One of my classes this semester is Discrete Math. I ended up in this class because of a scheduling problem. I originally had Linear Algebra MW 5:00-6:50, and then Prob & Stats 7:00-9:00. Unfortunately, my linear algebra class was cancelled, leaving me just the one class. I decided that an extra math class is always a good thing, and signed up for Discrete Math in the empty slot.
I didn't actually know what Discrete Math was, I think.
The "discrete" in discrete math contrasts basically with the continuity of, e.g., calculus. When we deal with functions, we are mostly dealing with functions in the natural numbers (1, 2, 3, ...). There are things like set theory, combinatorics, probability, and graph theory.
One of the most challenging topics for me so far has been recursively defined relations. These are things like, for instance, the Fibonacci sequence,
1, 1, 2, 3, 5, 8
where each number is the sum of the previous two.
We've been learning different techniques for determining the "closed form" rule for such a sequence, which allows you to do something like calculate the 100th term without calculating all of the ones in between. (The "closed form rule" is what you usually get for a function, like f(x) = x + 3, instead of it being defined in terms of the previous term or terms.)
So far, the class is very interesting. There are about 12 students, so they all become familiar pretty quickly, and our professor includes a lot of class discussion and has us lecture each other at the board a fair amount by asking questions like, "Can anyone come up here and explain why this makes sense?" or "Would someone repeat what I just said in a different way?"