I think it's hard to get those basics in an undergrad program. CS often has the problem that the math basics are not teached as rigorously as it should (I thin

I think it's hard to get those basics in an undergrad program. CS often has the problem that the math basics are not teached as rigorously as it should (I think calculus I/II and linear algebra I/II should be exactly the same as the lectures for math). Then it misses measure theory (usually in calc III) and therefore you are going to miss solid fundamentals in probability. Optimization is also usually absent, it's sometimes squeezed into the numerical math. lecture but it shouldn't since numerics (or better scientific computing) is so important. You also want some statistics course. Math usually lacks the whole machine learning canon, from SVM to NNs, from bayesian methods to statistical learning theory. I just see the same statistics lecture everywhere building upon probability and deriving good estimators and their properties and that's all. Also, you might miss CS basics like algorithms and struggle with the basics of scientific computing (programming in C, knowing all your matrix decompositions etc.). Also, no knowledge of git, how to navigate a server just with a shell etc. I think you will either have to learn the missing parts after your undergraduate, for example as your master, first year in your phd, or be really lucky! I think most miss a significant chunk of the topics after completing their undergraduate.