I think pre-university math should focus on algebra and univariate calculus. Also sophisticated freshman programs focus on linear algebra and multivariate calcu

I think pre-university math should focus on algebra and univariate calculus. Also sophisticated freshman programs focus on linear algebra and multivariate calculus and analysis. See e.g. Math 55a/b at Harvard. You do need calculus for non-trivial statistics and even for some topics of discrete mathematics where continuous approximations are useful. For example Stirling's approximation [1] which if I recall well is on the first page of McKay's Information Theory, Inference, and Learning Algorithms. I think that if we talk about more modern approaches for mathematics, logic, type theory and interactive theorem proving could be great. I've been toying with this idea for teaching a course, but I haven't found suitable materials. [1] https://en.wikipedia.org/wiki/Stirling%27s_approximation https://en.wikipedia.org/wiki/Stirling%27s_approximation