A brave new numbering system
It depends on many factors
My friend Steven insisted that his colleagues had missed a golden opportunity to adopt a thoroughly rational system for numbering their courses. When his college embarked on a program to renumber all their courses, Steve had proposed a brilliant new scheme:
“It makes total sense, Zee. Instead of assigning numbers practically at random, you begin by assigning prime numbers to the elementary introductory courses.”
“Okay,” I said, “at least you don't have to worry about running out of primes.”
“Right!” he replied.
“And,” I continued, “I infer that you intended to use composite numbers for the non-introductory courses—namely, those with prerequisites.”
“Right!” repeated Steve. “You get the idea, but do you know how the composite numbers would be assigned to the more advanced courses?”
“No. Tell me. You have a scheme for this?”
“More than a scheme. It's a thoroughly rational system. You see, the factors of the composite numbers would correspond to the prerequisite courses!”
I reflected on Steve's idea for a moment.
“Okay, Steve. I get it. Like trig, for example, which requires both geometry and algebra as prerequisites.”
“Yeah, that's the idea. If algebra were Math 2 and geometry were Math 7, then trigonometry could be Math 14. You can tell from the number what the prerequisites are.”
“Nice. But what about precalculus, which requires trig as a prerequisite? Since trig isn't prime, factoring the calculus number wouldn't necessarily tip you off that trig is a prereq. It's a problem, isn't it?”
“Well, the system isn't perfect yet, but it has potential.”
“Perhaps, Steve. Certainly students would be warned when a course has a large number attached to it. Can you imagine something like Math 343?”
Steven pondered for a fraction of a second.
“Okay. I'll bite. What would that be? Three hundred forty-three is just seven cubed.”
“Exactly. And if Math 7 is algebra, that would mean they'd have to take algebra three times before they're ready for Math 343.”
Steve laughed.
“Big deal,” he replied. “Many of my students are doing that already.”
