to your point about analysis, the folks with a CS education here (myself included) should ponder this quote from the intro: "...we have written this book to cover the theory likely to be useful in the next 40 years, just as an understanding of automata theory, algorithms and related topics gave students an advantage in the last 40 years. One of the major changes is the switch from discrete mathematics to more of an emphasis on probability, statistics, and numerical methods." some of the key stuff in statistical learning isn't even real analysis, it's functional analysis (usually two courses later).