The web is a great place to expand ones knowledge base. I've tried to keep abreast of interesting technical things by taking online classes from time to time using platforms like coursera.
The classes I have taken include:
The online Stanford class on probabilistic graphical models which you can read more about here. This involved a massive amount of work but I don't know of any other way to get such an introduction to this material. In all likelihood Bayesian networks will become the standard techniques for performing reasoning under uncertainty. My statement of accomplishment in the class can be found here.
The Columbia University course Financial Engineering and Risk Management which is now split into two classes. The first is here. You can find my statement of accomplishment for the original version here.
Worked Problems, Solution Manuals & Notes from Various Books
Here are some notes and problem solutions from a sample of the books I have studied from. I decided to put this material on-line because at some point I'd like to turn as many of these very informal "notes" into full fledged solution manuals. Currently, I am working on the solution manual for A First Course in Probability by Sheldon Ross.
This work was done for improving my own understanding of the material and I can't claim that every detail has been worked to completion. Often on a given problem or derivation when I felt I understood the rest of the required manipulations I would simply stop working.
Mathematical material is not always easy and it would be a lie to say that all of my attempts have been met with success. I have tried to work everything as correctly as possible and believe that many of the things I place here are correct, but I am only human and know some subjects much better than others. Please report any errors that you may find and I'll work to incorporate these into new versions (with credit of course). As a legal disclaimer: I can take no responsibility for any loss or damage that may be caused by using any of the notes placed here.
Finally, if anyone is looking for some practice with LaTeX I would be ecstatic to obtain even the smallest amount of LaTeX translations for any of the scanned (hand-written) notes. More information on LaTeX can be found here.