Math in 2D game programming - Examples?

[GetOutOfBox]

I've been programming for a while now, and in my experience I've just used Cartesian coordinates and addition/subtraction/multiplication/division (well operator logic too technically, but that's a given).

I'm curious too see some actual applications of other relevant maths to 2D game programming. I feel like my bottleneck is math and not C++ knowledge. Concept examples of using trig/inverse trig (i.e atan2(), etc), or any other math concepts would be great. Actual code snippets are not necessary, but would be very helpful.

Note that I did go to Google first, but I found a lot of answers to this question just list related math concepts without actually giving some examples of how they're useful. I tend to learn best when I can link a concept to a practical use.

Thanks!

[MiiNiPaa]

Trigonometry:
Create 7 floating companon in circle around you (polar coords mostly and sin/cos to translate into cartesian)
Find angle you should rotate to face another object (atan2).
Linear algebra:
Rotation matrices (self-descriptive).
Graph theory (Widely used in pathfinding). Fuzzy logic, set theory (Used in AI). Statistics and probability (AI, game balancing, setting some random dispersion in the game). Game theory (AI, game balancing)
Numerical analisys to aproximate complex functions.
Bunch of other concepts not related directly to games but used in alghorithms you will need:

[GetOutOfBox]

Good ideas so far!

In terms of rotation matrices, I'm assuming they are a lower level concept if you're righting your own OpenGL or DirectX code right? Is there any higher level use for them (in terms of use with an established rendering API like SDL or SFML)?

I hear about linear alegebra a lot, are there other relevant uses for it?