Disk BASIC was a TRS-80 product.

I think you completely misread what I'm suggesting. What I propose is that the OP, who describes himself as a neophyte when it comes to software, find someone with some experience in that field to be a mentor and help get him off to a good start.

Here's my rationale: I've been writing software for 31 years and have 25 years of industry experience. For the last seven years, I've been working for a company that is staffed mostly by electrical engineers who specialize in signal processing and are really, really good at it. A lot of what they write works, but software isn't their bailiwick, and it lacks the organization and forethought about how it might be used in the future that people who've been around the block tend to put into it.

By teaming up with someone in CS, the OP won't be figuring out how to do it right by trial and error and perhaps turning out ugly code in the first place, and he gets to spread some of the applied math gospel to the heathens over in CS. :-)

Don't take this the wrong way, but you're in math, not CS. Call the CS department, find someone who's willing to team up with you on this and work together on turning the mathematical end of your contributions into good code. You'll come out of it with a better understanding of how software should go together, your CS cohort will get some insight into applied math and both of you will be better for the experience.

...And don't think for a minute that the issuing bank doesn't keep records of which accounts were issued to what customers and when.