## Jeremy Côté

Bits, ink, particles, and words.

# Two Types of Mathematics

Broadly speaking, I classify mathematic into two bins. On the one hand, there’s the mathematics that many students in university must learn, such as calculus and linear algebra. These form the bedrock of many jobs in the corporate world, and so students from business, computer science, finance, and other disciplines have good reason to learn these topics. Likewise, there are parts of mathematics that are useful to scientific disciplines like physics, chemistry, biology, and so on. The common thread here is that these mathematical courses are operational.

# One-to-One and Onto

When learning about functions, a few properties come up over and over. In particular, we often hear about functions being one-to-one (injective) or onto (surjective). These are important properties of functions that allow one to set up correspondences between sets (bijections), as well as study other features of various functions. I wanted to go through these two properties in a slightly different way than what most sources will do to explain them, so hopefully this will be a good analogy to keep on mind when discussing these two properties.