# 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****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****Polynomials**can be used in a discrete sense to create**secret sharing**schemes, and can be recovered from points using**Lagrange Interpolation.**

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