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)
Doesnt this exclude heavy drinkers who died before the age of 55-65? This skews the results towards individuals whose bodies are presumably quite resilient against alcohol related health complications and managed to keep the person alive long enough to be included in this study. The title should read something more akin to "Late life heavy drinkers outlive late life nondrinkers"
Today's financial mathematicians are equally adept at programming and computational science. It seems unlikely that these guys are your run of the mill programmers.
As the author suggested, Is there any indication that they aren't preprogrammed flight trajectories? And with so many cameras, the instrument setting is so "brute forced" that it seems hard to imagine a setting where this work could be applied. This http://heli.stanford.edu/ seems a lot more impressive to me
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