Experiments which are performed and measured according to the discrete values or continuous values both have different perceptions. Introduction to discrete mathematics is the branch of mathematics that refers to objects having only distinct and separate values or it can be said that this deals with the countable sets. Graph theory of hyper graphs, coding, the design of blocks, combinatorial and discrete geometry, matrices etc. fields are covered by discrete mathematics. |

For example, to obtain taxi license in Las Vegas, a person must pass a written exam regarding different locations in the city. Number of attempts a person takes to attempt the test is an example of discrete data. A person could take it once, twice, and so on. The possible values are 1, 2, 3, ......

The topics of discrete mathematics are given below:

**A specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminates at any point.**

__Algorithm:__**Using mathematical techniques to systematically count objects.**

__Counting:__**Difference between the value of an observation and the mean of the population.**

__Deviation:____Rectangular arrays of numbers. Used in algebra, geometry, statistics, and probability, with many applications in science, business, and industry.__

**Matrices:****A rearrangement of the elements in an ordered list S into a one-to-one correspondence with S itself.**

__Permutation:__**Branch of mathematics concerning the study of finite or countable discrete structures.**

__Combinatorics:__**A graph that contains no cycles.**

__Graph:____The study of formal mathematical structures called graphs.__

**Graph Theory:**__A ratio is a relationship between two numbers of the same kind. Usually expressed as A : B.__

**Ratio:****A name given to a statement, when the two ratios are equal. It can be written using a colon, a : b = c : d**

__Proportion:__**This is the system of coordinates in which coordinates are defined with the help of angles.**

__Polar coordinates:__**Branch of mathematics that deals with the likelihood that a particular event will happen in the future. It is expressed as a number between 1 and 0 and can be expressed in fractions, ratios, percentage.**

__Probability:__Given below are some of the problems in discrete mathematics.

### Solved Examples

**Question 1:**Find the fifth perfect prime number.

**Solution:**

The fifth prime number is 11

The formula to find perfect prime number is (2$^{p-1}$) (2$^{p}$ - 1)

Plugging in 11 in the above formula, we get

(2$^{11-1}$) (2$^{11}$ - 1)

= 4096 x 8191

= 33550336

**Question 2:**Find the value of x in the 4 : 3 = x : 9

**Solution:**

4 × 9 = x × 3

x × 3 = 4 × 9

x = $\frac{4× 9}{3}$

x = 12

**Question 3:**When a die is rolled, what is the probability of obtaining an even number?

**Solution:**

Total number of sides = 6

Number of ways to roll an even number = {2, 4, 6} = 3