Reading the Comics, April 1, 2021: Why Is Gunther Taking Algebraic Topology Edition


I’m not yet looking to discuss every comic strip with any mathematics mention. But something gnawed at me in this installment of Greg Evans and Karen Evans’s Luann. It’s about the classes Gunther says he’s taking.

The main characters in Luann are in that vaguely-defined early-adult era. They’re almost all attending a local university. They’re at least sophomores, since they haven’t been doing stories about the trauma and liberation of going off to school. How far they’ve gotten has been completely undefined. So here’s what gets me.

Gunther, looking at sewing patterns: 'You want me to sew pirate outfits?' Bets: 'I'm thinking satin brocade doublet and velvet pantaloons.' Les, not in the conversation: 'Nerd.' Gunther: 'I'm thinking algebraic topology and vector calculus homework.' (He shows his textbooks.) Les: 'And nerdier. (Les pets a cat.)
Greg Evans and Karen Evans’s Luann for the 1st of April, 2021. This and other essays discussing topics raised by Luann are at this link. The overall story here is that Bets wants to have this pirate-themed dinner and trusts Gunther, who’s rather good at clothes-making, to do the decorating.

Gunther taking vector calculus? That makes sense. Vector calculus is a standard course if you’re taking any mathematics-dependent major. It might be listed as Multivariable Calculus or Advanced Calculus or Calculus III. It’s where you learn partial derivatives, integrals along a path, integrals over a surface or volume. I don’t know Gunther’s major, but if it’s any kind of science, yeah, he’s taking vector calculus.

Algebraic topology, though. That I don’t get. Topology at all is usually an upper-level course. It’s for mathematics majors, maybe physics majors.  Not every mathematics major takes topology.   Algebraic topology is a deeper specialization of the subject. I’ve only seen courses listed as algebraic topology as graduate courses. It’s possible for an undergraduate to take a graduate-level course, yes. And it may be that Gunther is taking a regular topology course, and the instructor prefers to focus on algebraic topology.

But even a regular topology course relies on abstract algebra. Which, again, is something you’ll get as an undergraduate. If you’re a mathematics major you’ll get at least two years of algebra. And, if my experience is typical, still feel not too sure about the subject. Thing is that Intro to Abstract Algebra is something you’d plausibly take at the same time as Vector Calculus.  Then you’d get Abstract Algebra and then, if you wished, Topology.

So you see the trouble. I don’t remember anything in algebra-to-topology that would demand knowing vector calculus. So it wouldn’t mean Gunther took courses without taking the prerequisites. But it’s odd to take an advanced mathematics course at the same time as a basic mathematics course. Unless Gunther’s taking an advanced vector calculus course, which might be. Although since he wants to emphasize that he’s taking difficult courses, it’s odd to not say “advanced”. Especially if he is tossing in “algebraic” before topology.

And, yes, I’m aware of the Doylist explanation for this. The Evanses wanted courses that sound impressive and hard. And that’s all the scene demands. The joke would not be more successful if they picked two classes from my actual Junior year schedule. None of the characters have a course of study that could be taken literally. They’ve been university students full-time since 2013 and aren’t in their senior year yet. It would be fun, is all, to find a way this makes sense.


This and my other essays discussing something from the comic strips are at this link.

A Timeline Of Mathematics Education


https://twitter.com/dannytybrown/status/670174694390239232

As Danny Brown’s tweet above promises, this is an interesting timeline. It’s a “work in progress” presentation by one David Allen that tries to summarize the major changes in the teaching of mathematics in the United States.

It’s a presentation made on Prezi, and it appears to require Flash (and at one point it breaks, at least on my computer, and I have to move around rather than use the forward/backward buttons). And the compilation is cryptic. It reads better as a series of things for further research than anything else. Still, it’s got fascinating data points, such as when algebra became a prerequisite for college, and when it and geometry moved from being college-level mathematics to high school-level mathematics.