Bill Shillito

Bill Shillito

@solidangles.bsky.social

Assistant Professor of Mathematics at Oglethorpe University. Views my own. Talk to me about anything combinatorial game theory related! He/him. Pronounced SHILL-lit-toe. Websites: https://www.solidangl.es, https://1dividedby0.com

1.1K followers1K following198 posts

Bill Shillito reposted

#HoagieHomies : it's more than a hashtag, people

PRIMUS@readprimus.bsky.social

"Humanizing Defining in Mathematics with Sandwiches" by Katz, Lewis, Bagley, Bockting-Conrad, Ho, Libertini, Owens, Pilgrim, Salomone & Shillito about modeling disciplinary and pedagogical practices. www.tandfonline.com/doi/full/10....

I feel this. I've had to return to handwritten exams, and I kind of hate it.

Charlotte Lydia Riley@lottelydia.bsky.social

AI is going to trash every single way that we had modernised university teaching and send us back to handwritten exams and vivas for every assessment. Which will bring back every problem with those assessment models (and make us seem even more out-of-touch even as we just try to do meaningful work).

It especially hurts because even though I've bent over backwards trying to make my classroom a place where you can make mistakes, learn from them, revise your work, and improve without it tanking your grade, a significant number of students will just bypass that and outsource their learning to AI.

Bill Shillito reposted

AI is going to trash every single way that we had modernised university teaching and send us back to handwritten exams and vivas for every assessment. Which will bring back every problem with those assessment models (and make us seem even more out-of-touch even as we just try to do meaningful work).

Joseph Rezek@rezekjoe.bsky.social

These evil mfs

Question for anyone who's taught multivariable calculus (without line/surface integrals — just up through multiple integrals). If you were to choose a "capstone" topic that ties multiple topics together, what would you choose? Teaching the Calculus sequence again soon and trying to plan ahead.

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For reference, at my school, Calculus III covers: * Thinking in higher dimensions * Partial derivatives (+ optimization) * Vector-valued functions * Gradients (+ Lagrange multipliers) * Multiple integrals (Cartesian coordinates only) Vector calculus stuff is pushed to Calculus IV.

This wouldn't be something I'd be testing students on, by the way — just a "wow that's cool" thing to do on the last day. So it's totally okay for it to be a little bit of a stretch. Any suggestions?

Question for anyone who's taught multivariable calculus (without line/surface integrals — just up through multiple integrals). If you were to choose a "capstone" topic that ties multiple topics together, what would you choose? Teaching the Calculus sequence again soon and trying to plan ahead.

One thought I had was a peek into calculus of variations, since it stretches how we think of dimensions by optimizing over an infinite-dimensional space of functions. But the problem is, I really want something that somehow involves multiple integrals, and I'm not sure how I could work that in.

WOOHOO! Our sandwiches paper has been published! 🥳 ...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪

Brian P Katz (BK)@thewordninjabk.bsky.social

My newest paper about defining sandwiches is out! @drew-lewis.com @sbagley.bsky.social @annemho.bsky.social Mary, Jessica, Bill, @matthematics.com Kate, Sarah www.tandfonline.com/doi/full/10....

It’s ironic that the people who seem to be able to benefit the most from AI tools are the ones who don’t actually need them.

Peter Williams@mathsimpact.bsky.social

I'm gonna keep banging this drum: AI is a useful tool for an expert, it can provide shortcuts and efficiencies in the same way as many other tech tools do. AI is a massive problem for anyone inexpert, because it makes stuff up. If you lack expertise you just can't tell how good the output is.

As my contribution to sharing subtraction strategies, here's how I do subtraction nowadays, using negative numbers! Made this up on the fly way back when I first started tutoring because I couldn't remember how to do multiple borrowing anymore and I never liked the lie of "you can't take 3 from 2".

Howie Hua@howiehua.bsky.social

A good subtraction strategy

The last step of subtracting from numbers with lots of zeros is done mentally. You can easily justify it using the "Same Distance, Same Difference" strategy in @howiehua.bsky.social's video. Although I first encountered it as a "Vedic Math" sutra — "All from nine and last from ten"!

Bill Shillito reposted

We are aware of an ongoing situation concerning our GitHub organization and Discord server (both of which have been deleted) and are working on resolving this as soon as possible. In the meantime we have setup discord.gg/fGG4TFSdKh as a new home on Discord for our community, come join us there!

discord.ggJoin the Manim Discord Server!Check out the Manim community on Discord – hang out with 95 other members and enjoy free voice and text chat.

Had a dream last night… except the main thing of the dream was that I stayed in bed until like 4 PM. There were other things going on too, but I think someone is trying to tell me to get more sleep. 😂

Anyone have any idea where I can find a direct reference to the following quote? Especially in its original script? I want to verify the translation. "Anantam api sankhyaatmakam iti budhyate. / Through numbers, even the infinite can be understood." — Madhava of Sangamagrama

Bill Shillito reposted

You kids and your six trig functions. Back in my day we had only one, and we used it for everything. sin(θ) sin(π/2 - θ) sin(θ)/sin(π/2 - θ) 1/sin(θ) 1/sin(π/2 - θ) sin(π/2 - θ)/sin(θ)

If you'd never seen the definitions for the dot product and the cross product, how might you have invented them for yourself? Who took two vectors, thought "I wonder how I multiply these", and came up with ... those? I've been toying with this since yesterday and would love to hear other thoughts.

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But where I'm stuck is how someone would have decided on those choices for i², ij, ji, and j². What would motivate them if you didn't already know to try them? I vaguely smell something about what should happen when vectors are parallel vs. perpendicular, but I'm having trouble making it precise.

Oh yeah, and I know you get the geometric product if you decide i² = j² = 1 and ij = -ji are bivectors, and you get lots of nice generalizations. But that would require you're comfortable a priori with the idea of adding two different-graded(?) objects together (scalars and bivectors).

If you'd never seen the definitions for the dot product and the cross product, how might you have invented them for yourself? Who took two vectors, thought "I wonder how I multiply these", and came up with ... those? I've been toying with this since yesterday and would love to hear other thoughts.

Personally my first instinct would have been something like this: If I have two vectors u = a i + b j and v = c i + d j, I would expect their product to "respect" distributivity: uv = ac i² + ad ij + bc ji + bd j² And if we stop here, if I understand right, this is the tensor product.

If you make certain choices about what i², ij, ji, and j² should be, you can then recover the other products: * If i² = j² = 1 and ij = ji = 0, you get the dot product. * If i² = j² = 0 and ij = –ji, you get the cross product if ij = k and the wedge product if ij is something new (a bivector).

Hey @desmos.com, any plans to have Desmos be able to choose between the math convention and the physics convention for θ and φ as a quick toggle? I've taught both math majors and physics majors, and it would be nice to allow them to choose the convention that their field uses. 🙂

How to graph y = cosh x: TI-84 CE: 1. Press [Y=]. 2. Press [2nd] [0] (CATALOG). 3. Press [PRGM] (C) to skip to the C functions. 4. Scroll down until you find cosh( and press [ENTER]. 5. Type the rest of the expression and press [GRAPH]. @desmos.com: 1. Type y = cosh x.

There's a part of math history that mystifies me. We used to have a whole bunch of interesting named curves — cissoid, tractrix, strophoid, involute, pedal curve, and so on. Now they've mostly been relegated to quaint examples in math textbooks. Why were these relevant? And what happened to them?

Question for anyone that teaches Calculus I. (Been asking this in a few chats.) What's the point of having students learn about the normal line? What's it good for specifically? (And "they'll see normals again in Calculus III" doesn't count.)

> Be me in 6th grade > Beat final boss > See these equations > Have to beat final boss again > Frantically scribble problems on paper > Beat final boss again to finish writing > Get calculator out > It only holds 8 digits > Work out answers by hand > Enter password > Incorrect password > Repeat...

Cool thing I just realized about f-means! If deg(f) < deg(g), then the f-mean of a data set is less than the g-mean. So since f(x)=log x has "degree" 0 and g(x)=x has degree 1, the geometric mean is less than the arithmetic mean. (I always forget which way it goes — now I'll always remember!)