Define Discrete Math

Introduction to Definition of  Discrete math:

Discrete mathematics is one of the major topics in mathematics. It defines the study of mathematical formation that is basically discrete rather than continuous. In disparity to real numbers that have the property of changeable "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements in logic.

Discrete math is branch of mathematics that deals Countable sets. Countable set define that have same cardinality as subsets of integers that comprises rational numbers but not a real numbers.

Dis create Math Application:

Presently researches in discrete mathematics were increased in latter half of twentieth century. The main purpose of study in discrete mathematics is discrete objects and analytic methods from continuous mathematics. Define discrete math contains Theoretical computer science, Information theory, Logic, Set theory, Combinatorial, Graph theory, probability theory, Discretization, Discrete analogues of continuous mathematics and so on.

Some of the main discrete math activities are given in below

Set theory:

Set theory is division of discrete mathematics. These commonly define the sets. Sets mean group of objects. The important development of set theory is infinite sets in outside the scope of discrete mathematics

Graph theory:

Graph theory is part of discrete mathematics. In this Graph theory mostly focus on graph and network. Graph theory is extensive in all the areas of mathematics and science.

Algebra:

Discrete mathematics discrete algebra defines the

Boolean algebra
The Boolean algebra commonly used in logic gates and programs

Relational algebra
In relational algebra commonly used in database side.

Algebraic coding theory
Discrete Semi group
Discrete modeling:

Discrete modeling is some time called as discrete analogue of continuous modeling. Case for Discrete modeling is recurrence relation.

Recurrence relationship formula is

`F(n)-f(n-1)=g(n)`

This above formula is discrete analogue of first order ordinary differential equation.

Example for Define Discrete Math:

Example 1:

Problem:

To solve the all ‘n>10’    n-2< (n^2-n)/12

Solution:

Default property of discrete mathematics is

p (n) is `P(n) ` : `k<=n(k>10 ; n>10)k-2<(k^2-k)/12`

Given Base case `n=15`

`15-2< ((15*15)-15)/12`

`13<210 br="br">
`13<17 br="br">
Using discrete mathematics property to solve the equation.