Jharkhand University of Technology, Jharkhand, Computer Engineering Semester 4, Discrete Mathematics Syllabus

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Unit - 1 Mathematical Logic

Unit 1

Mathematical Logic

1.1 Introduction Statements and Notation Connectives

1.2 Normal Forms Theory of Inference for the Statement Calculus

1.3 The Predicate Calculus

1.4 Inference Theory of the Predicate Calculus

Unit - 2 Set Theory

Unit 2

Set Theory

2.1 Introduction and basic Concepts of Set Theory

2.2 Representation of Discrete Structures

2.3 Relations and Ordering

2.4 Functions

2.5 Algebraic Structures Introduction

2.6 Algebraic Systems

2.7 Semi Groups and Monoids

2.8 Groups

2.9 Lattices as Partially Ordered Sets

2.10 Boolean Algebra

Unit - 3 Elementary Combinations

Unit 3

Elementary Combinations

3.1 Basic of Counting

3.2 Combinations and Permutations

3.3 Enumeration of Combinations and Permutations

3.4 Enumerating Combinations and Permutations with Repetitions

3.5 Enumerating Permutations with Constrained Repetitions

3.6 Binomial Coefficients The Binomial and MultiNominal Theorems

3.7 The Principle of InclusionExclusion

Unit - 4 Recurrence Relations

Unit 4

Recurrence Relations

4.1 Generating Functions of Sequences

4.2 Calculating Coefficients of Generating Functions

4.3 Recurrence relations

4.4 Solving Recurrence Relations by Substitution and Generating Functions

4.5 The Method of Characteristic Roots

4.6 Solutions of Inhomogeneous Recurrence Relations

Unit - 5 Graphs And Trees

Unit 5

Graphs and Trees

5.1 Basic Concepts

5.2 Isomorphisms and Subgraphs

5.3 Trees and Their Properties

5.4 Spanning Trees

5.5 Binary Trees

5.6 Planar Graphs

5.7 Euler’s Formula

5.8 Multigraphs and Euler Circuits

5.9 HamiltonianGraphs

5.10 Chromatic Numbers and the FourColor Problem

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Other Subjects of Semester-2
Operating system
Database management systems
Formal language and automata theory
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