Regarding the MSc it's more than I could ask for. There are introductory courses in statistics, programming, databases, machine learning etc and there are specific elective courses like Big Data Systems, Natural Language Processing etc.

TBH I think that especially the math/stats background is something invaluable that is not really learned by reading data science specific books, and usually it's neglected. It might not be what strictly prerequisite to work with machine learning algorithms but it's a huge help to delve deeper into it.