We will mainly concentrate in this course on the graphs of social networks. The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis. So here, you can see a map of Konigsberg. We will illustrate new knowledge, for example, by counting the number of features in data or by estimating the time required for a Python program to run. And the problem here is to tell whether we will have enough plates for everyone. Can you tell how many blue circles do you have in this picture without just counting them by hand? All Categories Anthropology Biology Business Chemistry Communication Computer Economics Education English Finance Foreign Language Geography Geology Health History Human Services Math Medical Philosophy Professional Psychology Thanks to all the professors, teachers, staffs and coordinators for making this course so interesting. You signed in with another tab or window. And the goal here is to tell how many objects do we have without actually counting them by hand. So in this state and we will have some objects. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. Here is another real life example we will discuss later in this course. To view this video please enable JavaScript, and consider upgrading to a web browser that We will illustrate new knowledge, for example, by counting the number of features in data or by estimating the time required for a Python program to run. And the model gives us a prediction, will the customer like our product? Let's count, how many edges come to A? We have 12 options for each letter, and the reason for this is the following. Our goals for probability section in this course will be to give initial flavor of this field. We will solve this problem later in this course. Thank you. We use essential cookies to perform essential website functions, e.g. So there is no way to visit each bridge exactly once. Very informative and practical. So a Euler path is a path in the graph. If nothing happens, download GitHub Desktop and try again. In the cyclic case, we cannot have any odd vertices. This gives us a contradiction. So it turns out that it is not always a trivial task, and there are many important ideas on how to count. But wait, the number of bridges which is adjacent to A is five, and five is an odd number. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. Well, if they coincide, then there should be one vertex and it should be even. Is it possible that there's exactly one odd vertex in a graph? [MUSIC], To view this video please enable JavaScript, and consider upgrading to a web browser that. Well, we can also take D, it has the same property. Coursera_Introduction-to-Discrete-Mathematics-for-Computer-Science, download the GitHub extension for Visual Studio. So the question is whether it is possible. And from these objects, we will get some features, and this will constitute our data. The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis. It has this Euler property, that each edge should be visited exactly once. Coursera and edX Assignments. The letters must look like similar to Latin letters, and Cyrillic letters like those that are depicted on the slides are not allowed. Probability is everywhere in Data Analysis and we will study it in much more details later. Suppose we need to count certain objects. On this license plate we have three digits, we have three letters. So now, we formulate our results. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. Repository for Coursera class Algorithm I & II by Princeton University. Well, a path through the graph is a sequence of vertices which are connected by edges. The course has helped me grasp some important topics. So suppose we can traverse this graph, we can make a path such that each bridge is visited exactly once. Especially enjoyed learning the theory and Python practical in chunks and then bringing them together for the final assignment. Do we need to create a list of all our data entries to check whether we have enough data to teach our ML model? Now, it is a city of Kaliningrad in Russia, from the times of Euler. Video created by National Research University Higher School of Economics for the course "Discrete Math and Analyzing Social Graphs". 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. Thanks to all the professors, teachers, staffs and coordinators for making this course so interesting. It is a Euler path which starts and ends at the same vertex. Use Git or checkout with SVN using the web URL. CP = Combinatorics and Probability IGT = Introduction to Graph Theory NTC = Number Theory and Cryptography DP = Delivery Problem Traveling Salesman problem Now, we have to move to formal definitions. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. The course has helped me grasp some important topics. We have 10 options for each digit. Let us elaborate on this last example. 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