Discreet Mathematics

Graphs Theory

A course in computing fundamental provides the mathematical background needed for all subsequent courses in computer science and for all subsequent courses in the many branches of discrete mathematics.

What you’ll learn

• What is the shortest path between two cities using a transportation system?.
• Find the shortest tour that visits each of a group of cities only once and then ends in the starting city..
• How can we represent English sentences so that a computer can reason with them?.
• How can it be proved that a sorting algorithm always correctly sorts a list?.
• Graph Theory.
• Binary Search Trees.
• Graphs and Graph Models.
• Graph Terminology and Special Types of Graphs.
• Representing Graphs and Graph Isomorphism.
• Euler and Hamiltonian Graphs.
• Shortest-Path Problems.
• Planar.
• Graph Coloring.

Course Content

• Overview of Discreet Mathematics –> 1 lecture • 2min.
• Graphs Definition –> 2 lectures • 13min.
• Degrees of Graphs and Adjacency Matrix –> 4 lectures • 55min.
• Graph Isomorphism –> 3 lectures • 1hr.
• Graph Connectivity –> 1 lecture • 15min.
• Euler and Hamilton Circuits –> 2 lectures • 25min.
• Shortest Path –> 2 lectures • 28min.
• Bipartite graph and Graph Colouring –> 2 lectures • 27min.
• Trees –> 4 lectures • 1hr 5min.

Requirements

A course in computing fundamental provides the mathematical background needed for all subsequent courses in computer science and for all subsequent courses in the many branches of discrete mathematics.

• What is the shortest path between two cities using a transportation system?
• Find the shortest tour that visits each of a group of cities only once and then ends in the starting city.
• How can we represent English sentences so that a computer can reason with them?
• How can it be proved that a sorting algorithm always correctly sorts a list?

• Mathematical Reasoning: is the Ability to read, understand, and construct mathematical arguments and proofs.
• Discrete Structures: Is an Abstract mathematical structures that represent objects and the relationships between them. Examples are sets, relations, graphs, trees, and finite state machines.

Applications and Modeling: It is important to appreciate and understand the wide range of applications of the topics in discrete mathematics and develop the ability to develop new models in various domains.

• Concepts from discrete mathematics have not only been used to address problems in computing, but have been applied to solve problems in many areas such as chemistry, biology, linguistics, geography, business, etc.
• Graphs and Graph Models
• Graph Terminology and Special Types of Graphs
• Representing Graphs and Graph Isomorphism
• Connectivity
• Euler and Hamiltonian Graphs
• Shortest-Path Problems
• Planar
• Graph Coloring