I just finished a Discrete course this spring. It was much different then any other math course I've taken. I ended up with a C+.
It relies heavily on Algebra principals, but doesn't use much else from the math fields. A lot of the things taught are new concepts that don't really fit neatly into any other class. That is one of the challenges of the class because you will be shifting between ideas so rapidly.
Here's a rough list of topics covered:
- Formal logic
- Sets, relations, matricies
- Functions
- Number theory and graph theory
- Counting principles, (sum rule, product rule)
- Probability
- Permutations and combinations
- Recurrence relations
- Mathematical induction, (big and complicated one)
Personally I found Khan Academy and Purple Math to be really helpful when I was going through homework or studying for a test.