20-02-2015, 11:29 AM

Anna University , Chennai

Department of B.E-Computer Science and Engg

(Common to B.Tech I.T)

Fifth Semester

MA2265 Discrete Mathematics

Scanned Handwritten Lecture Notes (All Units)

(Regulation 2013)

Discrete Mathematics (All Units) Handwritten Premium Lecture Notes, Prepared by Kamala Priya. Specially for Engineering Candidates. Syllabus Covered based on Anna University B.E CSE and B.Tech Engineering Fifth Semester, R2008 and R2013 Regulation.

Syllabus :

DISCRETE MATHEMATICS

UNIT -1 (pages: 24) : LOGIC ANG PROOFS

UNIT-2 (pages: 89) : COMBINATORICS

UNIT-3 (pages: 37) : GRAPHS

UNIT-4 (pages: 12) : ALGEBRAIC STRUCTURE

UNIT-5 (pages: 7) : LATTICES AND BOOLEAN ALGEBRA

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Content :

UNIT -1

LOGIC ANG PROOFS

Proposition

Connectives

Compound statements

Basic connectives

Truth table for connectives

Tautology

Contradiction

Contingency

Tautological implication

Normal forms

1. Elementary product

2. Elementary sum

3. Disjunctive normal form

4. Conjunctive normal form

Principle normal form

Principle disjunctive normal forms

Principle conjunvtive normal forms

UNIT-2

COMBINATORICS

Principle of mathematical induction

Pigeon hole principle

Generalized pigeon hole principle

Combination

Recurrence relation

Linear non – homogeneous RR with constant coefficient

Generating function

UNIT-3

GRAPHS

Graph

Self – loop

Parallel edges

Incident

Adjacent vertices

Adjacent edges

Simple graph

Isolated graph

Isolated vertex

Pendentant vertex

Directed edges

Digraph

Undirected graph

Mixed graph

Multi graph

Pseudo graph

Degree of vertex

In degree and out degree

Handshaking theorem

Regular graph

Bipartite graph

Complete bipartite graph

Path

Length of path

Cycle or circuit

Reachable

Connected graph

Sub graph

Adjacency matrix of a simple graph

Incidence matrix

Path matrix

Graph isomorphism

Complement of a graph

Unilaterally connected

Strongly connected

Euler’s graph

Eulerian circuit

Eulerian graph

Konisberg bridge problem

UNIT-4

ALGEBRAIC STRUCTURE

Semi group

Monoid

Cyclic monoids

Morphism of semi – groups

Order of a group

UNIT-5

LATTICES AND BOOLEAN ALGEBRA

Relation

R-is reflexive

R is symmetric

R- is transitive

R – is anti symmentric

Equivalence relation

Partial order relation

Patially ordered set

Least elements

Greatest elements

Upper bound and lower bound

Least upper bound

Greatest lower bound

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