You need calculus to understand probability and statistics, since probability is fundamentally a question about measures and statistics about integrals of varia

You need calculus to understand probability and statistics, since probability is fundamentally a question about measures and statistics about integrals of variables on measure spaces. Even if you don't know the details of measure theory, certainly you need some notion of limits. Calculus is not much more than a systematic application of limits to algebra and geometry. Even for discrete math you need to understand ideas like convergence, otherwise probability is filled with paradoxes. "Pick a number!" "Any number?" "Well, numbers that are big are less likely to be picked." "How much less likely do they need to be in order for your question to have a sensible answer?" "Let's talk about convergence" You also need algebra and trig. How else would you know what an inner product is without trig? Or that correlation is just an inner product? You need some linear algebra as well to understand cross products and inner products, otherwise they will be these magical things. Many ideas in discrete math should be understood as the discrete versions of ideas in continuous math, with the continuous math ideas often being more natural and easy to understand. Sometimes one of the best ways to estimate an infinite sum is via an integral that is much easier to solve. A lot of complicated sums seem magical until you see that they are just the discrete versions of integrals -- sometimes path integrals -- with various weights that come from measures on the spaces of interest. So if your interest is blind computation, you don't need a lot of discrete math at all, you just need to learn what the symbols mean and how to look recipes up in books. But if your focus is on understanding what you are doing, then there is not a magic barrier between discrete and continuous math, most discrete math can be viewed as a discretization of continuous ideas, and in some cases ideas in continuous math can be better understood as limiting cases of a discrete result. The sad thing is that this is all stuff you will get in a good gymnasium in Europe but you may need to wait until college to get it in the U.S. Absolutely no reason why a teenager can't learn calculus, limits, trig, probability and statistics, as well as basic ideas in group theory. Really algebra, geometry and trig you should get in elementary school so that you can get calculus, probability and statistics, basics of differential equations and some topology in high school. Then you can take specialized courses in algorithms if you are into CS or say PDEs if you are into engineering -- this is all stuff that should be taught in high school. College tracked teenagers in Europe often learn that and more, and not just in math centered gymnasiums, but the price of that is tracking, otherwise you have to go as the slowest learner who has no interest in a specific major in college.