Discrete mathematics

is the part of mathematics devoted

to the study of discrete (as opposed to continuous) objects.

Discrete mathematics

What are the examples of discrete mathematics

integers, steps taken by a

computer program, distinct paths to travel from point A to

point B on a map along a road network, ways to pick a

winning set of numbers in a lottery.

Ability to read,

understand, and construct mathematical arguments

and proofs.

Mathematical reasoning

Techniques for counting

objects of different kinds.

Combinatorial analysis

is a sequence of steps that

can be followed to solve any instance of a particular problem.

Algorithm

certain property is true for all elements in the set

universal statement

says one things is true then the some other thing is also true

conditional statement

there is at leats one thing for which the statement is true

existensial statement

key word in universal statement

all or for all

key word in conditional statement

if and then

key word in existensial statement

there is and there exist

is a sequence of steps that

can be followed to solve any instance of a particular problem.

Universal conditional statement

Is statement that is universal because its firts part says that a certain property is true for all given types, and it is existensial because its second part asserts the existence of something

Universal existensial statement

asserts that a certain object exist and is universal because of its second part says that the object satisfiies a certain property for all things of the same kind

Existensial Universal statement