09-07-2015, 02:14 PM

Discrete Mathematics (All Units) Handwritten Premium Lecture Notes, Prepared by Deepthi. Specially for Engineering Candidates. Syllabus Covered based on Anna University B.Tech IT, R2008 and R2013 Regulation.

CONTENT:

UNIT-1 LOGIC AND PROOFS (No.of.pg:34)

UNIT-2 COMBINATIONS (No. of Pg:20)

UNIT-3 GRAPHS (No. of pg:34)

UNIT-4 ALGEBRIC STRUCTURE (No. of. Pg: 25)

UNIT-5 LATTICES AND BOOLEAN ALGRBRA (No .of .pg:20)

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UNIT-1

LOGIC AND PROOFS

Definition: proposition

Atomic IC statements

Molecular statement

Truth table

Negation or not

Conjuction

Conditional statement

Bi conditional statement

Contrapositive

Translating sentence into logical expression or symbolic form

Tautology

Contradiction

Fallacy

Duality

Disjunction

Conjunctive normal form

Principle conjunction normal form

Quantifiers

Rules of inference

Rules in quantifiers

1. Universal specification

2. Existential specification

3. Existential specification

4. Universal generalization

Hypothesis

Analisis

Conclusion

UNIT-2

COMBINATIONS

Principle of mathematical induction

Strong induction

Pigeonhole principle

Generalization pigeonhole principle

Extended pigeonhole principle

Linear recurence relation

Generating function

Inclusion and exclusion

UNIT-3

GRAPHS

Adjacent vertices

Simple graph

Parallel edges

Multi graph

Simple directed graph

Directed graph

Mixed graph

Loop

Weighed graph

Underlying undirected graph

Pseudo graphs

In degree

Out degree

Complete graph

N-cube

Star graph

Sub graph

Union

Representation graph and graph isomorphism

Properties of adjacency matrix

Connectivity

Path

Connected and disconnected graph

Connectedness in D.G

UNIT-4

ALGEBRAIC STRUCTURE

Binary operation

General properties of algebraic structure

1. Closure properties

2. Associativity

3. Commutativity

4. Identity

5. Element

6. Distributivity

7. Cancellation property

Semi graph

Monoid

Semi graph homomorphism

Monoid homomorphism

Sub monoid

Group

Abelian group

Properties of group

Langrange’s thm

Normal sub group

Kernel of a homomorphism

Isomorphism

Cosets

Integral domain

UNIT-5

LATTICES AND BOOLEAN ALGRBRA

Partial order relation

Poset

Totally ordered set

Well ordered

Hasse diagram or partially ordered set diagram

Lattice

Greatest lower band and upper post

Some properties of lattices

Theorems

Boolean algebra

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