Introduction to Crash Course Mathematics

Hello everyone my name is David Rybka and welcome to "Crash Course: Mathematics." I don't technically have a right to use this title. And currently, I am making no money off of this so please don't sue me Hank Green. cue intro, For those of you who are unaware, mathematics is kind of important. It is the foundation for most of the technology, reasoning and scientific thought that we use today. So if we want to continue improving on it, it might be a good idea to learn about it. Many people find mathematics hard to understand for a variety of reasons. Large parts of how mathematics is described is in a constructed pseudo-language. It is designed to describe very specific abstract ideas that were developed over literally centuries. It makes sense that it can be a little confusing.

This course is intended to explain the language of mathematics as well as the abstract concepts behind them. I want to give you a broader understanding of mathematical concepts as well as practical methods that may help you on your homework in school if possible. The idea is to show you how these concepts are defined then show you how mathematics expresses these ideas and maybe even some of the stories and histories behind the ideas.

Mathematics is one of the oldest recorded intellectual subjects. There are cave counting sticks tools that are literally the first conceptualization of numbers. As agriculture developed, so did bureaucracy and the need to record numbers developed in what we call Mesopotamia. Specifically it was in Egypt and Babylon. This also required teaching, Egypt had the first examples of math quizzes. They also helped to develop the concept of ratio for equitable pay and geometry to define property.  Babylon had the first place value system of numbers. Greeks developed large parts of geometry and one of their number created a textbook in the subject we still use to some extent today. It is actually one of the most published and translated piece of literature other than the Christian Bible. China created the beginnings of matrices and what we call linear algebra. India developed the concept of zero in the old world (kind of a big deal as I hope to get into later). and in the Americas the Mayans had a base 20 number system that had a placeholder digit that we call zero. This lead to the number system that we use today. Which made it's way through the Islamic Middle East. Which is also why they are called Arabic numerals. The Islamic empire also gave us the beginnings of variables and what we call algebra and it is also where we get the word for "algorithm". Both algebra and algorithm are words based on the names of Arabic scholars. Then we make our way to Europe which took all of these tools and turned them into some of the most advanced mathematical subjects we have today. We have Probability and Statistics (Pascal), Calculus (Leibniz and Newton), Abstract Algebra or Group Theory (Abel and Galois), Topology (Euler), Graphing (Descartes), as well as many others.

I intend to discuss the history, the methods and the concepts of mathematics. Hopefully, in a way that is useful to those who read this. I do plan on going over basic ideas in a way that leads to some of the broader concepts behind the things you learned in elementary school. Eventually, I plan on walking through some of the more advanced ideas in math using this framework. Given the fact that this is a draft. I want people to ask me questions, ask for citation, and point out when I am wrong or confusing. I hope to have fun with this.