Linear Algebra
Differential Equations

Thinking about the origins of our mathematics in its current state, I wish to describe the building blocks which can constucted what we have today. Why do we do mathematics? With no mathematical training, can someone do what mathematics does? What exactly does mathematics accomplish?

Mathematics uses numbers to perform calculations. Numbers are a way of simply recording amounts. Arithmetic is a structure of operations which is performed on numbers. Geometry uses numbers to provide measurement and relation. Numbers, and their system of relation, are a fundamental mathematical tool for discovering truths about the universe.

Then we introduce algebra, and we completely forget about numbers. Instead we use symbols and analyze patterns. Functions allow us to categorize patterns and compare the behaviour of different patterns.  

Mathematics by induction isolates behaviour of a system and anaylzes it. Probability is a mathematical mode of investigation used when extracting information from a certain occurance.

Linear Algebra provides further methods for relating patterns of information. Calculus analyzes changes between these patterns to help predict and imagine percieved outcomes. Differential Equations combine many tools in mathematics to create models of systems to help further understand them.

There is so much to know, and even this is not everything! But what is the point? Why would I bother learning mathematics? Click through this online textbook to find out!