Fundamentals of Graph Theory and Rook Polynomials for AI
What you'll learn
- You will learn about Properties of Trees in Graph Theory
- Applications of Trees in Graph Theory such as Sorting is also shown
- You will learn about Binary Trees in Graph Theory
- Properties of Binary Trees in Discrete Mathematics is also shown
- Learn what are Rook polynomials and how to calculate them
- Rook Polynomials-The Journey Continues
- Learn the basics of Generating Functions
Requirements
- Any course requirements?
- A basic knowledge of graph theory . You can refer to my course" Beginner's guide to Graph theory" if you want.
Description
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.
Who this course is for:
- Who will benefit from taking this course?
- College Mathematics Course -College students would benefit from this.
- College Discrete Mathematics Course-Students learning Discrete Math would benefit.
- College Mathematics examples-Student wanting solutions to Properties of Trees in Graph Theory
- College Mathematics help- Anyone wanting help in understanding a Tree in Graph Theory
Instructor
- 3.9 Instructor Rating
- 16 Reviews
- 3,197 Students
- 18 Courses
I have been a mathematics educator for over 25 years teaching mathematics both at the high school and graduate level. Presenting a set of courses on Class 11 and 12 maths and College maths.
These courses are designed to help you understand the basic nuances of Mathematics. Each topic in mathematics is like a language which makes sense, only if it is understood. My mission in each of these courses is to help any student understand the subject better and develop a liking for Mathematics.
The courses are self explanatory. A lot of importance is given to problem solving
You can contact me for any feedback about course topics. I would love to hear from you!