A Brief Primer on Discrete Mathematics

A Brief Primer on Discrete Mathematics

A WOPRIMERRD ABOUT THE. This primer is by no means exhaustive of the subject. Treat it as what you’d learn before you’re fully introduced to the subject.

A WORD ABOUT THE PRIMER

This primer is by no means exhaustive of the subject. Treat it as what you’d learn before you’re fully introduced to the subject. I hope this brief primer on Discrete Mathematics will be of some use to you. This subject is extremely useful in describing objects and problems in computer science especially in these topics: algorithms, programming languages, databases, and cryptography. In the future, I intend on going into depth into each of the main areas that’ll be discussed in this primer. Enjoy!

WHAT IS DISCRETE MATHEMATICS?

It is the branch of mathematics that only deals with objects that can only assume distinct separated values.

There are five main areas we will discuss, in the following order:

  • Logic
  • Set theory
  • Relations
  • Functions
  • Combinatorics
  • Graphs

LOGIC

What is Logic?

It is the study of correct reasoning. We will be focusing on idealization and then formalization. Informal logic is the use of natural language arguments.

Formal logic is the study of inference with purely formal content eg. of formal logic would be symbolic logic and syllogistic logic (for example found in Aristotle’s work).

Let us begin by setting the foundations. Take this natural language statement

“If I am hungry, then I eat”.

Let ‘hungry’ be the premise A and ‘eat’ be the conclusion B. We would try and formalize it like this,

A => B, (which reads, A implies B)

N.b. a premise and a conclusion are both propositions.

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