Overview
A function represents a mapping from a set of elements, called the domain, to another set of elements, called the range. It is a central notion in mathematics, and has had multiple definitions over time. However, the Set Theory Definition has come to be the standard definition in abstract mathematics.
Classical Analysis
- Function Spaces
- Banach Spaces - a standard space that can represent function space well. Generally required for doing the basics of analysis.
- Hilbert Spaces - function spaces with Lebesgue measure also form Hilbert spaces, which are critical spaces in many areas of mathematics and physics.
- Operator Theory
Additional Function Topics
- Arity - classifies a function by the number of arguments
- Category Theory - represents an algebra of functions
- Lambda Calculus - used in computer science to represent function computation.
- Generalized Functions
- Approximation Theory