**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.”

## 5 comments:

That's the same problem I immediately pinged on. I always loved the numbering system back at UMD, probably because it was reminiscent of the Dewey decimal system.

The first number cut up courses (*very* roughly) into years. 000s were remedial, 100s-400s were freshman through senior level, 500s were masters, 600s were into doctoral, 700s were advanced doctoral, and beyond that was generally "some number to use for original research". Within that, each department had their own system, and obviously I was looking at math.

The next number (at least in the math department) was used for a rough sense of a field within mathematics. x30s were real analysis, for instance, x60s were complex analysis, and x00s were algebra. I forget the exact details of all the fields.

The third digit signified the level of a course, usually in some sort of sequence.

An undergrad's first course in abstract algebra would be 400, which followed on to 401 to go deeper into field and Galois theory. A grad student preparing for their algebra qualifier would start with 600 and move on to 601. (Theoretical) linear algebra would be thrown into 405, being an undergrad algebra course. There were grad-level sequences in real analysis (630-1) and complex analysis (660-1), and I took a course there in "one and several complex variables" (663).

One-off special topics courses in fields often got the xx9 slot, while independent study and original research fell into x98 and x99.

The lower levels were a bit fuzzier, mostly due to having to cram more intro-level classes in. But still 140-1 was calculus, and 240 was multivariable calculus. 250-1 (now 350-1) was a

melangeof advanced calculus and linear algebra offered by invitation only to outstanding freshmen to give them a high-speed ramp up into proof.The upshot was that I could tell you from the course number roughly what was in a given course. And it all made perfect sense.

We had a system rougly like the one unapologetic describes when I was at the University of Western Ontario. First year undergraduate courses were always prefixed by "02" unless they were introductory language courses (which start below the level you'd normally be required to have coming out of high school in any given language), which were 01. Most of the first-year level courses that were the prerequisites for the second-year courses were numbered "020." Others were "021, 2, 3" etc. Second-year level general-interest courses (ie. pure electives) were numbered "1xx." Second-year level degree-requirement courses were numbered "2xx." Third year level degree courses were numbered "3xx." Seminar courses and senior thesis courses were numbered "4xx." Undergraduate/graduate seminars were numbered "7xx." (Yes, there were courses that you could take as an undergraduate where you might be in the same class as grad students. And I thought being a Master's student in a room full of PhD students was bad enough!)

I thought it made perfect sense when I was there, but OTOH, I had four years to get used to it. Of course, they've completely changed the course numbers now...

Of course, that might be sweet for the math students, but the rest of the university might object.

But so many of the second year courses have the same prerequisites.

You can't use the same number for pointset topology and PDEs even if they both only require calculus and linear algebra.

What about classes with a choice of prereqs? At my university, there were at least three different ways to do your initial calculus sequence: calc I and II, Review calculus (for students who had it in high school, does both in one semester), or Honors Calculus (for masochists). Any one of those options would satisfy the "basic calculus" requirement.

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