Discrete Structure Syllabus - BEX (TU)

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Logic, Induction and Reasoning (12 hours)
1. Proposition and Truth function
2. Propositional Logic
3. Expressing statements in Logic Propositional Logic
4. The predicate Logic
5. Validity
6. Informal Deduction in Predicate Logic
7. Rules of Inference and Proofs
8. Informal Proofs and Formal Proofs
9. Elementary Induction and Complete Induction
10. Methods of Tableaux
11. Consistency and Completeness of the System
Finite State Automata (10 hours)
1. Sequential Circuits and Finite state Machine
2. Finite State Automata
3. Language and Grammars
4. Non‐deterministic Finite State Automata
5. Language and Automata
6. Regular Expression and its characteristics
Recurrence Relation (8 hours)
1. Recursive Definition of Sequences
2. Solution of Linear recurrence relations
3. Solution to Nonlinear Recurrence Relations
4. Application to Algorithm Analysis
Graph Theory (15 hours)
1. Undirected and Directed Graphs
2. Walk Paths, Circuits, Components
3. Connectedness Algorithm
4. Shortest Path Algorithm
5. Bipartite Graphs, Planar Graphs, Regular Graphs
6. Planarity Testing Algorithms
7. Eulerian Graph
8. Hamiltonian Graph
9. Tree as a Directed Graph
10. Binary Tree, Spanning Tree
11. Cut sets and Cut vertices
12. Network Flows, Maxflow and Mincut Theorem
13. Data Structures Representing Trees and Graphs in Computer
14. Network Application of Trees and Graphs
15. Concept of Graph Coloring

Kenth Rosen, “Discrete Mathematical Structures with Applications to Computer Science”, WCB/ McGraw Hill
G. Birkhoff, T.C. Bartee, “Modern Applied Algebra”, CBS Publishers
R. Johnsonbaugh, “Discrete Mathematics”, Prentice Hall Inc.
G.Chartand, B.R.Oller Mann, “Applied and Algorithmic Graph Theory”, McGraw Hill
Joe L. Mott, Abrahan Kandel, and Theodore P. Baker, “Discrete
Mathematics for Computer Scientists and Mathematicians”, Prentice‐Hall of India

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