Often, we come across functions that we do not know how to evaluate without having qualitative knowledge of the input value. For example, $\sin(x)$, $\max(x, y)$^{1} , and $|x|$.

For example, how do we compute $\min(x,y)$ without knowing beforehand what $x$ and $y$ are, using only a basic calculator^{2}?

This question, along with many others, will be answered in this short course.

$\max$ stands for

*maximum*. $\max(x,y)$ will always return the larger value out of $x$ and $y$. Similarly, $\min(x,y)$ (*minimum*) returns the smaller of $x$ and $y$.↩For the purpose of this course, we will assume our calculator to have the following capabilities:

- Addition, Subtraction, Multiplication, and Division
- Exponentiation
- including square roots

- Floor and Ceiling

These basic capabiities will enable us to construct other, more complex capabilities.↩