Is Discrete Mathematics hard? Is it pure or applied math?
Don't you think this is a rather subjective question?
Besides that, it depends on where you start from, which ways of thinking suits you more and which less. E.g. I'm pretty bad when it comes to counting, so combinatorics isn't really one of my favorites. But there are people, who like it.
In it's principles, it is pure math. Its applications on the other hand vary from information science over to operations research and strike almost everything you can think of. It's a discrete world out there.
It's as hard as you would like. Both pure and applied.
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