If youre looking to learn mathematics as a tool rather than an end goal the list above seems far too abstract. A good foundation in analysis is probably as abst

If youre looking to learn mathematics as a tool rather than an end goal the list above seems far too abstract. A good foundation in analysis is probably as abstract as you'll need for a majority of applied fields. For computational science and learning you need to know (albeit very well): linear algebra (strang, trefethen, golub and van loan) optimization (nocedal, bertsekas) probability (rice, casella & berger, grimmett) statistical learning (tibshirani, bishop) A good free online book was recently an HN topic: http://news.ycombinator.com/item?id=1738670 http://news.ycombinator.com/item?id=1738670