions like: How can we be certain a solution exists? Am I sure my program computes the optimal answer? Do each of these objects meet the given requirements?

### Combinatorics and Probability

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.

### Introduction to Graph Theory

We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them.

### Number Theory and Cryptography

We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about numbers’ properties for thousands of years. And for thousands of years it was more or less just a game that was only interesting for pure mathematicians. Famous 20th century mathematician G.H. Hardy once said “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the word nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this short course, we will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest!

### 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.

### 검토

#### 4.6

##### INTRODUCTION TO DISCRETE MATHEMATICS FOR COMPUTER SCIENCE의 최상위 리뷰

This final course in 5 course specialization is relatively easy one, although the last problem takes little bit time to solve. Provides good introduction to difficult to learn Delivery problem.

A fun conclusion to the specialization that brings all of the mathematics of combinatorics and graph theory together to show how it can be applied to some real world problems.

The teachers are informative and good. They explain the topic in a way that we can easily understand. The slides provide all the information that is needed. The external tools are fun and informative.

Appreciate the structure and the explanations with examples. The practice tool before every lesson not makes it fun to learn but also sets the student in the context and can anticipate the concept.

Was pretty fun and gave a good intro to graph theory. Definitely felt inspired to go deeper and understood the most basic proof ideas. The later lectures can spike in difficulty though. Very nice!

I applaud the instructors for their efforts in explaining the concepts as they could be abstract and hard to explain in words! More examples to illustrate the concepts will be even more helpful!

I loved this course! So many interesting things to think about, thoughtfully explained by brilliant instructors. The puzzles really get you thinking. Such genius to put them before the lectures!

Contents are very good for starting.....\n\nBut the Teachers way of explaining is not up to the mark. I need to search in youTube or google for understanding any topic even watching the videos.

## 자주 묻는 질문

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하나의 강좌에만 등록할 수 있나요?

네! 시작하려면 관심 있는 강좌 카드를 클릭하여 등록합니다. 강좌를 등록하고 완료하면 공유할 수 있는 인증서를 얻거나 강좌를 청강하여 강좌 자료를 무료로 볼 수 있습니다. 전문 분야 과정에 있는 강좌에 등록하면, 전체 전문 분야에 등록하게 됩니다. 학습자 대시보드에서 진행 사항을 추적할 수 있습니다.

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해당 강좌를 무료로 수강할 수 있나요?

이 강좌는 100% 온라인으로 진행되나요? 직접 참석해야 하는 수업이 있나요?

이 강좌는 100% 온라인으로 진행되므로 강의실에 직접 참석할 필요가 없습니다. 웹 또는 모바일 장치를 통해 언제 어디서든 강의, 읽기 자료, 과제에 접근할 수 있습니다.

전문 분야를 완료하는 데 얼마나 걸리나요?

Time to completion can vary based on your schedule, but most learners are able to complete the Specialization in 6-8 months.

What background knowledge is necessary?

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 I need to take the courses in a specific order?

We recommend taking the courses in the order presented, as each subsequent course will build on material from previous courses.

전문 분야를 완료하면 대학 학점을 받을 수 있나요?

Coursera courses and certificates don't carry university credit, though some universities may choose to accept Specialization Certificates for credit. Check with your institution to learn more.

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