"Basic Category Theory" by Tom Leinster is the best intro to Category Theory, IMO. On top of that, you can get it for free legally on arxiv: https://arxiv.org/abs/1612.09375

#Funkwhale #podcast helpers! Our next meeting for podcast/channel development is tomorrow, December 7, at 17:00 UTC in our podcast room: https://matrix.to/#/#funkwhale-podcasts:matrix.org

You don't have to wait for our meeting times if you'd like to contribute! The Matrix room is available anytime for discussion and so is our development forum: https://governance.funkwhale.audio/g/SdKlQIvD/funkwhale-development

More #LaTeX draft writing tricks,

\usepackage{setspace}

\doublespacing

I can't be the only one who had ream length print-outs in programming or English classes, corrected them by hand with lots of margin notes and inline scribbles with the text either double or _triple_ spaced, then typed in the corrections afterward.

If that's your edit flow, the normal dense script of LaTeX can get really annoying to annotate. So I started double spacing my drafts .. and my edit pace went up!

Does anyone have recommendations for online whiteboards? With or without collaborative features?

Or at least screen recording apps for android?

I would like to be able to stream my work on occasion, or at least create videos, or do virtual tutoring sessions. All of which is way more awesome with the right tools.

I cleaned up a lot of my writing today.

Then I spent a couple hours making another hopeful attempt at something involving generators differing by a square... All of which was grounded in yet another typo.

A typo I'd already caught days ago, and then somehow made again in a new way. Thank goodness for simple example cases. With no compiler, just pen and page, a test suite is my only hope.

I'm fascinated by both etymology and the encyclopaedists (or Encyclopédistes).

That toot was inspired by a pleasantly productive HN thread on information, quantity, LibGen, and past and future directions of information:

"Training in a circle" enkyklios paedeia.

Or as you may know it, "encyclopaedia". Or "encyclopedia", for USians.

"Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra"

#LaTeX tricks,

\newcommand{\todo}[1][]{\marginpar[\(\to\) #1]{}}

\todo[cleanup]

This allows me to put margin notes for future edit locations.

When writing proofs, how do you tell whether your case structure is inherent or incidental?

It's common in algebraic number theory to end up in a massive number of cases, as fields intersect or don't in myriad ways. But cases can also arise simply due to weak techniques that only mostly work, to such an extent that I had professors at my old school who considered any proof with cases suspect. So how you do you tell these situations apart in practice?

One step back, two steps forward...

I'm still not happy with 'just take a power series over the uniformizer' because it glosses over that you need to pass to the local field first to get a discrete valuation ring before you can do that. But it basically comes out in the wash.

Yesterday (and several days prior) were a computer induced frustration -- turns out sometimes PARI hands you \(-\zeta\) for \(\zeta\). So no longer chasing that, I was finally able to apply the technique where I meant to.

Is there a way to tell #PARI that a variable is an integer?

I like getting expansions over complex values by default but I really need to simplify this.

It's 10:20am; the eduroam network has slowed to a crawl.

Carefully, in frustration, I perform a variable substitution... replacing each variable appearing in a selection of products with a different prime. Let the computer believe I mean numbers; I can extract the factors at the end.

Except for one, which appears in sums, so cannot be scrubbed away. Bravely the computer returns \[\frac{x}{(-1)^{2b}-1}\] where \(b\) is an integer.

Apparently, if I want results, I will be doing this by hand.

Heathen cyborg mathematician. No gluten. (Mathematician aspect)

Assume the hypotenuse :boardwrite:,

not the contusion :headdesk:.

Joined May 2018