# Discrete Math Overview

## What even is discrete math? #

According to
Wikipedia, “*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**and sets give us the**language**we need to talk about discrete math.- ****
**Proofs****** allow us to demonstrate**how**and**why**things work the way they do. **Stable Matching**explores how we can apply sets to create optimal matches between two groups with preferences.**Graph theory**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**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****** is an interesting application of how modular arithmetic is used to encrypt and decrypt messages using a public-private key pair. **Polynomials**can be used in a discrete sense to create**secret sharing**schemes, and can be recovered from points using**Lagrange Interpolation.**