best languages to learn as a newcomer
TomOfTTB: It depends what platform she wants to develop her solution for.If she's doing web based development I'd suggest Javascript.  Javascript has a lot of superflous non-sense in it but if you learn it the right way it's a very powerfult language.  More importantly if she wants to develop web applications that do a lot of math calculations she's probably better off learning a browser based technology (so the burden for all those calcs won't be on the server)Anyway, I'd suggest Javascript: The Good Parts as a book to start with if she goes that way.If she's doing desktop apps I'd probably suggest learning Actionscript and Adobe AIR (which provides the most cross-platform bang for the buck)