Format of final exam

The exam will roughly have two parts: the first part to mainly decide if you pass the course or not, and the second part to mainly decide your score.
To get enough points in the first part, I want you to have basic but precise understanding of the principles behind this course. For example, you want to know how to mathematically model various
concepts, but ¡°pop-sci¡± style explanation in plain words would not be enough. On the other hand, you do not have to give precise reasoning in this part.
The second part is more advanced, so you are expected to give rigorous formulations and reasoning. However, you do not have to memorize proofs of various theorems. It is more important that, given a mathematical problem and a tool to study it, be able to explain how to use that tool to study such problem, with an illustrating example.