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DISCRETE STRUCTURES AND GRAPH THEORY
Neeraj Yadav

DISCRETE STRUCTURES AND GRAPH THEORY

Neeraj Yadav | 03-Dec-2015 |
Set Theory , Relations , Functions , Natural numbers , Algebraic Structures , Partial order set , Boolean algebra , Propositional Logic , Predicate logic , Trees , Graphs , Recurrence Relation & Generating function , Combinatorics ,

Hi friends, here Neeraj Yadav uploaded notes for DISCRETE MATHEMATICS with title DISCRETE STRUCTURES AND GRAPH THEORY. You can download this lecture notes, ebook by clicking on the below file name or icon.

SYLLABUS
Unit-I
Set Theory: Introduction, Combination of sets, Multisets, Ordered pairs,Set Identities.
Relations: Definition, Operations on relations, Properties of relations, Composite Relations,
Equality of relations, Order of relations.
Functions: Definition, Classification of functions,Operations on functions, Recursively
defined functions.
Natural Numbers: Introduction, Mathematical Induction, Variants of Induction, Induction
with Nonzero Base cases.
Unit-II
Algebraic Structures: Definition, Groups, Subgroupsand order, Cyclic Groups,
Cosets,Lagrange's theorem, Normal Subgroups, Permutation and Symmetric groups, Group
Homomorphisms, Definition and elementary propertiesof Rings and Fields, Integers Modulo n.
Unit-III
Partial order sets: Definition, Partial order sets,Combination of partial order sets, Hasse
diagram.
Lattices: Definition, Properties of lattices – Bounded, Complemented, Modular and Complete
Lattice,Morphisms of lattices.
Boolean Algebra: Introduction, Axioms and Theorems of Boolean algebra, Algebraic
manipulation of Boolean expressions. Simplificationof Boolean Functions, Karnaugh maps,
Logic gates, Digital circuits and Boolean algebra. Combinational and sequential Circuits.
Unit-IV
Propositional Logic: Proposition, well formed formula, Truth tables, Tautology, Satisfiability,
Contradiction, Algebra of proposition, Theory of Inference ,Natural Deduction.
Predicate Logic: First order predicate, well formedformula of predicate, quantifiers, Inference
theory of predicate logic.
Unit-V
Trees : Definition, Binary tree, Binary tree traversal, Binary search tree.
Graphs: Definition and terminology, Representation of graphs, Multigraphs, Bipartite graphs,
Planar graphs, Isomorphism and

 

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