profkinyon.bsky.social
Mathematics professor at the University of Denver. Quasigroups, Semigroups, Automated Deduction. He/Him. Also hanging out at Mathstodon.
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Fine, I guess. Better than "C-set"
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Oh, that's what you meant. Well, in that case: tensor products. Over the years I've heard *many* grad students complain that they are expected to already know it when it was never covered in undergrad.
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I'm not saying those topics *should* be done, but I think they fit your criteria.
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I guess you mean topics which could, in principle, be covered in undergrad with a minimum of prereqs. A couple of things come to mind close to my own interests:
Semigroups/monoids (algebra courses usually just cover groups & rings),
Latin squares (combinatorics courses usually skip them)
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As a US calculus student, I learned concave up/down. When I took my first real analysis class, it was announced we were switching to to convex/concave.
In conversation, I mentioned that I often had trouble remembering which is which. The professor said:
It's easy. "e^x is convex". It rhymes!
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Yep. Just like the sine function and many others.
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Yeah, I didn't know if Farrell was serious or just trolling.
Oh well. RIP, I guess. With his passing, I doubt Word Ways will come back.
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I tried merging them but jealenvousy sounds like a skin condition
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These are called, amusing enough, "vowel movements". My favorite is l@st. Here is an article that discusses these and variations:
digitalcommons.butler.edu/cgi/viewcont...
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The one we call "un" for short
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"...the term 'Future Perfect' has been abandoned since it was discovered not to be."
(Douglas Adams, The Restaurant at the End of the Universe, Chap. 15, the bit on time travel and grammar)
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Oh, well, you can avoid the action jargon:
(1) the size of any conjugacy class divides |G|,
(2) H is a union of conjugacy classes
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Yeah, I was going to say something but you seemed rather lost in thought. I just assumed you were thinking about commutators as we all do from time to time.
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Consider the action of G on H by conjugation. The size of any orbit is no larger than p and divides |G|. So the hypothesis implies that any nontrivial orbit must have size precisely p. Does that help?
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I hope you will be thinking about how to avoid the idiots in cars "accidentally" trying to run you off the road.
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In a similar vein:
Let G be a finite group, let p be the smallest prime dividing the order of G, and let H be a normal subgroup of G of order p. Prove that H ≤ Z(G)
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The accepted answer here pretty much explains it:
math.stackexchange.com/questions/53...
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Axler doesn't get to eigenvalues until about 130 pages in, so I wouldn't say it's that early. 😀 (It's a very good book, of course!)
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(This was just a stream-of-consciousness post after reflecting on how silly it sounds when calculus textbooks include "early transcendentals" in the title. And yes, I know why publishers do that, I spent half of my career teaching "late transcendentals" calculus.)
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I thought it was fun.
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(Yes, that was an oblique Undertale reference.)
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What is "ReLU"?
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Yes, same origin, as far as I know
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I haven't.
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I know my audience
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Heh. My coauthors and I ran into that problem when we were doing a literature search on different notions of conjugacy in semigroups. We would search for "conjugation" and hit "complex conjugation," which was not at all what we wanted.
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Yes! I still say that sometimes but of course, no one knows what I'm referencing.
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Cool! What age group is it aimed at? Square One was aimed at middle schoolers
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That cover hurts my eyes
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Not the first to coin that word, but definitely the worst
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I always joke about this in abstract algebra class: GL(1,R) is just R^* in square brackets
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We got an email from the dean about an hour ago. Nothing from the research office or other higher administrators yet. All the dean said is that the situation is being monitored.
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Yeah, it's too loopy to be a group