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PROGRAM CORE
Credit hour : 3
Synopsis
Discrete Mathematics is a field of study integral to the Computer Sciences. It lays the foundations for mathematical thinking in its coverage of proofs. This course focus on the introduction to the primary themes in discrete mathematics. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. The course includes topics such as logic, proof types, and proof-writing. The course coverage will provide students with a solid understanding of the mathematics for computer science as it relates to their immediate field of study.
Course Content
Topic 1: The Foundations: Logic & Proof
Proposition Logic
Propositional Equivalences
Predicates and Quantifies
Nested Quantifiers
Rules of Inference
Boolean Functions
Logic Gates
Topic 2: Basic Structures: Set, Functions, Sequences, Sums and Matrices
Sets and Sets Operation
Functions (surjections, injections, bijections, inverse, composition)
Sequence and Summations
Cardinality of Sets
Relations (Reflexivity, symmetry, transitivity, equivalence relations, partial orders)
Matrices
Topic 3: Proof, induction and recursion
Introduction to Proofs
Proof Methods and Strategy
Mathematical Induction and Well-ordering
Recursive Definition and Structural Induction
Recursive Algorithms
Topic 4 : Graph
Graph and Graph Models
Graph Terminology and Special Types of Graphs
Representating Graphs and Graph Isomorphism
Connectivity
Eular and Hamilton Path
Shortest-path Problems
Planar Graphs
Graph Colorings
Topic 5: Trees
Introduction to Trees
Application of Trees
Trees Traversal
Spanning Trees
Minimum Spanning Trees
References
Kenneth H. Rosen.Discrete Mathematics and Its Applications 8th Edition McGraw Hill; 8th edition (July 9, 2018)
Oscar Levin. Discrete Mathematics: An Open Introduction 3rd Edition Independently published (December 31, 2018) http://discrete.openmathbooks.org/dmoi3.html
Prepared By :
Amiza
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