supports HTML5 video. supports HTML5 video. For example, yeah, suppose we are producing some product, and we are interested in whether customers will like our product. Is it possible that there's exactly one odd vertex in a graph? So if there exists a Euler path, then the graph has at most two odd vertices. Graphs represent objects and relations between them in a compact geometric form. So here, you can see a map of Konigsberg. Next, we will apply our knowledge in combinatorics to study basic Probability Theory. This means that actually, we can think it has no start and no end. Counting is one of the most basic tasks related to mathematics. For example, for us the following applications will be important. We will provide you with relevant notions from the graph theory, illustrate them on the graphs of social networks and will study their basic properties. The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis. And how much data you need to teach a model? CP = Combinatorics and Probability IGT = Introduction to Graph Theory NTC = Number Theory and Cryptography DP = Delivery Problem Traveling Salesman problem The letters must look like similar to Latin letters, and Cyrillic letters like those that are depicted on the slides are not allowed. Finally, we will study the combinatorial structure that is the most relevant for Data Analysis, namely graphs. So suppose we can traverse this graph, we can make a path such that each bridge is visited exactly once. Probability is everywhere in Data Analysis and we will study it in much more details later. So again, we start with a path, we find out that inner vertex, any vertex we visit in the middle should be even, it should not be odd, and at most, through this is the start and the end. We will mainly concentrate in this course on the graphs of social networks. To view this video please enable JavaScript, and consider upgrading to a web browser that Topological Sorting. So there is a specific kind of Euler path which is called the Euler cycle. The Euler path is a specific path which visits each edge exactly once. During this week, we introduce basic notions of graph theory and discuss basic algorithms on graphs. Our goals for probability section in this course will be to give initial flavor of this field. So here city areas, this is islands and banks of the river are represented as vertices, we have four vertices in the graph. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. So at each visit, we'll use two bridges. Video created by National Research University Higher School of Economics for the course "Discrete Math and Analyzing Social Graphs". 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. [Coursera] Introduction to Discrete Mathematics for Computer Science Specialization Topics coursera discrete-mathematics graph-theory combinatorics probability number-theory cryptography coursera-discrete-mathematics So objects will be our customers. In this module we will give an introduction to this field that will help us to answer basic versions of the above questions. All these questions are addressed by a mathematical field called Combinatorics. Suppose we need to count certain objects. It is a Euler path which starts and ends at the same vertex. Is there a way to tell whether our algorithm will run in a reasonable time before implementing and actually running it? Well, if they coincide, then there should be one vertex and it should be even. And then features will be some some properties of customers, maybe residential area, car model, phone model, and so on. Learn more. Coursera_Introduction-to-Discrete-Mathematics-for-Computer-Science, download the GitHub extension for Visual Studio. And here is two example. We will solve this problem later in this course. Graphs can be found everywhere around us and we will provide you with numerous examples. 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. Now, we have to move to formal definitions. So why do we need counting here? In the cyclic case, we cannot have any odd vertices. We use one as an entrance to A, and the other one as an exit. So it turns out that it is not always a trivial task, and there are many important ideas on how to count. Can you tell how many blue circles do you have in this picture without just counting them by hand? We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. You can always update your selection by clicking Cookie Preferences at the bottom of the page. Thank you. Counting is the first task that children study when we start to learn mathematics. And 78 on the right is a regional code. Discrete Math and Analyzing Social Graphs, National Research University Higher School of Economics, Mathematics for Data Science Specialization, Construction Engineering and Management Certificate, Machine Learning for Analytics Certificate, Innovation Management & Entrepreneurship Certificate, Sustainabaility and Development Certificate, Spatial Data Analysis and Visualization Certificate, Master's of Innovation & Entrepreneurship. Â© 2020 Coursera Inc. All rights reserved. So the number of bridges which are adjacent to A should be 2k. You can see that we have four parts of the city. The quiz and programming homework is belong to coursera and edx and solutions to me. Bridges are represented by edges, there are seven edges. The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis. We will provide you with relevant notions from the graph theory, illustrate them on the graphs of social … Counting is the first mathematically related task that humanity encountered, but why do we need to study counting? In the end of the course we will have a project related to social network graphs. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. On this license plate we have three digits, we have three letters. Here is another real life example we will discuss later in this course. We will provide you with relevant notions from the graph theory, illustrate them on the graphs of social networks and will study their basic properties. Especially enjoyed learning the theory and Python practical in chunks and then bringing them together for the final assignment. We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. We will mainly concentrate in this course on the graphs of social networks. Graphs can be found everywhere around us and we will provide you with numerous examples. In the end of the course we will have a project related to social network graphs. Learn more. Do we need to create a list of all our data entries to check whether we have enough data to teach our ML model? Suppose that our vertex is visited during our tour say k times, k is a natural number. We use essential cookies to perform essential website functions, e.g. As the third definition is technical, we call a vertex odd if it has an odd number of edges adjacent to it. This repository is aimed to help Coursera learners who have difficulties in their learning process. Coursera Assignments. This gives us a contradiction. Offered by National Research University Higher School of Economics. We'll talk about different types of cycles, and we'll start with a well-known quiz by Euler from the Ancient Center, which is called, The Problem of The Seven Bridges of Konigsberg. Suppose that our tour starts at B and end at C. Now, A is a vertex which was visited in the middle. We have 12 options for each letter, and the reason for this is the following.

Holmes Junior High School, Buying A House When One Spouse Has Bad Credit, Navdeep Singh Virk Wiki, Grand Jury Meaning In Tamil, Last Minute Sub Plans, Pears With Ginger And Honey, Carbon Tax Waiver Upsc, Task-based Language Learning Willis, Anime Sword Girl Wallpaper,