I'm trying to understand machine learning at the moment, but I keep realising I don't have the math background for some of it.

If anyone has any relevant like 'get up to speed on matrix calculus' level stuff, would appreciate links /advice!

The Eudoxus Real Numbers
Article by Arthan, R. D.
In collection: Unusual arithmetic
This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the well-known construction of the real numbers using Dedekind cuts, the idea is inspired by the ancient Greek...
URL: arxiv.org/abs/math/0405454
PDF: arxiv.org/pdf/math/0405454v1
Entry: read.somethingorotherwhatever.

Just a few weeks ago, my colleagues and I published a review article on a problem I like to think of as the TARDIS of math: It looks small, but it's bigger on the inside, and it takes you to unexpected places. mdpi.com/2075-1680/6/3/21

I tried to make the bibliography comprehensive, but new work has come out, so it's already outdated: scirate.com/arxiv/1707.09911

And this morning I was sent a draft of a new paper, so it'll be outdated yet again soon

This is a good thing!

"Good mathematicians see analogies between theorems; great mathematicians see analogies between analogies."

Inspired by Alison Kiddle, I've made an Auto-Santa 3000: given a list of naughty things, add up the scores of the things you did. Then it uses the total to tell you the things you did! mathstodon.xyz/media/wabXGCyuS mathstodon.xyz/media/BiBHC_ZU9

The editorial board for the Journal of Algebraic Combinatorics left to continue the journal under a new name in Open Access form:

gowers.wordpress.com/2017/07/2

#mathematics

Just spent half an hour with my summer student getting into the subtleties of the conditions required for "throwing two dice" to have 36 possible outcomes.
I came up with a good example: I'm colourblind, so if we throw a red and a green die at the same time, the student can distinguish them, but I can't. So the outcomes are a property of the observer, not the trial itself.

Pentagon Tiling Proof Solves Century-Old Math Problem, _Quanta Magazine_, quantamagazine.org/pentagon-ti

I already posted about this a couple of months ago (plus.google.com/10000362860341) but now there's this nice popular-press article, and confirmation on the correctness of "the most important half of Rao's proof" by Thomas Hales.

I wish I could express how exciting it is to have a SIC solution in dimension 844:

arxiv.org/abs/1707.02944

844^2 = 712,336 lines, in a space where map coordinates use the square root of minus one, and every pair of those lines meet at exactly the same angle
#quantum #physics / #mathematics

Today in #quantum #physics / #mathematics: I updated our introductory review article on complex equiangular lines, a.k.a. symmetric informationally complete quantum measurements.

arxiv.org/abs/1703.07901

The bibliography is caught up to this week's news, and the historical overview section is more comprehensive than it was in the previous version.

Early career researchers: have you been bullied into doing bad science? Pressured to publish only in "prestigious", non-open journals?
There's a letter to sign.
bulliedintobadscience.org/

Today in #mathematics and #quantum stuff: I have apparently talked myself into writing a thing about how the sporadic SICs relate to the exceptional Lie algebras. (The Hesse SIC is secretly in alliance with E6, and the Hoggar SIC with E7 and E8.)

Campus is not filled with undergrads, but the coffee place in my building is closed. Net loss.
@tobascodagama

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