Mathoverflow.net

An incredibly rich resource for questions and answers:
http://mathoverflow.net/

Evan Miller's essay: The Mathematical Hacker

http://www.evanmiller.org/mathematical-hacker.html

Desmos.com - Online Graphing Calculator

I experimented for a bit this evening with  a very cool online graphing calculator:
 https://www.desmos.com/

The interface is clean and intuitive - and the responsiveness of the web application is excellent.

Checkout some of the recent graphs here:
https://www.desmos.com/recent

WhyDoMath.org

http://www.whydomath.org/

Terence Tao

While reading a recent posting by Cal Newport on his Study Hacks blog, I was intrigued by his reference to Terence Tao's mathematics blog

PyMC examples by Mat Kelcey

http://matpalm.com/blog/2012/12/27/dead_simple_pymc/

The St. Petersburg paradox

http://en.wikipedia.org/wiki/St._Petersburg_paradox

In economics, the St. Petersburg paradox is a paradox related to probability theory and decision theory. It is based on a particular (theoretical) lottery game (sometimes called St. Petersburg Lottery) that leads to a random variable with infinite expected value, i.e., infinite expected payoff, but would nevertheless be considered to be worth only a very small amount of money. The St. Petersburg paradox is a classical situation where a naïve decision criterion (which takes only the expected value into account) would recommend a course of action that no (real) rational person would be willing to take. Several resolutions are possible.