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# Formal Science Overview
This document provides an overview of the different topics within Formal Science.

## Table of Contents

| Topic               | Description                                                                         |
|---------------------|-------------------------------------------------------------------------------------|
| Computer Science    | The study of computation and computer systems                                       |
| Mathematics         | The study of quantity, structure, space, and change                                 |
| Applied Mathematics | The use of mathematical methods to solve practical problems                         |
| Pure Mathematics    | The study of mathematics for its own sake, without regard to practical applications |

## Computer Science
Computer Science is the study of computation and computer systems. It includes a wide range of topics such as algorithms, programming languages, computer architecture, operating systems, and databases. Computer scientists work to develop new software, hardware, and computing techniques that can help solve practical problems and improve our lives.

## Tools
Tools in computer science refer to software and hardware that help in the development, debugging, and testing of computer programs. Examples of tools include integrated development environments (IDEs), version control systems, debuggers, and profilers. These tools can help programmers write better code more efficiently and can make the development process more streamlined.

## Mathematics
Mathematics is the study of quantity, structure, space, and change. It is a broad field that includes many sub-disciplines, such as applied mathematics and pure mathematics. Mathematicians work to discover new mathematical structures and relationships, and to apply these structures to solve problems in fields such as physics, engineering, and economics.

## Applied Mathematics
Applied Mathematics is the use of mathematical methods to solve practical problems in fields such as physics, engineering, and finance. Examples of applied mathematics include differential equations, optimization, and numerical analysis. Applied mathematicians use mathematical models to understand real-world phenomena and to make predictions about future behavior.

## Pure Mathematics
Pure Mathematics is the study of mathematics for its own sake, without regard to practical applications. It includes areas such as algebra, geometry, and analysis. Pure mathematicians work to discover new mathematical structures and relationships, and to prove mathematical theorems using rigorous logical reasoning. The results of pure mathematical research often have surprising and unexpected applications in other fields.
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