What is needed to know to study algorithms?

I just started to read Thomas H. Cormen's book "Introduction to algorithms" (2nd edition) and just figured out that from first 40 pages I'd understand about 30%-40%.

Can you help to realize what parts of math must I know to be more familiar with that book and/or algos at all? Also important to know in what sequence should I study that things.

Let's say I'm starting from arithmetic then algebra+geometry. Then what? Heard about math logic (right?).

That can help me to know such important things and be ready to help to my children.

Just help if you can, please.

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What didn't you understand from Cormen's book? This happens to be the same book I first learned algorithms from. If I recall correctly, the only technical material comes from its use of recurrence relations and $O(\cdot), \Theta(\cdot),$ and $\Omega(\cdot)$ style estimates, all of which it defines in-book. –  mixedmath Aug 3 '12 at 22:59
Although i do agree with @mixedmath that Cormen's book should be sufficient on it's own, but in general the subject of algorithms, would require primarily basic algebra, Discrete Mathematics, some real analysis (sequences and series + limits) and asymptotic analysis. –  Hardy Aug 3 '12 at 23:14
It also helps to know something about the basics of probability and matrix algebra. The chapters on data structures won't seem very relevant if you've never programmed before. –  user17794 Aug 3 '12 at 23:38
I think that I don't know algebra. My school education was too poor and in university we were taught only 1 semester of factorials (humanity specialization) and simple statistics. So I decided to learn math from scratch (arithmetic, algebra, analysis, etc.) but I've stucked with the choice of subjects to learn. Another thing that confusing me is order of subjects studying. I.e. what I need to know first - matrix algebra or discrete Mathematics and so on. –  Крайст Aug 4 '12 at 10:10