Krishna's Discrete Structures & Graph Theory - 9th Edition - 700+ Pages: Discrete Maths

by J.P. Chauhan

SYLLABUS- DISCRETE STRUCTURES & GRAPH THEORY, Unit-I Set Introduction, Combination of sets, Multisets, Ordered pairs. Proofs of some general identities on sets. Definition, Operations on relations, Properties of relations, Composite Relations, Equality of relations, Recursive definition of relation, Order of relations. Definition, Classification of functions, Operations on functions, Recursively defined functions. Growth of Functions. Natural Introduction, Mathematical Induction, Variants of Induction, Induction with Nonzero Base cases. Proof Methods, Proof by counter example, Proof by contradiction. Unit-II Algebraic Definition, Groups, Subgroups and order, Cyclic Groups, Cosets, Lagrange's theorem, Normal Subgroups, Permutation and Symmetric groups, Group Homomorphisms, Definition and elementary properties of Rings and Fields, Integers Modulo n. Unit-III Partial order Definition, Partial order sets, Combination of partial order sets, Hasse diagram. Definition, Properties of lattices Bounded, Complemented, Modular and Complete lattice. Boolean Introduction, Axioms and Theorems of Boolean algebra, Algebraic manipulation of Boolean expressions. Simplification of Boolean Functions, Karnaugh maps, Logic gates, Digital circuits and Boolean algebra. Unit-IV Propositional Proposition, well formed formula, Truth tables, Tautology, Satisfiability, Contradiction, Algebra of proposition, Theory of Inference. Predicate First order predicate, well formed formula of predicate, quantifiers, Inference theory of predicate logic. Unit-V Trees : Definition, Binary tree, Binary tree traversal, Binary search tree. Definition and terminology, Representation of graphs, Multigraphs, Bipartite graphs, Planar graphs, Isomorphism and Homeomorphism of graphs, Euler and Hamiltonian paths, Graph coloring, Recurrence Relation & Generating Recursive definition of functions, Recursive algorithms, Method of solving recurrences. Introduction, Counting Techniques, Pigeonhole Principle, Polya's Counting Theory.

Genres: Mathematics

Kindle Edition

Published July 12, 2020