## Book description

Discrete Mathematical Structures provides comprehensive, reasonably rigorous and simple explanation of the concepts with the help of numerous applications from computer science and engineering. Every chapter is equipped with a good number of solved examples that elucidates the definitions and theorems discussed. Chapter-end exercises are graded, with the easier ones in the beginning and then the complex ones, to help students for easy solving.

1. Cover
2. Title Page
3. Contents
4. Dedication
5. Preface
6. Acknowledgements
8. 1. Set Theory
1. 1.1 Introduction
2. 1.2 Sets
3. 1.3 Cartesian Product of Sets
4. 1.4 Multiset
5. Exercises
9. 2. Relations and Digraphs
1. 2.1 Introduction
2. 2.2 Binary Relation
3. 2.3 Equivalence Class
4. 2.4 Partition of a Set
5. 2.5 Congruence Modulo Relation
6. 2.6 Pictorial Representation of Relation
7. 2.7 Digraphs
8. 2.8 Power of Relation
9. 2.9 Paths in Relations and Digraphs
10. 2.10 Matrix Representation of Composite Relations
11. 2.11 Connectivity Relation
12. Exercises
10. 3. Functions
1. 3.1 Introduction
2. 3.2 Definition
3. 3.3 Domain and Range of a Function
4. 3.4 Difference Between Relation and Function
5. 3.5 Different Types of Functions (or Mappings) Constant Function
6. 3.6 Composition of Functions
7. 3.7 Functions for Computer Science
8. 3.8 Some Special Functions Used in Discrete Mathematics
9. 3.9 Some Important Theorems and Problems
10. 3.10 Ackermann’s Function
11. 3.11 Fuzzy Sets
12. 3.12 Time Complexity of Algorithm
13. 3.13 Connectivity Relation
14. Exercise – A
15. Exercise – B
11. 4. Mathematical Logic and Methods of Proofs
1. 4.1 Introduction
2. 4.2 Statement (Proposition)
3. 4.3 Propositional Variables, Simple and Compound Propositions (or Statements)
4. 4.4 Basic Logical Operations
6. 4.6 Logically Equivalent or Equivalent Propositions
7. 4.7 Logical Arguments
8. 4.8 Predicates
9. 4.9 Methods of Proof
10. Exercise – A
11. Exercise – B
12. 5. Combinatorics
1. 5.1 Introduction
2. 5.2 Basic Principle of Counting
3. 5.3 Permutations
4. 5.4 Ordered and Unordered Partitions
5. 5.5 Circular Permutations
6. 5.6 Combinations
7. 5.7 Derangements
8. 5.8 The Pigeonhole Principle
9. 5.9 Elements of Probability
10. 5.10 Multiplication Theorem (Independent Events)
11. 5.11 Baye’s Theorem
12. 5.12 Concept of a Random Variable
13. 5.13 Binomial Distribution
14. 5.14 Poisson Distribution
15. Exercise – A
16. Exercise – B
17. Exercise – C
18. Exercise – D
13. 6. Recurrence Relations and Generating Functions
1. 6.1 Introduction
2. 6.2 Sequences
3. 6.3 Linear Recurrence Relation with Constant Coefficients
4. 6.4 E and Δ Operators Method
5. 6.5 Method of Generating Functions
6. Exercises
14. 7. Algebraic Structures
1. 7.1 Introduction
2. 7.2 Binary Operation
3. 7.3 Algebraic Structures
4. 7.4 Congruences
5. 7.5 Permutations
6. 7.6 Integral Powers of an Element
7. 7.7 Cyclic Group
8. 7.8 Subgroups
9. 7.9 Coset Decomposition
10. 7.10 Isomorphism and Homomorphism of Groups
11. 7.11 Algebraic Systems with Two Binary Operations
12. 7.12 Ring, Subring and Ideals
13. 7.13 Integral Domain
14. 7.14 Field
15. Exercises
15. 8. Ordered Sets and Lattices
1. 8.1 Introduction
2. 8.2 Partially Ordered Set
3. 8.3 Product of Two Posets
4. 8.4 Hasse Diagram
5. 8.5 Lexicographic Ordering
6. 8.6 Upper and Lower Bounds
7. 8.7 Dual of a Poset
8. 8.8 Isomorphism of Posets
9. 8.9 Well-ordered Set
10. 8.10 Properties of Well-ordered Sets
11. 8.11 Lattices
12. 8.12 Lattice in Terms of Algebraic Structures
13. 8.13 Sublattices
14. 8.14 Bounded Lattices
15. 8.15 Duality
16. 8.16 Complete Lattice
17. 8.17 Isomorphic Lattices
18. 8.18 Complimented Lattice
19. 8.19 Chain and Antichain
20. 8.20 Distributive Lattices
21. 8.21 Modular Lattice
22. 8.22 Boolean Lattice
23. Exercises
16. 9. Boolean Algebra
1. 9.1 Introduction
2. 9.2 Definition: Boolean Algebra
3. 9.3 Disjunctive and Conjunctive Normal Forms (Canonical Forms)
4. 9.4 Switching Network from Boolean Expression
5. 9.5 Karnaugh Map
6. Exercises
17. 10. Topics in Graph Theory
1. 10.1 Introduction
2. 10.2 Graph Definition
3. 10.3 Planar and Non-planar Graphs
4. 10.4 Region
5. 10.5 Operations on Graphs
6. 10.6 Bipartite Graph
7. 10.7 Isomorphism
8. 10.8 Representation of Graphs in Computer Memory
9. 10.9 Representation of Multi Graph
10. 10.10 Walk in a Graph
11. 10.11 Sub-Graph
12. 10.12 Connected and Disconnected Graphs
13. 10.13 Graph Colouring
14. 10.14 Chromatic Polynomial
15. 10.15 Shortest Path Problems
16. 10.16 Shortest Path in a Weighted Graph
17. 10.17 Travelling Salesman Problem
18. 10.18 Network Flows
19. 10.19 Matchings
20. Exercise – A
21. Exercise – B
18. 11. Trees
1. 11.1 Introduction
2. 11.2 Rooted Structure
3. 11.3 Binary Tree of an Algebraic Expression
4. 11.4 Tree Searching or Tree Traversal
5. 11.5 Binary Search Tree
6. 11.6 Spanning Trees
7. 11.7 Minimal Spanning Trees
8. Exercises
19. 12. Vector Spaces
1. 12.1 Introduction
2. 12.2 Definition
3. 12.3 Vector Subspace
4. 12.4 Calculus of Subspaces
5. 12.5 Linear Dependence and Indepence of Vectors
6. 12.6 Dimension and Basis
7. 12.7 Linear Transformation
8. 12.8 Normed and Inner Product Spaces
9. Exercise – A
10. Exercise – B