關於此 專項課程

28,913

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.

立即開始，按照自己的計劃學習。

設置並保持靈活的截止日期。

建議 12 小時/週

字幕：英語（English）, 希臘語, 中文（簡體）

Apply basic algorithmic techniques such as greedy algorithms, binary search, sorting and dynamic programming to solve programming challenges.

Apply various data structures such as stack, queue, hash table, priority queue, binary search tree, graph and string to solve programming challenges.

Apply graph and string algorithms to solve real-world challenges: finding shortest paths on huge maps and assembling genomes from millions of pieces.

Solve complex programming challenges using advanced techniques: maximum flow, linear programming, approximate algorithms, SAT-solvers, streaming.

Graph TheoryNumber TheoryCryptographyProbability

立即開始，按照自己的計劃學習。

設置並保持靈活的截止日期。

建議 12 小時/週

字幕：英語（English）, 希臘語, 中文（簡體）

Coursera 專項課程是幫助您掌握一門技能的一系列課程。若要開始學習，請直接註冊專項課程，或預覽專項課程並選擇您要首先開始學習的課程。當您訂閱專項課程的部分課程時，您將自動訂閱整個專項課程。您可以只完成一門課程，您可以隨時暫停學習或結束訂閱。訪問您的學生面板，跟踪您的課程註冊情況和進度。

每個專項課程都包括實踐項目。您需要成功完成這個（些）項目才能完成專項課程並獲得證書。如果專項課程中包括單獨的實踐項目課程，則需要在開始之前完成其他所有課程。

在結束每門課程並完成實踐項目之後，您會獲得一個證書，您可以向您的潛在雇主展示該證書並在您的職業社交網絡中分享。

4.4

（472 個評分）

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?
In the course, we use a try-this-before-we-explain-everything approach: you will be solving many interactive (and mobile friendly) puzzles that were carefully designed to allow you to invent many of the important ideas and concepts yourself.
Prerequisites:
1. We assume only basic math (e.g., we expect you to know what is a square or how to add fractions), common sense and curiosity.
2. Basic programming knowledge is necessary as some quizzes require programming in Python....

4.6

（235 個評分）

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....

4.6

（224 個評分）

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.
In this course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible!
By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics.
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....

4.6

（135 個評分）

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!
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....

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....

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...

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完成专项课程需要多长时间？

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.

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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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