SE CSE SEM 3 – DISCRETE STRUCTURES & GRAPH THEORY

Module 1 – Logic
5 Topics
1.1 Propositional Logic, Predicate Logic
1.2 Laws of Logic
1.3 Quantifiers, Normal Forms
1.4 Inference Theory of Predicate Calculus
1.5 Mathematical Induction
Module 2 – Relations & Functions
8 Topics
2.1 Basic concepts of Set Theory
2.2.a Relations – Definition, Types of Relations, Representation of Relations
2.2.b Relations – Closures of Relations
2.2.c Relations – Warshall’s algorithm
2.2.d Relations – Equivalence relations and Equivalence Classes
2.3.a Functions – Definition, Types of functions
2.3.b Functions – Composition of function
2.3.c Functions – Identity and Inverse function
Module 3 – Possets & Lattice
5 Topics
3.1 Partial Order Relations, Poset
3.2 Hasse Diagram
3.3 Chain and Anti chains
3.4 Lattice, Types of Lattice
3.5 Sub lattice
Module 4 – Counting
5 Topics
4.1.a Basic Counting Principle-Sum Rule, Product rule
4.1.b Inclusion-Exclusion Principle
4.1.c Pigeonhole Principle
4.2.a Recurrence relations
4.2.b Solving recurrence relations
Module 5 – Algebric Sructures
8 Topics
5.1.a Algebraic structures with one binary operation – Semi group, Monoid
5.1.b Algebraic structures with one binary operation – Groups, Subgroups
5.1.c Algebraic structures with one binary operation – Cyclic group
5.1.d Algebraic structures with one binary operation – Abelian Group
5.1.e Algebraic structures with one binary operation – Isomorphism
5.2 Algebraic structures with two binary operations: Ring
5.3.a Coding Theory – Coding, binary information and error detection
5.3.b Coding Theory – Decoding and error correction
Module 6 – Graph Theory
12 Topics
6.1 Types of graphs
6.2 Graph Representation
6.3 Sub- Graph
6.4 Operations on Graphs
6.5 Walk, Path, Circuit
6.6 Connected Graphs, Disconnected Graph
6.7 Components
6.8 Homomorphism and Isomorphism of Graphs
6.9 Euler and Hamiltonian Graphs
7 Planar Graphs
7.1 Cut Set, Cut Vertex
7.2 Applications of graphs
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5.1.e Algebraic structures with one binary operation – Isomorphism

SE CSE SEM 3 – DISCRETE STRUCTURES & GRAPH THEORY Module 5 – Algebric Sructures 5.1.e Algebraic structures with one binary operation – Isomorphism
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