MA6566 Discrete Mathematics Scanned Lecture Notes (All Units) - Lavanya Edition

[Srini]

   

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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