Toots for jsiehler@mathstodon.xyz account

Written by jsiehler on 2025-01-19 at 15:01

Kind of a plug: One of the perks of working at my school is that we have a subscription to the Naxos Music Library. It's awesome, one of my favorite things on the internet. Maybe your school has it too.

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Written by jsiehler on 2025-01-17 at 19:58

It isn't obvious

To me or to you

But Euler said it

So it's probably true

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Written by jsiehler on 2025-01-13 at 13:54

"Spreadsheet" is too long, let's make it "spreet" from now on.

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Written by jsiehler on 2025-01-07 at 18:05

Media images of mathematicians with their whiteboards/blackboards always look SO COOL with probably some homology and an exact sequence and some commutative diagrams and a couple of graphs and other photogenic stuff. Mine almost always looks like this and I bet mine is closer to the realistic average than the media version is.

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Written by jsiehler on 2024-12-13 at 13:35

A nice problem from "A Mathematical Orchard."

Consider the (n\times n) array whose entry in the (i)-th row, (j)-th column is ((i+j-1)). What is the smallest product of (n) numbers from this array, with one coming from each row and one from each column?

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Written by jsiehler on 2024-12-12 at 20:24

"I will teach a topics course on 4-manifolds," said Frog.

"You will have to explain 'gropes' to undergraduates," said Toad.

"I will choose a different topic," said Frog.

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Written by jsiehler on 2024-11-27 at 14:14

Here's a pleasing Putnam problem for your idle moments today. It's not super hard, but it's kind of fun to write down your gut-feeling guess first and then do the calculation to check yourself.

Two real numbers (x) and (y) are chosen at random in the interval ((0,1)), with respect to the uniform distribution. What is the probability that the closest integer to (x/y) is even?

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Written by jsiehler on 2024-11-12 at 15:26

I have long found it curious that the function (1\over 1-x),which occurs as the sum of the archetypal geometric series, has order 3 under composition.

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Written by jsiehler on 2024-10-21 at 14:39

Yeah that doesn't work in Excel.

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Written by jsiehler on 2024-10-11 at 13:23

F., a toddler: DADDY! MAKE ME TOAST!

Me: Can you ask more politely?

F: Daddy, you MAY make me toast.

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Written by jsiehler on 2024-10-07 at 19:13

The organ video that someone shared reminds me that my mother was a church organist, so I spent a fair bit of time in organ lofts as a wee lad. And I once got in a bit of trouble because, at that time, I knew how to play "Crazy Train" on a keyboard but I did not know what the stop marked "Carillon" did.

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Written by jsiehler on 2024-09-15 at 18:12

Something about it is rather like a sewing machine.

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Written by jsiehler on 2024-09-15 at 18:10

Enjoy, if you think you might enjoy this sort of thing, this animation. I recommend slowing it down to something like 0.2 times the default.

https://www.desmos.com/calculator/fvgoenc6ls

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Written by jsiehler on 2024-09-15 at 18:05

The graphs you get from functions of the form (\displaystyle{\cos(m x)\over\cos(nx)}) make pretty trippy wallpaper.

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Written by jsiehler on 2024-09-04 at 13:26

Strong candidate for my all-time favorite comment on a course evaluation (from a few years back):

"I was disinterested in taking such a theoretical course, I felt like it was not going to be useful, but I never thought of the fact that I might just enjoy it. "

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Written by jsiehler on 2024-08-27 at 12:42

Learned a new proof of the infinitude of primes this morning.

"Saidak argues the infinitude of primes as follows. Let (a_0 = 1), and define (a_n = a_{n−1}\left(a_{n−1} + 1\right)) for (n \ge 1). Since (a_n) and (a_n + 1) have no common divisors, it follows that (a_n) has at least one more prime factor than (a_{n-1}), and thus by induction, (a_n) has at least (n) distinct prime factors."

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Written by jsiehler on 2024-08-12 at 12:31

Superhero landing pose.

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Written by jsiehler on 2024-08-01 at 18:23

I always like to try to put a small "curiosity inducing" picture at the top of a course page. Here's the one I'm using for abstract algebra in the fall; I like it.

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Written by jsiehler on 2024-08-01 at 14:20

Is there some (perhaps historical) context around functions of the form (\sin^n x\cdot \cos^m x) which justifies the amount of time spent on techniques for integrating them in typical calculus texts?

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Written by jsiehler on 2024-07-29 at 17:43

A common annoyance for me is that Moodle matching questions (in quizzes) cannot use LaTeX in the answers. It's allowed in the questions, but not in the answers. Does anyone have a workaround for this?

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