Book description
About The Author –
Uma Shanker Gupta joined the department of mathematics, the University of Roorkee (presently IIT-Roorkee), in 1967, after teaching for five years at Ewing Christian Degree College, Allahabad. He was awarded PhD (Mathematics) by the University of Roorkee in 1971. He joined the Department of Applied Science and Humanities, ABES Engineering College, Ghaziabad, as professor in 2006 and subsequently held positions of Professor and Head, Applied Science and Humanities, Professor and Head MCA Dept and Director, MCA Institute.
He was a visiting faculty of Mathematics in the School of Vocational Studies and Applied Science, Gautam Buddha University, UP, in the autumn semester of 2010–2011. He has been a reviewer of many International journals like Journal of Applied Mechanics, Journal of Sound and Vibration to name a few. He became EMERITUS FELLOW in 2004 and held this position till 2006.
Book Contents –
1. Set Theory
2. Relations and Digraphs
3. Functions
4. Mathematical Logic and Methods of Proofs
5. Combinatorics
6. Recurrence Relations and Generating Functions
7. Algebraic Structures
8. Ordered Sets and Lattices
9. Boolean Algebra
10. Topics in Graph Theory
11. Trees
12. Vector Spaces
13. ANSWER TO EXERCISEs
14. References
15. Index
Table of contents
- Front Cover
- Contents (1/2)
- Contents (2/2)
- Preface
- Acknowledgements
- About The Author (1/2)
- About The Author (2/2)
-
Set Theory
- 1.1 INTRODUCTION
-
1.2 SETS
- 1.2.1 Types of Sets
- 1.2.2 Subset
- 1.2.3 Proper Subset
- 1.2.4 Power Set
- 1.2.5 Venn Diagram
- 1.2.6 Set Operations
- 1.2.7 Disjoint Sets
- 1.2.8 Complement of a Set
- 1.2.9 Laws of Sets
- 1.2.10 Symmetric Difference of Two Sets
- 1.2.11 The Inclusion and Exclusion Principle
- 1.2.12 Some Simple Results on Cardinality of Sets
- 1.3 CARTESIAN PRODUCT OF SETS
- 1.4 MULTISET
-
Relations and Digraphs
- 2.1 INTRODUCTION
-
2.2 BINARY RELATION
- 2.2.1 Domain and Range of Relation
- 2.2.2 Types of Relations
- 2.2.3 Properties of Relation on a Set
- 2.2.4 Equivalence Relation
- 2.2.5 Complementary Relation Boolean...Equation
- 2.2.6 Closure of Relation
- 2.2.7 Reflexive Closure
- 2.2.8 Symmetric Closure
- 2.2.9 Composition of Relations
- 2.2.10 Transitive Closure
- 2.3 EQUIVALENCE CLASS
- 2.4 PARTITION OF A SET
- 2.5 CONGRUENCE MODULO RELATION
- 2.6 PICTORIAL REPRESENTATION OF RELATION
- 2.7 DIGRAPHS
- 2.8 POWER OF RELATION
- 2.9 PATHS IN RELATIONS AND DIGRAPHS
- 2.10 MATRIX REPRESENTATION OF COMPOSITE RELATIONS
- 2.11 CONNECTIVITY RELATION
-
Functions
- 3.1 INTRODUCTION
- 3.2 DEFINITION
- 3.3 DOMAIN AND RANGE OF A FUNCTION
- 3.4 DIFFERENCE BETWEEN RELATION AND FUNCTION
- 3.5 DIFFERENT TYPES OF FUNCTIONS (OR MAPPINGS) CONSTANT FUNCTION
- 3.6 COMPOSITION OF FUNCTIONS
- 3.7 FUNCTIONS FOR COMPUTER SCIENCE
- 3.8 SOME SPECIAL FUNCTIONS USED IN DISCRETE MATHEMATICS
- 3.9 SOME IMPORTANT THEOREMS AND PROBLEMS
- 3.10 ACKERMANN’S FUNCTION
- 3.11 FUZZY SETS
- 3.12 TIME COMPLEXITY OF ALGORITHM
- 3.13 CONNECTIVITY RELATION (1/2)
- 3.13 CONNECTIVITY RELATION (2/2)
- Mathematical Logic and Methods of Proofs
-
Combinatorics
- 5.1 Introduction
- 5.2 BASIC PRINCIPLE OF COUNTING
- 5.3 PERMUTATIONS
- 5.4 ORDERED AND UNORDERED PARTITIONS
- 5.5 CIRCULAR PERMUTATIONS
- 5.6 COMBINATIONS
- 5.7 DERANGEMENTS
- 5.8 THE PIGEONHOLE PRINCIPLE
- 5.9 ELEMENTS OF PROBABILITY
- 5.10 MULTIPLICATION THEOREM (Independent Events) (1/2)
- 5.10 MULTIPLICATION THEOREM (Independent Events) (2/2)
- 5.11 BAYE’S THEOREM
- 5.12 CONCEPT OF A RANDOM VARIABLE
- 5.13 BINOMIAL DISTRIBUTION
- 5.14 POISSON DISTRIBUTION
- Recurrence Relations and Generating Functions
-
Algebraic Structures
- 7.1 INTRODUCTION
- 7.2 BINARY OPERATION
- 7.3 ALGEBRAIC STRUCTURES
- 7.4 CONGRUENCES
- 7.5 PERMUTATIONS
- 7.6 INTEGRAL POWERS OF AN ELEMENT
- 7.7 CYCLIC GROUP
- 7.8 SUBGROUPS
- 7.9 COSET DECOMPOSITION
- 7.10 ISOMORPHISM AND HOMOMORPHISM OF GROUPS
- 7.11 ALGEBRAIC SYSTEMS WITH TWO BINARY OPERATIONS
- 7.12 Ring, SUBRING and Ideals
- 7.13 INTEGRAL DOMAIN
- 7.14 FIELD
-
Ordered Sets and Lattices
- 8.1 INTRODUCTION
- 8.2 PARTIALLY ORDERED SET
- 8.3 PRODUCT OF TWO POSETS
- 8.4 HASSE DIAGRAM
- 8.5 LEXICOGRAPHIC ORDERING
- 8.6 UPPER AND LOWER BOUNDS
- 8.7 DUAL OF A POSET
- 8.8 ISOMORPHISM OF POSETS
- 8.9 WELL-ORDERED SET
- 8.10 PROPERTIES OF WELL-ORDERED SETS
- 8.11 LATTICES
- 8.12 LATTICE IN TERMS OF ALGEBRAIC STRUCTURES
- 8.13 SUBLATTICES
- 8.14 BOUNDED LATTICES
- 8.15 DUALITY
- 8.16 COMPLETE LATTICE
- 8.17 ISOMORPHIC LATTICES
- 8.18 COMPLIMENTED LATTICE
- 8.19 CHAIN AND ANTICHAIN
- 8.20 DISTRIBUTIVE LATTICES
- 8.21 MODULAR LATTICE
- 8.22 BOOLEAN LATTICE
- Boolean Algebra
-
Topics in Graph Theory
- 10.1 INTRODUCTION
- 10.2 GRAPH definition
- 10.3 PLANAR AND NON-PLANAR GRAPHS
- 10.4 REGION
- 10.5 OPERATIONS ON GRAPHS
- 10.6 BIPARTITE GRAPH
- 10.7 ISOMORPHISM
- 10.8 REPRESENTATION OF GRAPHS IN COMPUTER MEMORY
- 10.9 REPRESENTATION OF MULTI GRAPH
- 10.10 WALK IN A GRAPH
- 10.11 SUB-GRAPH
- 10.12 CONNECTED AND DISCONNECTED GRAPHS
- 10.13 GRAPH COLOURING
- 10.14 CHROMATIC POLYNOMIAL
- 10.15 SHORTEST PATH PROBLEMS
- 10.16 SHORTEST PATH IN A WEIGHTED GRAPH
- 10.17 TRAVELLING SALESMAN PROBLEM
- 10.18 NETWORK FLOWS
- 10.19 MATCHINGS
- Trees
- Vector Spaces
- ANSWER TO EXERCISEs (1/29)
- ANSWER TO EXERCISEs (2/29)
- ANSWER TO EXERCISEs (3/29)
- ANSWER TO EXERCISEs (4/29)
- ANSWER TO EXERCISEs (5/29)
- ANSWER TO EXERCISEs (6/29)
- ANSWER TO EXERCISEs (7/29)
- ANSWER TO EXERCISEs (8/29)
- ANSWER TO EXERCISEs (9/29)
- ANSWER TO EXERCISEs (10/29)
- ANSWER TO EXERCISEs (11/29)
- ANSWER TO EXERCISEs (12/29)
- ANSWER TO EXERCISEs (13/29)
- ANSWER TO EXERCISEs (14/29)
- ANSWER TO EXERCISEs (15/29)
- ANSWER TO EXERCISEs (16/29)
- ANSWER TO EXERCISEs (17/29)
- ANSWER TO EXERCISEs (18/29)
- ANSWER TO EXERCISEs (19/29)
- ANSWER TO EXERCISEs (20/29)
- ANSWER TO EXERCISEs (21/29)
- ANSWER TO EXERCISEs (22/29)
- ANSWER TO EXERCISEs (23/29)
- ANSWER TO EXERCISEs (24/29)
- ANSWER TO EXERCISEs (25/29)
- ANSWER TO EXERCISEs (26/29)
- ANSWER TO EXERCISEs (27/29)
- ANSWER TO EXERCISEs (28/29)
- ANSWER TO EXERCISEs (29/29)
- References
- Index (1/2)
- Index (2/2)
Product information
- Title: Discrete Mathematical Structures by Pearson
- Author(s):
- Release date: May 2024
- Publisher(s): Pearson India
- ISBN: 9781322128603
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