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CH 00

The document outlines the syllabus for a Discrete Mathematics course, detailing evaluation criteria, course objectives, and content topics. Key topics include graph theory, algorithms for searching and finding paths, spanning trees, network flow, and graph coloring. The course aims to equip students with practical skills in discrete mathematics applicable to Information Technology and Telecommunications.

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nguyenducdung1112005
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13 views7 pages

CH 00

The document outlines the syllabus for a Discrete Mathematics course, detailing evaluation criteria, course objectives, and content topics. Key topics include graph theory, algorithms for searching and finding paths, spanning trees, network flow, and graph coloring. The course aims to equip students with practical skills in discrete mathematics applicable to Information Technology and Telecommunications.

Uploaded by

nguyenducdung1112005
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Discrete Mathematics 2

Introductory Lecture
Trong-Thua Huynh, PhD. – htthua@ptithcm.edu.vn
Updated on Dec 31, 2024
Evaluation
• Attendance: 10%
• Assignment/Exer + Midterm test: 30%
– Class assignments: 15% (grading for assigns/excers,
default is 3 points)
– Midterm-Test: 15%
• Final exam: 60%
• Exam Disallowance: no component score or
absence for 4 or more classes.

2
Course Objectives
• Knowledge of discrete and applied mathematics in the
Information Technology, Telecommunications
• Thereby, students have to implement algorithms of
methods on computer systems according to specific
applications
• To study well in this subject, students must know how to
combine theory and practice
Content (1/3)
1. The Concept of Graphs
▪ Graph definition
▪ Basic terms on undirected graphs
▪ Basic terms on directed graphs
▪ Some special types of graphs
2. Represent the graph on Computer
▪ Represent the graph with the adjacency matrix
▪ Represent the graph using a vertex-edge membership matrix
▪ Representing a graph using an edge list
▪ Representing a graph using an adjacency list
3. Searching on the Graph
▪ Depth First Search (DFS)
▪ Breadth First Search (BFS)
▪ Applications of DFS and BFS
4
Content (2/3)
4. Euler Graph and Hamilton Graph
▪ Eulerian graph
▪ Find Euler's cycle
▪ Hamiltonian graph
▪ Find the Hamiltonian cycle
▪ Some practical problems
5. Spanning Tree of Graphs
▪ Tree and its properties
▪ Some special trees
▪ Tree traversals
▪ Applying trees to encode information
▪ Construct the spanning tree
▪ Minimum spanning tree problem
▪ Algorithms to find the minimum spanning tree
5
Content (3/3)
6. Finding the shortest path
▪ Problem statement
▪ Dijkstra's algorithm
▪ Bellman-Ford Algorithm
▪ Floyd's algorithm
7. Network and Flow
▪ Definitions
▪ Maximum flow problem
▪ Ford-Fulkerson algorithm to find the maximum flow
8. Graph Coloring
▪ Stable set of graph
▪ The chromatic number (sắc số) of the graph
▪ Coloring problem

6
References
1. Kenneth H. Rossen, Discrete Mathematics And Its Applications 8th Edition, Mcgraw
Hill, 2018
2. Susanna S. Epp, Discrete Mathematics With Applications, 5th Edition, Cengage
Learning, 2019
3. Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd Edition, 2021

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