Posts (page 3 of 4)
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The graph Laplacian and cohomology
I'm leading a directed study with a student about spectral graph theory this semester. (Long story short, he was in my linear algebra class, another student saw a cool thing about clustering using eigenvalues of the graph Laplacian in Tim Chartier's book, and the three of us did some summer research work about it.) This means that I am learning a lot of stuff about graph theory and linear algebra, and this often bleeds out into other weird branches of mathematics. Here's a good example, the moral of which is that if something is hard or annoying, you may be looking at it wrong.
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Midpoint vs trapezoid estimates
Today I have been playing around trying to justify an observation that we made in my Calculus II class, which is as follows:
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Assumptions about grading
I was in a panel today at The Grading Conference (twitter @Grading4Growth) whose title was “Rethinking Assumptions.” We went mostly in the direction of assumptions about ungrading, so I wanted to write down a few other thoughts about assumptions about grading writ large.
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Remote proctoring is an Orwellian nightmare machine
And we cannot acquiesce to it.
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Mathematical autobiography assignment
Various people have asked me recently about my mathematical autobiography assignment, about which I have previously tweeted, so I decided to put it on my blog here for easier reference.
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A really dirty trick
It's probably been said, and if not then I'm saying it right here, that differential equations is the systematic study of dirty tricks. Here's a good one I encountered in the 1924 monograph on the calculus of variations that I'm rendering into an online PreTeXt book.
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My announcement to my classes
In case it's helpful for other people, here's the announcement I just sent out to my classes through Canvas. Your course setup is probably different from mine, but I think it may be helpful to see examples of how other professors are communicating with students. Some of my classes have slightly different structures, so I've tried to indicate the ways I changed the announcement between those courses.
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Three pretty good reasons why the cross product of parallel vectors is zero
Pretty much, if the cross product is to have any of the properties we'd like it to have, then we're forced to conclude that the cross product of parallel vectors must be zero.
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The four pillars of IBL and my teaching philosophy
I'm up for contract review this year, and I'm also eligible for promotion, so I just completed my teaching narrative. I got real self-indulgent on this thing and ended up writing almost 3500 words (yikes; sorry, committee). There's one section in particular that I thought would be useful to share.
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Yesterday was a good day
It's Friday afternoon, I'm pretty much caught up with grading, nothing is pressing, so it seems like a good time for a moderately self-indulgent blog post. I had a really good day in the classroom yesterday – no, you know what, scratch that, I felt like I kicked ass – and I think it might be useful for me to recap what happened and reflect on why I felt so good about stuff.