# mathematics

## Table of Contents

## 1. Mathematics is Logic

With a couple of set theory axioms. One might describe it as an extrapolation framework without grounding (i.e. a set of implications; if p then q, but never specifying if p is a property of a real system or not). Therefore, mathematics is suitable for modeling other things if we believe those other things have some rules and are logically consistent.

There are many subfields in math, ranging from group theory to calculus. However, much of the time we are able to find morphisms between these different fields in mathematics, which we model using category theory.

### 1.1. Mathematical Models

There are many fields where mathematics is the main method of analysis.

#### 1.1.1. Physics

Physics is the study of the natural world and its laws, usually resorting to a mathematical framework.

#### 1.1.2. Economics

the study of human behavior; generally speaking, economists use mathematical models for models of the macroeconomy.