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Discrete mathematics

Discrete mathematics is part of mathematics devoted to study of discrete objects (distinct or unconnected object)

Why

• Ability to understand and create mathematical arguments
• Provides foundation for many computer science courses including data structures, algorithms, compiler design, etc;

What kind of problems can be solved by discrete mathematics

• How many ways to choose valid password on a computer system?
• How many steps is required to do such sorting ?
• How can it proved that sorting algorithm correctly sorts a list?
• How many valid internet addresses are there ?

Logic and proof

Logic

The rules of logic specify the meaning of mathematical statements and helps us understand and reason with statements such as
There exists number which is not sum of two squares,
For every positive integer n, sum of positive integers not exceeding n is n*(n+1)/2.
Logic is basis for all mathematical reasoning and computed reasoning.

Proof

To understand mathematics, we must understand what makes up a correct mathematical argument, that is proof.
One we prove mathematical argument is true, we call a theorem, a collection of theorem on a topic organize what we know about a topic.
Proofs are used to verify that computer program produce correct output for all possible input values to show that algorithm always produce correct result
to establish security of the system.