Discovering Epic LaTeX IDEs

So, today my adviser and I went over a few really good $LATEX$ IDEs and ended up choosing Texmaker as our default one for writing publishable, mathematical articles and journals.

I felt like typing one homework from my differential geometry class and this is what I ended up with (it's incomplete):

Differential Geometry Homework 2

I'm still pretty new to this, but hopefully I can end up putting really good-looking documents together (hopefully no one cheats off of this, lol).