Introduction to Graph Theory
- Offered byCoursera
- Public/Government Institute
Introduction to Graph Theory at Coursera Overview
Duration | 21 hours |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Beginner |
Official Website | Explore Free Course  |
Credential | Certificate |
- Overview
- Highlights
- Course Details
- Curriculum
Introduction to Graph Theory at Coursera Highlights
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Course 3 of 5 in the Introduction to Discrete Mathematics for Computer Science Specialization
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Beginner Level
- Approx. 21 hours to complete
- English Subtitles: Arabic, French, Portuguese (European), Greek, Italian, Vietnamese, German, Russian, English, Spanish
Introduction to Graph Theory at Coursera Course details
- 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.
Introduction to Graph Theory at Coursera Curriculum
What is a Graph?
Airlines Graph
Knight Transposition
Seven Bridges of Konigsberg
What is a Graph?
Graph Examples
Graph Applications
Vertex Degree
Paths
Connectivity
Directed Graphs
Weighted Graphs
Paths, Cycles and Complete Graphs
Trees
Bipartite Graphs
Slides
Slides
Slides
Slides
Glossary
Puzzle: Guarini's Puzzle
Puzzle: Bridges of Konigsberg
Definitions
Puzzle: Make a tree
Graph Types
CYCLES
Handshaking Lemma
Total Degree
Connected Components
Guarini Puzzle: Code
Lower Bound
The Heaviest Stone
Directed Acyclic Graphs
Strongly Connected Components
Eulerian Cycles
Eulerian Cycles: Criteria
Hamiltonian Cycles
Genome Assembly
Slides
Slides
Slides
Glossary
Puzzle: Connect Points by Segments
Computing the Number of Edges
Number of Connected Components
Number of Strongly Connected Components
Eulerian Cycles
Puzzle: Plow Truck
Puzzle: Hamiltonian Cycle
Graph Classes
Road Repair
Trees
Minimum Spanning Tree
Job Assignment
Bipartite Graphs
Matchings
Hall's Theorem
Subway Lines
Planar Graphs
Euler's Formula
Applications of Euler's Formula
Slides
Slides
Slides
Glossary
Puzzle: Road Repair
Trees
Puzzle: Job Assignment
Bipartite Graphs
Puzzle: Subway Lines
Planar Graphs
Graph Parameters
Map Coloring
Graph Coloring
Bounds on the Chromatic Number
Applications
Graph Cliques
Cliques and Independent Sets
Connections to Coloring
Mantel's Theorem
Balanced Graphs
Ramsey Numbers
Existence of Ramsey Numbers
Antivirus System
Vertex Covers
Konig's Theorem
Slides
Slides
Slides
Slides
Glossary
Puzzle: Map Coloring
Graph Coloring
Puzzle: Graph Cliques
Cliques and Independent Sets
Puzzle: Balanced Graphs
Ramsey Numbers
Puzzle: Antivirus System
Vertex Covers
Flows and Matchings
An Example
The Framework
Ford and Fulkerson: Proof
Hall's theorem
What Else?
Why Stable Matchings?
Mathematics and Real Life
Basic Examples
Looking For a Stable Matching
Gale-Shapley Algorithm
Correctness Proof
Why The Algorithm Is Unfair
Why the Algorithm is Very Unfair
Slides
Slides
The algorithm and its properties (alternative exposition)
Gale-Shapley Algorithm
Project Description
Glossary
Choose an Augmenting Path Carefully
Constant Degree Bipartite Graphs
Base Cases
Algorithm
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