# Introduction to Discrete Mathematics

Introduction to Discrete Mathematics

LESSON 1: WHAT IS DISCRETE MATHEMATICS?

## The World of Integers

The World of Integers

Discrete mathematics is the study of countable things.

It is not a branch of mathematics.

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

## Main Questions

Main Questions

Discrete mathematics aims to answers a variety of problems:

What is known?

What can be summarized?

What can be computed?

## Information

Information

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

## Summarization

Summarization

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

## Computation

Computation

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

## History

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, including:

## Discrete Mathematics Today

Discrete Mathematics Today

Nowadays, discrete mathematics is strongly associated with technology.

## Why Study Discrete Mathematics?

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

About This Course

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

This exploration is facilitated by the use of Wolfram Language, a language with discrete computation as its core philosophy.

This course is separated into seven small sections:

Logic

Discrete Structures

Counting

Algorithms

Proofs and Recursion

Recurrence Relations

Graphs

## Who Is This Course For?

Who Is This Course For?

The Wolfram U course on discrete mathematics is most useful for:

## Summary

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.

In the next lesson, the course will begin with the two simplest discrete values: true or false.