## Groups, fields, finite fields, zzzzz…

I’m admiring mathematicians for the consistency, strictness and clarity in defining and extracting patterns into definitions and theorems.

The good thing about math is to learn about discipline and consistency, and I’m still working hard on digesting those symbols that appear so similar yet define totally different thing.

I always get confused when I ask myself what’s the difference between $Z_{p}$, $F_{p}$ and $F_{p^m}$ and $GF(p^m)$.

Here’s the definitions, thank God I finally found this, from the same book:

There are also $F_{q}$ and $F_{q}^*$. Uffhhh, it’s amazing how one symbol could represent so many things…