> For the complete documentation index, see [llms.txt](https://cs70.bencuan.me/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cs70.bencuan.me/discrete-math/overview.md).

# Overview

## What even is discrete math?

According to [Wikipedia](https://en.wikipedia.org/wiki/Discrete_mathematics), "*Discrete mathematics* is the study of mathematical structures that are fundamentally discrete rather than continuous." Very helpful, thank you Wikipedia. The floor is indeed made of floor rather than sky.

The word **discrete** means "distinct" or "countable". This suggests that discrete math has to do with **countable numbers** like integers, rather than the continuous $$f(x)$$functions we're used to seeing that are defined for any real$$x$$, even ones we don't know the exact value of like $$\pi$$.

 Dealing with countable integers is nice because **that's how computers work.** Behind the scenes, every floating point number is actually just a whole bunch of bits, which are countable :) I would say that dealing with integers makes things nicer too (since we no longer have to deal with decimals), but you might be inclined to disagree.

## A brief summary of the contents covered

Discrete math is an extremely wide field of mathematics. Here, we'll be covering the basics as well as a few important applications:

* [**Propositional logic**](/discrete-math/propositional-logic.md) and sets give us the **language** we need to talk about discrete math.
* [**Proofs**](/discrete-math/proofs.md) allow us to demonstrate **how** and **why** things work the way they do.
* [**Stable Matching**](/discrete-math/stable-matching.md) explores how we can apply sets to create optimal matches between two groups with preferences.
* [**Graph theory** ](/discrete-math/graphs.md)provides a highly visual representation of a wide variety of mathematical relationships using vertices, edges, and faces. One of the most important concepts here is **Euler's Formula** which relates the number of vertices, edges, and faces together.
* [**Modular arithmetic** ](/discrete-math/modular-arithmetic.md)explores what happens when when all numbers are remainders of dividing itself by another number. There are some really important theorems here, like the **Chinese Remainder Theorem, Euclid's Algorithm,** and **Fermat's Little Theorem.**
* [**RSA Cryptography**](/discrete-math/rsa-cryptography.md) is an interesting application of how modular arithmetic is used to encrypt and decrypt messages using a public-private key pair.
* [**Polynomials** ](/discrete-math/polynomials.md)can be used in a discrete sense to create **secret sharing** schemes, and can be recovered from points using **Lagrange Interpolation.**