Senthil Kumar B.V., Dutta H. Discrete Mathematical Structures: A Succinct Foundation

Boca Raton: CRC Press, 2020. — 275 p.This book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension.FeaturesOffers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean Algebra Provides end of chapter solved examples and practice problems Delivers materials on valid arguments and rules of inference with illustrations Focuses on algebraic structures to enable the reader to work with discrete structuresAuthors
Logics and ProofsProposition
Compound Propositions
Truth Table
Logical Operators
Negation
Conjunction
Disjunction
Molecular Statements
Conditional Statement [If then] [ → ]
Biconditional [If and only if or iff] [↔ or ⇌]
Solved Problems
Tautology
Contradiction
Contingency
Equivalence Formulas
Equivalent Formulas
Duality Law
Tautological Implication
Some More Equivalence Formulas
Solved Problems
Normal Forms
Principal Disjunctive Normal Form or Sum of Products Canonical Form
Principal Conjunctive Normal Form or Product of Sum Canonical Form
Solved Problems
Inference Theory
Rules of Inference
Solved Problems
Indirect Method of Proof
Method of Contradiction
Solved Problems
Method of Contrapositive
Solved Problems
Various Methods of Proof
Trivial Proof
Vacuous Proof
Direct Proof
Predicate Calculus
Quantifiers
Universe of Discourse, Free and Bound Variables
Solved Problems
Inference Theory for Predicate Calculus
Solved Problems
Additional Solved Problems
CombinatoricsMathematical Induction
Principle of Mathematical Induction
Procedure to Prove that a Statement P(n) is True for all Natural Numbers
Solved Problems
Problems for Practice
Strong Induction
WellOrdering Property
Pigeonhole Principle
Generalized Pigeonhole Principle
Solved Problems
Another Form of Generalized Pigeonhole Principle
Solved Problems
Problems for Practice
Permutation
Permutations with Repetitions
Solved Problems
Problems for Practice
Combination
Solved Problems
Problems for Practice
Recurrence Relation
Solved Problems
Linear Recurrence Relation
Homogenous Recurrence Relation
Recurrence Relations Obtained from Solutions
Solving Linear Homogenous Recurrence Relations
Characteristic Equation
Algorithm for Solving k[sup(th)]order Homogenous Linear Recurrence Relations
Solved Problems
Solving Linear Nonhomogenous Recurrence Relations
Solved Problems
Problems for Practice
Generating Functions
Solved Problems
Solution of Recurrence Relations Using Generating Function
Solved Problems
Problems for Practice
Inclusion—Exclusion Principle
Solved Problems
Problems for Practice
GraphsGraphs and Graph Models
Graph Terminology and Special Types of Graphs
Solved Problems
Graph Colouring
Solved Problems
Representing Graphs and Graph Isomorphism
Solved Problems
Problems for Practice
Connectivity
Connected and Disconnected Graphs
Eulerian and Hamiltonian Paths
Hamiltonian Path and Hamiltonian Circuits
Solved Problems
Problems for Practice
Additional Problems for Practice
Algebraic StructuresAlgebraic Systems
Semigroups and Monoids
Solved Problems
Groups
Solved Problems
Subgroups
Cyclic Groups
Homomorphisms
Cosets and Normal Subgroups
Solved Problems
Permutation Functions
Solved Problems
Problems for Practice
Rings and Fields
Solved Problems
Problems for Practice
Lattices and Boolean AlgebraPartial Ordering and Posets
Representation of a Poset by Hasse Diagram
Solved Problems
Problems for Practice
Lattices, Sublattices, Direct Product, Homomorphism of Lattices
Properties of Lattices
Theorems on Lattices
Solved Problems
Problem for Practice
Special Lattices
Solved Problems
Problems for Practice
Boolean Algebra
Solved Problems
Problems for Practice