Before Wolfram changes their mind: http://www.wolfram.com/products/mathematicahomeedition/ $295 best deal on the planet. Don't think just do it.
Q: How is Mathematica Home Edition different from the professional version of Mathematica? Mathematica Home Edition is a fully functional version of Mathematica Professional with the same features. Amazing. $2,495 you can get for $295. That will cover my Friday loss.
It won't cover anywhere near our Friday's losses. It makes a great gift for junior high schooler, all the way to the professional that needs to use computer assisted math or visualization in their work.
The demonstration project are super cool. For example: http://demonstrations.wolfram.com/MercurysPerihelionPrecession/ Here is all of them: http://demonstrations.wolfram.com/topics.html
I realize most here prefer Matlab or Maple but I've used Mathematica for years and have found it to be crucial for my trading and various other projects. I suppose it boils down to what works for/with you. Trials are a good start.
Am I correct in assuming that for one to even begin to make use of this tool at its most elemental level, one has to be well versed in the mathematics field and have a fairly robust knowledge of economic theory and practice?
Not necessarily, as with most programs, gui and layers of complexity has evolved over time and become more intuitive and simplistic. Jr. High students use Mathematica so I would imagine almost anyone with normal intelligence and determination would be able to leverage Mathematica's power. Of course, it's just a tool, and like all tools, they have limitations and results may be proportionately related to the user.
You can load up a solution developed by someone else and modify the parameters to your needs. The software will show you the result for your case. Like this example developed by Stephen Schulist, is about the Kelly criterion. http://demonstrations.wolfram.com/KellyPortfolioAnalysis/ There are probably thousands of solutions to choose from. Like you can model this: If my win% is 60% how many trades do I need per month to achieve a 95% probability that my result will be consistent every month. You can see that there will be a difference between making 3 trades per month or 100 per month. With 3 trades per month with 60% success rate your monthly result will vary allot. With 100 trades you will get a very consistent monthly result but how many trades will give you 95% confidence level? Using Monte Carlo with Mathematica you can find out. You can also do it with Excel. But not as nice of a solution.
Let me just say that whatever you are doing in math, if you want to visualize it, mathematica is the way to go.