(Ebook) Discrete mathematics structures 1st Edition by G Shankar Rao ISBN 9788122426694 8122426697

(Ebook) Discrete mathematics structures 1st Edition by G Shankar Rao ISBN 9788122426694 8122426697

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ISBN 10: 8122426697
ISBN 13: 9788122426694
Author: G Shankar Rao

(Ebook) Discrete mathematics structures 1st Edition Table of contents:

1.3 Laws of Formal Logic
1.4 Connectives and Compound Statements
1.6 Solved Examples
Exercise 1.1
1.7 Conditional Statements
1.8 Well Formed Formulas
1.13 Solved Examples
1.14 Laws of Logic
1.16 Solved Examples
1.17 Logical Implication
1.18 Other Connectives
1.19 Normal Forms
Exercise 1.2
1.20 Solved Examples
Exercise 1.3
1.21 Quantifiers
1.22 Methods of Proof
Exercise 1.4

2.2 Sets and Operations on Sets
2.3 Subsets
2.5 Singleton
2.10 Disjoints Sets
2.13 Properties of Union Operations
2.15 Properties of Intersection Operation
2.16 Distributive Laws
2.18 Properties of Complementation
2.19 Properties of Difference
2.21 Properties of Symmetric Difference
2.22 Venn Diagrams
Exercise 2.1
2.25 Sets of Numbers
2.26 Cardinality
2.27 Cartesian Product of Sets
Exercise 2.2

3.1 Concept of Relation
3.2 Properties of Relations
3.3 Miscellaneous Examples
3.7 Universal Relation
3.10 Equivalence Classes
3.12 Tabular Form of a Relation
3.14 Transitive Closure
3.15 Matrix Representation of Relations
3.16 Relations and Digraphs
3.17 Composition of Relations
Exercise 3.1

4.2 Function
4.3 One-to-One Mapping (Injection One-to-One Function)
4.7 Composition of Functions
4.10 Inverse Mapping
4.12 Solved Examples
Exercise 4.1
4.13 Recursion and Recurrence Relations
4.14 Recurrence Relations and Solutions of Recurrence Relations
4.15 Generating Functions
4.16 Solution of Non-Homogeneous Linear Recurrence Relations
Exercise 4.3

5.3 Totally Ordered Set
5.5 Hasse Diagram
5.6 Lexicographic Ordering
5.8 Least and Greatest Elements
5.9 Minimal and Maximal Elements (Members)
5.10 Upper and Lower Bounds
5.13 Choice Functions
5.16 Lattices
5.17 Some Properties of Lattices
5.19 Bounded Lattices
5.20 Sub Lattices, Direct Products
Exercise 5.1
5.21 Boolean Algebra
5.22 Sub-Boolean Algebra
5.25 Atoms of Boolean Algebra
5.26 Boolean Expressions and Minimization of Boolean Functions
5.27 Minimization of Boolean Expressions
Exercise 5.2

6.1 Introduction
6.2 Gates and Boolean Algebra
6.3 Applications
6.4 Special Sequences
Exercise 6.1

7.2 Basics of Counting
Exercise 7.1
7.3 Permutations and Combinations
7.4 Solved Examples
7.5 Permutations with Like Elements
7.6 Circular Permutations
Exercise 7.2
7.7 Combinations
7.8 Power Set
7.9 Basic Identities
7.10 Partition and Cross Partitions
7.11 Permutations and Combinations with Unlimited Repetitions
Exercise 7.3
7.12 The Pigeonhole Principle
7.13 Binomial Theorem
7.14 Solved Examples
7.15 Multinomial Theorem
Exercise 7.5

8.2 Basic Definitions
8.3 Incidence and Degree
8.5 Size of a Graph
8.6 Solved Examples
Exercise 8.1
8.8 Adjacency
8.9 Matrix Representation of Graphs
8.10 Linked Representation (or Adjacency Structure)
8.11 The Cycle Matrix
8.12 Path Matrix
Exercise 8.2
8.13 Walks, Paths and Circuits
8.14 Subgraphs
8.15 Removal of Vertices and Edges from a Graph
8.17 Operations on Graphs
8.18 Complement of a Graph
8.19 Connected Graph
8.20 Partitions
8.23 Wheel Graph
8.24 Bipartite Graph
8.25 Solved Examples
8.26 Isomorphism
8.27 Solved Examples
Exercise 8.3
8.28 Forest
8.31 Cut Set
8.33 Labeled and Weighted Graphs
8.34 Connectivity
8.35 Trees and Some Properties of Trees
8.36 Distance
8.37 Spanning Tree
8.38 Rooted Tree
8.40 Binary Tree
8.41 Solved Examples
8.43 High Balanced Binary Tree
8.45 Distance between Spanning Trees of a Graph
8.47 Rank and Nullity
8.48 Planar Graphs
8.49 Homeomorphic Graphs
8.50 Dual of a Graph
8.51 Solved Examples
Exercise 8.6
8.52 Euler’s Graphs
Exercise 8.7
8.53 Hamiltonian Graphs
Exercise 8.8
8.54 Graph Colouring
Exercise 8.9
8.55 Digraphs
8.56 Relations and Digraphs
8.57 Arborescence
8.58 Warshall’s Algorithm
Exercise 8.10

9.3 General Properties
Exercise 9.1
9.5 Algebraic Structures (Algebraic Systems)
9.7 Homomorphism of Semi-Groups
9.9 Monoid
9.11 Groups
9.12 Solved Examples
9.13 Addition Modulo m
9.14 Multiplication Modulo P
9.16 Congruences
Exercise 9.2
9.17 Elementary Properties of Groups
9.18 Alternative Postulates for a Group
9.19 Order of an Element
9.20 Sub-Group
9.22 Cosets
9.23 Index of a Sub-Group
Exercise 9.3
9.24 Isomorphism
9.25 Properties of Isomorphism
9.26 Cyclic Groups
Exercise 9.4
9.27 Normal Sub-Groups
9.28 Permutation Groups
9.29 Cyclic Permutation
9.30 Group Homomorphism
9.31 Kernel of a Homomorphism
9.32 Solved Examples
Exercise 9.5
9.33 Algebraic System with Two Binary Operations
9.34 Special Types of Rings
9.35 Properties of Rings
9.37 Coefficients and Exponents
Exercise 9.6

10.1 Introduction
10.2 Transition Table
10.3 Transition Diagram (State Diagram)
10.4 Finite State Machine (Alternative Definition)
10.5 Equivalence of Finite State Machines
10.6 Covering
10.7 Finite State Homomorphism
Exercise 10.1
10.8 Formal Language, Grammar
10.9 Finite Automata
Exercise 10.2
10.10 Non-Deterministic Finite Automaton (NDFA)
10.11 Finite Automata with Outputs

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