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Capla comments on The "best" mathematically-informed topics? - Less Wrong Discussion
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Epidemiology
As the token epidemiologist in the Less Wrong community, I should probably comment on this.
The utility of learning epidemiology will depend critically on what you mean by the word:
If you interpret "epidemiology" as the modern theory of causal inference and causal reasoning applied to health and medicine, then learning epidemiology is very useful, so much so that I believe that a course on causal reasoning should be required in high school. If you are interested in learning this material, my advisor is writing a book on Causal Inference in Epidemiology, part of which is freely available at http://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/ . For more mathematically oriented readers, Pearl's book is also great.
If you interpret "epidemiology" to mean the material you will learn when taking a course called "Epidemiology", or to mean the methods used in most papers published in epidemiologic journals (ie endless Cox models, p-hacking, model selection algorithms and incoherent reasoning about confounding), then what you will get is a broken epistemology with negative utility. Stay far away from this - people who don't have the time to learn proper causal reasoning are better off with the heuristic "if it is not randomized, don't trust it" . This happens to be the mindset of most clinicians, and appropriately so.
[Hey, I thought I was the token epidemiologist! ;) ]
I largely agree with Anders' comment (leave Pearl be for now; it's a difficult book), but there are some interesting non-causal mathy epidemiology topics that might suit your needs.
Concretely: study networks. Specifically, pick up the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World (or download the free pdf, or take the free MOOC).
It presents a smooth slope of increasing mathematical sophistication (assuming only basic high school math at the outset), and is endlessly interesting as it gently builds and extends concepts. It eventually touches many of the topics you've indicated interest in (game theory, voting, epidemic dynamics, etc), giving you some powerful mathematical tools to reason with. Advanced sections are clearly marked as such, and can be passed over without losing coherence.
And hey, if the math in the advanced sections frustrates your understanding... that's basically what you've said you want!
If I was once employed by a Dept. of Epidemiology does that also make me the token epidemiologist? :)
Epidemiology is defined to be things done by people in Departments of Epidemiology, correct?
That makes you an expert on epidemiology, duh :-)