Graph Theory from Udemy

What is this course about?

Graph Theory is an advanced topic in Mathematics. On a university level, this topic is taken by senior students majoring in Mathematics or Computer Science; however, this course will offer you the opportunity to obtain a solid foundation in Graph Theory in a very short period of time, AND without requiring you to have any advanced Mathematical background.

The course is designed to be understood by a 12th grader since the structure of the course starts with the very basic idea of how to create a Graph, and with each step the ideas get more and more complex. The course consists of several sections and in each section, there are video lectures where I explain a few concepts. There are quizzes (with solutions) after every lecture so you can test what you have learned in that lecture.

The structure of the course goes as following starting with the first section:

Supplements
Fundamentals
Paths
Graphs Types
Trees
Digraphs and Tournaments
Planar Graphs
Graphs Operations
Graph Colorings

YOU WILL ALSO GET:

Lifetime Access
Q&A section with support
Access on mobile and TV
Certificate of completion
30-day money-back guarantee

How are the concepts delivered?

Each lecture is devoted to explaining a concept or multiples concepts related to the topic of that section. There are example(s) after the explanation(s) so you understand the material more. The course is taught in plain English, away from cloudy, complicated mathematical jargon and that is to help the student learn the material rather than getting stuck with fancy words.

How to learn better?

Take notes and repeat the lectures to comprehend the concepts more. Also, there are quizzes after every lecture so you can test what you have learned.

What's inside

Learning objectives

Master fundamental concepts in graph theory
Understand eulerian and hamiltonian paths and circuits. and many related topics to paths.
Get to know a wide range of different graphs, and their properties.
Be able to preform elementary, advanced operations on graphs to produce a new graph

Understand graph coloring.
Know how to turn a graph into a matrix and vice versa.
Obtain a solid foundation in trees, tree traversals, and expression trees.

Master fundamental concepts in graph theory
Understand eulerian and hamiltonian paths and circuits. and many related topics to paths.
Get to know a wide range of different graphs, and their properties.
Be able to preform elementary, advanced operations on graphs to produce a new graph
Understand graph coloring.
Know how to turn a graph into a matrix and vice versa.
Obtain a solid foundation in trees, tree traversals, and expression trees.

Syllabus

Supplements

Course Overview

Textbook Recommendations

Tools

Sets

Number Sets

Parity

Terminologies

Fundamentals

Intro

Graphs

Quiz

Subgraphs

Degree

Sum of Degrees of Vertices Theorem

Adjacency and Incidence

Adjacency Matrix

Incidence Matrix

Isomorphism

Paths

Walks, Trails, Paths, and Circuits

Examples

Eccentricity, Diameter, and Radius

Connectedness

Euler Trails and Circuits

Fleury’s Algorithm

Hamiltonian Paths and Circuits

Ore's Theorem

Dirac's Theorem

The Shortest Path Problem

Graph Types

Trivial, Null and Simple Graphs

Regular Graphs

Complete, Cycles and Cubic Graphs

Path, Wheel and Platonic Graphs

Bipartite Graphs

Trees

Cayley's Theorem

Rooted Trees

Binary Trees

Binary Tree Traversals

Binary Expression Trees

Binary Search Trees

Spanning Trees

Forests

Digraphs and Tournaments

Digraphs

Walks, Paths and Cycles

Tournaments

Planar Graphs

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Examines fundamental principles of Graph Theory highly relevant to Computer Science and Mathematics

Offers a solid foundation in Graph Theory, even for learners without an advanced Mathematical background

Taught by an instructor with experience in Graph Theory

Includes 9 sections with video lectures, and quizzes for assessing understanding

Provides lifetime access and support for Q&A, and a certificate of completion

Does not require any prior advanced Mathematical background knowledge

Reviews summary

Introductory graph theory

Students say that this course provides a neat and concise introduction to graph theory. Though the content is suitable for beginners, some learners wish that there were more examples of real-life applications. However, the material is well received by students and they found it to be a good starting point to graph theory.

Concise intro to graph theory

"Neat and concise."

Few real-life applications

"I wish there would be more examples of applications in real life however."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Graph Theory with these activities:

Review prerequisites for Graph Theory

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Reviewing the essential mathematical concepts covered in the Supplements section of the course will provide a stronger foundation for understanding the more advanced topics.

Browse courses on Sets

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Review the materials on sets, number sets, and parity
Complete the practice problems in the textbook

Solve practice problems on graph fundamentals

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To master the fundamental principles of graph theory, dedicate time to solving practice problems. This activity will reinforce your understanding and prepare you for more advanced topics.

Browse courses on Graphs

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Collect practice problems from the textbook or online resources
Set aside dedicated time to work on solving the problems
Review your solutions and identify any areas where you need further clarification

Follow video tutorials on different types of graphs

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To expand your understanding of various types of graphs, explore video tutorials that provide clear explanations and examples. This will supplement your learning from the course.

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Search for video tutorials on different types of graphs
Select reputable and informative tutorials
Take notes or summarize the key points presented in the tutorials

Four other activities

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Join a study group or online forum for graph theory

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Engaging with a study group or online forum provides opportunities to discuss complex topics, share knowledge, and get support from peers.

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Seek out a study group or online forum dedicated to graph theory
Introduce yourself and engage in discussions
Share your understanding and insights
Ask questions and seek clarification from others

Design a flowchart to represent a given graph

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Creating a flowchart representation of a given graph not only enhances your understanding of the graph structure but also improves your problem-solving and analytical skills.

Browse courses on Flowcharts

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Choose a graph to represent
Identify the nodes and edges of the graph
Use appropriate symbols to represent the nodes and edges in a flowchart
Connect the nodes and edges according to the graph structure

Contribute to open-source graph theory projects

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Contributing to open-source graph theory projects allows you to apply your knowledge practically, collaborate with other developers, and deepen your understanding of advanced graph concepts.

Browse courses on Open Source

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Identify active open-source projects related to graph theory
Choose a project that aligns with your interests and skill level
Review the project documentation and tutorials
Make code contributions or provide feedback to existing discussions

Create a blog post or article on a specific graph theory topic

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Writing a blog post or article allows you to synthesize your knowledge, develop your written communication skills, and share your understanding with a wider audience.

Browse courses on Blogging

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Choose a specific graph theory topic that you want to focus on
Research and gather information from credible sources
Organize your thoughts and create an outline
Write a clear and concise blog post or article

Career center

Learners who complete Graph Theory will develop knowledge and skills that may be useful to these careers:

Data Engineer

A Data Engineer builds and maintains data pipelines and infrastructure. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in data engineering. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and designing data pipelines.

See salaries and explore the career path for Data Engineer

Machine Learning Engineer

A Machine Learning Engineer builds and deploys machine learning models. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in machine learning. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and designing machine learning models.

See salaries and explore the career path for Machine Learning Engineer

Data Scientist

A Data Scientist uses data to solve business problems and improve decision-making. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in data science. Additionally, the course covers topics such as network analysis and machine learning, which are important for understanding and building data science models.

See salaries and explore the career path for Data Scientist

Operations Research Analyst

An Operations Research Analyst uses mathematical and statistical models to solve business problems and improve decision-making. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in operations research. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and solving business problems.

See salaries and explore the career path for Operations Research Analyst

Network Administrator

A Network Administrator manages and maintains computer networks. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in network administration. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and managing computer networks.

See salaries and explore the career path for Network Administrator

Computer Scientist

A Computer Scientist designs, develops, and maintains computer systems. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in computer science. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and designing computer systems.

See salaries and explore the career path for Computer Scientist

Mathematician

A Mathematician uses mathematical models to solve problems and advance knowledge. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in mathematics. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and solving mathematical problems.

See salaries and explore the career path for Mathematician

Financial Analyst

A Financial Analyst uses mathematical and statistical models to analyze financial data and make investment decisions. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in financial analysis. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and managing financial risk.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

A Quantitative Analyst uses mathematical and statistical models to analyze financial data and make investment decisions. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in financial modeling. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and managing financial risk.

See salaries and explore the career path for Quantitative Analyst

Actuary

An Actuary uses mathematical and statistical models to assess and manage risk. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in actuarial science. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and managing risk.

See salaries and explore the career path for Actuary

Statistician

A Statistician uses mathematical and statistical models to analyze data and draw conclusions. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in statistics. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and analyzing data.

See salaries and explore the career path for Statistician

Software Engineer

A Software Engineer designs, develops, and maintains software systems. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in software development. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and designing software systems.

See salaries and explore the career path for Software Engineer

Data Analyst

A Data Analyst gathers, cleans, and interprets data to help organizations understand trends and make informed decisions. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in data analysis. Additionally, the course covers topics such as network analysis and data visualization, which are important for understanding and communicating data.

See salaries and explore the career path for Data Analyst

Business Analyst

A Business Analyst uses data to understand business problems and improve decision-making. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in business analysis. Additionally, the course covers topics such as network analysis and optimization, which are important for understanding and solving business problems.

See salaries and explore the career path for Business Analyst

Market Researcher

A Market Researcher uses data to understand consumer behavior and trends. This course in Graph Theory can be useful in this field, as it provides a foundation in data structures and algorithms that are used in market research. Additionally, the course covers topics such as network analysis and visualization, which are important for understanding and communicating consumer data.

See salaries and explore the career path for Market Researcher