You are to be commended for your desire to keep your mathematical and analytical skills in good working order. The world needs more people with your attitude.
One way of starting to learn something is to be motivated by its potential to help you or give you new insights into today's world. While I always liked math, it wasn't until I found some good, practical applications that I decided to build a career around it.
What turned the corner to me was the field of Operations Research, which applies mathematics and computing to real-world decision problems. Problems like work scheduling, vehicle routing, staff planning, production and inventory management, queueing, quality control, and general optimization. The basic approach is to identify the underlying problem, build a decision model, solve the mathematical model, and implement the results. Check into such classic models as linear programming, the transportation problem, integer programming, network flows, queueing theory, and Monte Carlo simulation.
Others can explain this better, and a good place to start is:
which describes Operations Research (O.R.) as "the science of better" and defines it as "The discipline of applying advanced analytical methods to help make better decisions." That site has lots of examples and links to more information. Other good sites are:
In O.R., mathematics underlies everything, but is always applied to a wide variety of real problems. Without the applications, the field would simply be applied mathematics or statistics. By combining the two, the problems become not only interesting, but relevant and, sometimes, quite profitable.
Good luck in your quest, and thanks for asking...
