# Introduction to Discrete Mathematics for Computer Science 專項課程

Build a Foundation for Your Career in IT. Master the math powering our lives and prepare for your software engineer or security analyst career

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## 您將獲得的技能

## 關於此 專項課程

## 應用的學習項目

We’ll implement together an efficient program for a problem needed by delivery companies all over the world millions times per day — the travelling salesman problem. The goal in this problem is to visit all the given places as quickly as possible. How to find an optimal solution to this problem quickly? We still don’t have provably efficient algorithms for this difficult computational problem and this is the essence of the P versus NP problem, the most important open question in Computer Science. Still, we’ll implement several efficient solutions for real world instances of the travelling salesman problem. While designing these solutions, we will rely heavily on the material learned in the courses of the specialization: proof techniques, combinatorics, probability, graph theory. We’ll see several examples of using discrete mathematics ideas to get more and more efficient solutions.

無需相關領域的預備知識無需相關經驗。

無需相關領域的預備知識無需相關經驗。

### 此專項課程包含 5 門課程

### 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!

### 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.

## 常見問題

完成专项课程后我会获得大学学分吗？

此专项课程不提供大学学分，但部分大学可能会选择接受专项课程证书作为学分。查看您的合作院校，了解详情。Coursera 上的在线学位和 Mastertrack™ 证书提供获得大学学分的机会。

Can I just enroll in a single course?

如果订阅，您可以获得 7 天免费试听，在此期间，您可以取消课程，无需支付任何罚金。在此之后，我们不会退款，但您可以随时取消订阅。请阅读我们完整的退款政策。

我可以只注册一门课程吗？

可以！点击您感兴趣的课程卡开始注册即可。注册并完成课程后，您可以获得可共享的证书，或者您也可以旁听该课程免费查看课程资料。如果您订阅的课程是某专项课程的一部分，系统会自动为您订阅完整的专项课程。访问您的学生面板，跟踪您的进度。

Can I take the course for free?

是的，Coursera 可以为无法承担费用的学生提供助学金。通过点击左侧“注册”按钮下的“助学金”链接可以申请助学金。您可以根据屏幕提示完成申请，申请获批后会收到通知。您需要针对专项课程中的每一门课程完成上述步骤，包括毕业项目。了解更多。

我可以免费学习课程吗？

完成注册课程后，您可以学习专项课程中的所有课程，并且完成作业后可以获得证书。如果您只想阅读和查看课程内容，可以免费旁听该课程。如果您无法承担课程费用，可以申请助学金。

此课程是 100% 在线学习吗？是否需要现场参加课程？

此课程完全在线学习，无需到教室现场上课。您可以通过网络或移动设备随时随地访问课程视频、阅读材料和作业。

完成专项课程需要多长时间？

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.

Will I earn university credit for completing the Specialization?

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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