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所在平台: Udemy |
课程主页: https://www.udemy.com/course/beginners-guide-to-graph-theory-discrete-mathematics/
课程评论：没有评论
**课程名称：** 图论入门（面向人工智能） **课程概述：** 本课程旨在以简单易懂的方式，帮助学习者掌握图论的基础知识，并了解其在数学、数据科学和计算机科学中的重要性。课程由拥有三十年数学教学经验的Suman Mathews讲授，致力于让数学变得易于理解。 **课程内容简介：** 课程从图论的基本概念入手，介绍顶点（vertices）、边（edges）、连通图（connected graphs）及其相关问题。随后，将深入探讨图中的路径（trails）和回路（circuits）。 接着，课程将讲解图的一些基本性质，例如顶点的度数之和。学习者还将了解二分图（bipartite graphs），特别是完全二分图（complete bipartite graph），并学习如何计算其总边数。课程还将涉及到同构图（isomorphic graphs）的概念及其判断方法。 此外，课程还会介绍顶点的入度和出度（in degree and out degree），以及欧拉图（Eulerian graphs）和欧拉回路（Eulerian circuits）的概念，并教导如何判断一个连通图是否具有欧拉回路或欧拉试验。学习者还将接触到哈密顿图（Hamiltonian graphs）及其相关问题的解决。 课程还将提供对正则图（regular graphs）、图的补集（complement of a graph）、图的并集和交集（union and intersection of a graph）、图的环和（ring sum of a graph）、图的分解（graph decomposition）等概念的概述。顶点和边的标记（labeling）方法也将被详细讲解。 在矩阵表示方面，课程将教授如何写出图的矩阵表示，以及如何理解图的关联矩阵（incidence matrix）和邻接矩阵（adjacency matrix）。 课程还会介绍有向图（Digraphs），以及如何为有向图构造关联矩阵。最后，将学习平面图（planar graphs）和欧拉定理（Euler's Theorem），该定理揭示了顶点、边和区域数量之间的关系。 **核心优势：** * **易于理解：** 课程以简单明了的方式讲解图论概念。 * **广泛适用：** 图论是人工智能、数据科学等领域的重要基础。 * **实践导向：** 鼓励学习者通过练习来加深理解。 **建议：** 为了获得清晰的理解，请务必练习课程中介绍的所有概念。
Graph theory plays an important role in Mathematics, Data Science and Computer Science. This Introductory course on Graph theory will help you understand the basics of Graph theory in an easy manner. I am Suman Mathews, math educator and teacher.Having a teaching experience of three decades in Mathematics, I try to make math easy to understand for all students. The course starts with a basic knowledge of Graph theory and some standard terms such as vertices and edges. You'll learn about connected graphs and solve problems based on these. Learn what are trails or circuits in graphs.Moving on, you'll learn simple properties of graphs, such as the sum of the degrees of the vertices of a graph. You'll also learn what is a complete bipartite graph and how to calculate the total number of edges in it. The course progresses to isomorphic graphs and how to check for isomorphism in graphs.Learn about in degree and out degree of vertices. An important concept which you'll learn next is Eulerian graphs and Eulerian circuits. Learn to determine when a connected graph has an Eulerian circuit or an Eulerian Trial. You'll also learn what are Hamiltonian graphs and how to solve problems on these.You'll get a basic overview of regular graphs, complement of a graph, union and intersection of a graph. Also learn about ring sum of a graph and graph decomposition. Labeling the vertices and edges of a graph is also explained.Learn how to write the Matrix representation of graphs and how to understand the incidence and adjacency matrix of a graph.Also learn what are Digraphs and how to construct the incidence matrix for a digraph. Learn about planar graphs and Euler's Theorem which gives a relation between number of vertices, edges and regions.Get an introduction to Eulerian graphs and it's properties.An easy course for you to learn. Would you care to share this knowledge with other students. Spread the word around!Hope you will be benefited from this course. Note that you need to practice all these to get a clear understanding. Thank you!
