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.

Investing: Kelly Criterion

Over the last few years - while researching trading strategies - I happened to learn about the Kelly Criterion:
http://en.wikipedia.org/wiki/Kelly_criterion

In probability theory, the Kelly criterion, or Kelly strategy or Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any essentially different strategy in the long run. It was described by J. L. Kelly, Jr in 1956

http://www.bjmath.com/bjmath/kelly/kellyfaq.htm