The reason why many tutorials on collision detection are written in a cryptic and almost impossible to understand manner is actually quite simple.
It's because you don't have enough understand of geometry. More specifically vector calculus, and, if the author is a real dick, linear algebra or even higher level stuff.
Often the authors of these tutorials are university/college students or majors. They learn that the solution is not as important as how you derived the solution. So, they often go into great length to explain how the solution is derived.
This becomes especially annoying if the author is good at mathematics. As HE will use advanced mathematical terms and rules. Often not caring to explain them. For anyone not familiar with higher level math, a double integral mixed in with matrix math looks more like a cryptic message than anything meaningful.
These tutorials are not written in layman terms. Many won't even show an implementation. If they do it's often written in very smart c ++, so it's extremely fast and contains four blocks of assembly code mixed in with template meta programming for extremely fast execution.
Anyway, point is, want to do programming, and especially game programming. Better get familiar with mathematics.
Gatleos, if you are just using simple slopes, you could technically just compute the height at any point on the slope.
If we say point A is height 10 and B is height 0, then it descents linearly from A to B. Essentially, you just truncate your AABB from A to B, and calculate the maximum height at the lower bound of the AABB.
It's simple and with some fiddling it will work just fine.
For more advanced and general collision, use learn about ray/shape intersection. This should give you a good idea on how to do more useful shape collision sweeps.
If anyone wants, I could write some collision detection example codes. Like, ray/sphere intersection, ray/plane and ray/triangle?