But again, what does “easily accessed and manipulated by programs commonly available to the public.” mean? I hope you understand that I'm truly trying to figure this out, because replacing the software that we run (if it doesn't meet this nebulous standard) could cost millions in terms of software, hardware and staff time.

You might want to look back on your cavalier admission of laziness and ask yourself what's wrong with this picture. THAT, it seems to me, is what YOU need to "learn rather quickly."

As to the course…

No matter how good a programmer someone might be, his/her custom application of slick code sitting atop a lousy database design will be a bust. Database design is its own kind of art form. This course, clearly, covers much of what one needs to know in order to create a good and flexible database structure before one begins writing the code to make it functional and useful.

A very, very simple example of bad database design: Not separating the name field into logical sub-parts. In other words, not having a "First Name" field, and then a separate "Middle Name or Initial" field, and then a separate "Last Name" field. If one puts the entire first, middle and last name into the same field, then how, later, does one print-out a report wherein the name is in the format "last-comma-first"?

Of course, one can write a semi-sophisticated parsing algorithm, but no amount of sophistication can successfully cope with things like last names which have spaces in them, for example. Computers join things together really well, but they don't bust them apart very accurately. Good database design, therefore, ensures that all data is broken down and stored in said database in the smallest and most logical constituent parts possible so it will be easier for the computer to put things back together however one desired it at report time.

That is the kind of stuff that that course teaches… only, obviously, including much, much more sophisticated stuff than my simple example. I'm just trying to help you understand the essence of it.

Databases have parts which "relate" to one another so that one doesn't have to keep entering the same information over and over into different parts of the system. Building and organizing those parts can be tricky. If not done right, the database will be cumbersome to use, and slow. Good structural and access optimzation techniques are called for to figure it all out… and that means a lot of "what if" kind of mathematics… hence the requirement for algebra and calculus.

This is not the sort of course in which one may be "lazy." If you're not prepared to do the work, then don't take the course.

Hope that helps.