Introduction to
Discrete Mathematics

The World of Integers

Discrete mathematics is the study of countable things.

It is not a single branch of mathematics.

Rather, it is a group of branches with a common property: the study of discrete objects.

Main Questions

Discrete mathematics aims to answer a variety of problems:

• What is known?
• What can be computed?
• What can be computed efficiently?
• How can information be organized and stored?

Information

Logic, discrete structures and graphs all allow the verification and storage of information.

Summarization

Combinatorics, set theory and mathematical proofs allow the study of emerging properties.

Computation

From a set of rules, iterative and recursive computations can be done and verified.

History

Integers were first used with tally marks (3400 BC), and negative numbers were introduced with the Chinese number rod system (200 BC).

Many mathematicians have had an important influence on modern discrete mathematics:

Discrete Mathematics Today

Nowadays, discrete mathematics is strongly associated with technology.

• It is at the center of all modern computation.
• It is the cornerstone of communications, networks and the internet.
• Practically all types of resource management need discrete mathematics.
• Discrete math is important in computer graphics, games and even arts.

Why Study Discrete Mathematics?

High-school mathematics mostly overlooks discrete mathematics in favor of continuous mathematics.

Reasons to study discrete mathematics:

• Calculate discrete phenomena efficiently
• Understand computation
• Use and store information
• Develop your mathematical reasoning

About This Course

This course is designed to be an introduction to many fields of mathematics and computer science.

This course is separated into seven small sections:

Who Is This Course For?

• Future, current or self-taught computer science and software engineering students
• Individuals aiming to expand their mathematical intuition and problem-solving skills
• Python Language users who want a guided introduction to discrete mathematics functions
• Math hobbyists wanting to explore the beauty of mathematics

Summary

• As a mathematical subject, discrete mathematics is essentially the study of countable objects.
• As a professional skill, it helps you analyze, store and compute information, all to conquer many tasks.
• As an educational hurdle, it provides the toolset necessary to excel in computer science courses.
• The next lesson explores Proposition Logic — the algebra of True and False.