Mathochism: Unexpected gaps

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

Under the compass of Damocles As I’ve been studying math these past three years, I’ve worried that, in spite of trying my best, there would be gaps in my knowledge. And, since it’s all cumulative, these gaps would eventually widen to such an extent that I couldn’t follow along any more.

This hasn’t happened, exactly. The anxiety that paralyzed me last semester doesn’t count, since the knowledge was always in my brain. I was just too freaked out to access it. In calmer moments, it all returned.

In today’s class, though, I realized that there were gaps not of my making. For example, I never learned about greatest integer functions, either in intermediate algebra or in pre-calculus. This is dismaying, because while I tried to guard against gaps while in the Brofessor’s class, I didn’t think I would have to do that in the Youthful Professor’s class.

True, YP acknowledged he wasn’t able to get to everything. Half-angle trig identities were on that list, but he at least told his students about them so that they could work on their own. And so I did.

But greatest integer functions? Not a word on those. Perhaps he thought we’d covered them before (if so, FU, Brofessor, for wasting my time with your BS digressions on global warming). Who knows? I do remember them coming up in the Calc Dementor’s class last spring, but he didn’t go into specifics, no doubt assuming we already knew. I just sort of fumbled along, because by that time I had lost my math confidence. I just looked at those nested brackets and shrugged.

My new professor (and I’m still working on a nickname), however, was willing to enlighten us, and for that, I am grateful. For most in the class, it was review. For me, it wasn’t, so now I need to through my other textbooks, and my online resources, to make sure I understand what is going on.

When I got home from class, I ranted to my spouse about the fact that, in spite of starting at the beginning in the same department, with presumably the same curriculum, some professors didn’t prepare their students appropriately.

“That happens everywhere,” he informed me peevishly. “Some professors skip some parts and emphasize others. That’s just the way it is.”

To be fair to my spouse, he is buried in work this week, and exhausted, and when that happens, he gets both peevish and fatalistic. I should have held my rant for after he had sucked down that cup of tea. But I get the feeling he is also right, as infuriating as that may be. So there’s another obstacle identified: how do I cope with concepts deemed necessary by some professors, yet not by others? And how does a student prevent a gap from starting when the next professor just assumes the previous one covered something already?

All text copyrighted by A.K. Whitney, and cannot be used without permission.



  • The greatest integer function really isn’t that important except that it illustrates several concepts in math, so it does pop up several times as an instructive example. It’s not surprising at all that your previous professor would skip over it; that’s one of those things that your current professor should mention and ask if everyone is familiar with it and explain if not. I know it’s daunting to ask questions, but it really is a necessary part of math education; an instructor can never be 100% sure that the whole class has covered all the material given as a prerequisite for the course.

  • Hi Antonia, great to see you!
    Thanks for your insight on this function. I was feeling dismayed that I had somehow missed something crucial. I really appreciate this new professor being willing to review it and not assume; by doing that, she has already set a different tone from the other guy. That’s good — or at least I hope it is!

  • Pretty much any function outside of the ones they typically teach you to draw before you take calculus isn’t terribly important, thank goodness. I do math in part because I can’t memorize things. 😉

    I’m glad you finally have someone open to questions teaching you! Talking to yourself in front of a chalkboard is such an ineffective teaching method, but it’s also a pretty common one. I still don’t understand why people do it. If I’m teaching a class, I already know the material, so teaching it to myself is really boring! 🙂

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