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所在平台: Udemy |
课程主页: https://www.udemy.com/course/properties-of-trees-in-graph-theory-discrete-mathematics/
课程评论：没有评论
## 课程总结：图论与车轮多项式在人工智能中的基础 本课程由数学教育家 Suman Mathews 主讲，旨在为对图论和离散数学感兴趣的学习者提供一个坚实的基础。图论在数据科学和计算机应用领域拥有广泛的应用。 **核心内容概览：** * **树 (Trees) 的入门：** * 课程从树的定义开始，介绍与树相关的概念，如环 (cycle) 和完全图 (complete graph)。 * 深入理解树的定义，即一个连通图，若其有 n 个顶点和 n-1 条边，则它是一棵树。 * 探讨树中顶点数与边数的关系，并给出图论中树的性质证明，例如顶点的度数之和。 * 学习解决与树相关的问题。 * 介绍根树 (rooted trees) 及其性质，包括根 (root)、m-元树 (m-ary tree) 的概念。 * 学习叶子节点 (leaves)、内部顶点 (internal vertices) 与顶点总数之间的关系。 * 学习图论中的二叉树 (binary trees)。 * **算法与概念：** * **归并排序 (Merge-Sort Method):** 学习如何使用归并排序算法对数字进行排序。 * **森林 (Forest):** 将森林定义为树的集合，并探讨如何找到两个树的顶点集之间的关系，这取决于它们的边集基数。 * **悬挂顶点 (pendant vertices):** 学习如何计算给定度数序列的树中悬挂顶点的数量。 * **公式手册：** 课程最后提供一份公式手册。 * **车轮多项式 (Rook Polynomials) 和生成函数 (Generating Functions):** * 学习如何构造基本车轮多项式，涵盖 4x4、5x5、6x6 和 7x7 的棋盘。 * 了解车轮多项式在现实生活中的应用。 * 学习生成函数的基础知识。 **课程价值：** 本课程为学习者提供了图论中“树”这一重要概念的全面介绍，并结合实际应用，如归并排序和车轮多项式。通过深入的概念讲解、性质证明和实际问题解决，学习者将能够掌握这些核心知识，并为进一步探索人工智能和计算机科学领域打下坚实基础。 **强烈推荐您报名参加本课程，与朋友分享，共同学习图论中的精彩内容！**
You are interested in Graph Theory and Discrete Mathematics. Graph Theory has tremendous applications in Data Science and Computer Applications. I am Suman Mathews, math educator and teacher. I have a double master's in Mathematics and have taught Math to college students and High school students. This course will introduce you to trees, a very important part of Graph Theory.The course starts with the definition of trees, a cycle, a complete graph in relation to a tree. You learn that a connected graph with n vertices and n-1 edges is a tree. The relationship between number of vertices and number of edges in a tree is also shown.Properties of a tree in Graph Theory such as sum of the degrees of vertices of a tree are discussed with proof. Problems on a tree are also shown.Rooted trees and it's properties are discussed. What is a root? What is an m-ary tree? You will learn about the relationship between the leaves, internal vertices and number of vertices. Binary trees in Graph Theory is also introduced.The Merge-Sort Method is taught which teaches you to sort numbers.You will be introduced to a Forest as a collection of trees. Given 2 trees, and their edge set cardinality, you will learn how to find a relation between their vertex sets. You'll learn about pendant vertices.If a tree has three vertices of degree two , four vertices of degree three , three vertices of degree four, you will learn how to find the number of pendant vertices in the tree and similar problems.There is a formula handbook at the end. Learn about Rook polynomials and how to construct basic rook polynomials for 4,5,6,7 squares. Also learn how to apply Rook Polynomials in real life situations.Learn the basics of Generating Functions.Enrol for this course and enjoy Trees in Graph Theory. Share this course with your friends who may use this topic.
