Introduction to Graph Theory

开始时间: 08/01/2020 持续时间: Unknown

所在平台: Coursera

课程类别: 计算机科学

大学或机构: CourseraNew



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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. Do you have technical problems? Write to us:

图论概论:我们邀请您参加图论的迷人之旅,该领域将绘画的优雅与数学的严谨联系在一起;很简单,但并不简单。图论不仅为我们提供了一种以图形方式表示许多主要数学结果的简便方法,还为我们提供了深入了解其背后的深层理论的能力。 在本课程中,除其他有趣的应用程序外,我们还将了解GPS系统如何找到最短路径,工程师如何设计集成电路,生物学家如何组装基因组,为什么政治地图总是可以使用几种颜色进行着色。我们将研究拉姆西理论,该理论证明在大系统中,完全的混乱是不可能的! 在课程结束时,我们将实现一种算法,该算法可以找到学生到学校的最佳分配。该算法由David Gale和Lloyd S. Shapley开发,后来被诺贝尔经济学奖授予。 作为前提条件,我们仅假设基本数学(例如,我们希望您知道什么是平方或如何添加分数),Python中的基本编程(函数,循环,递归),常识和好奇心。我们的目标受众是所有有志或计划在IT领域工作的人,从积极进取的高中生开始。 你有技术上的问题吗?写信给我们


What are graphs? What do we need them for? This week we'll see that a graph is a simple pictorial way to represent almost any relations between objects. We'll see that we use graph applications daily! We'll learn what graphs are, when and how to use them, how to draw graphs, and we'll also see the most important graph classes. We start off with two interactive puzzles. While they may be hard, they demonstrate the power of graph theory very well! If you don't find these puzzles easy, please see the videos and reading materials after them.





We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of pa


离散数学 数学 数学基础 离散数学公开课 离散数学课程 图论 计算机科学 图论导论