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

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"

The study is about a population aged between 55 and 65 and what happens to them in the following 20 years according to their drinking patterns. So it's not fair to say that the results are skewed. It only excludes 40-year-old drunks in a trivial way: the study is not about them.

Analogy: suppose we have a study about the effect of using or not using sunscreen on a Caucasian population. It wouldn't be fair to say that the results are skewed just because they didn't include non-Caucasians.

>The title should read something more akin to "Late life heavy drinkers outlive late life nondrinkers"

Indeed, the title of the paper is "Late-life alcohol consumption and 20-Year mortality".

I understand it's normal to be skeptical of whether the results apply to younger people but, as someone else mentioned, I doubt that so many alcoholics die before 55. There's probably also some practical difficulty of doing an analog study for a younger range.

He was referring to the title of the article in the last sentence. I think if there is a better article on their research, it may help in explaining better as this article seems shy on explanations.

Also, the article cites that the nondrinkers may be more likely to be poor. This means a) less medical care to have doctors find things early, b) less stress, and c) they are not benefiting from escaping any stress they do have. Really, this article seems more like, "Stress kills, alcohol relieves stress temporarily, those who drink often have less responsibilities." So an alternative to alcohol: relaxation.

It also (as far as the article) does not go into detail about how many were from natural causes, etc. I'd be interested in whether the nondrinkers were more prone to heart attacks and this caused the discrepancy in deaths.

I can see so many holes in the research that I think it is far from conclusive on the matter.

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.

Sure they are smart. Question is: do they want to invest time to master the internals, needed to achieve high performance? Takes years to get there.

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