¿Quieres saber qué es una #funcion en #matematicas
Te lo explico en este vídeo.
https://www.youtube.com/watch?v=1sKeeZ4mFJk

A fundamental result in universal algebra is the Subdirect Representation Theorem, which tells us how to decompose an algebra \(A\) into its "basic parts". Formally, we say that \(A\) is a subdirect product of \(A_1\), \(A_2\), ..., \(A_n\) when \(A\) is a subalgebra of the product
\[
A_1\times A_2\times\cdots\times A_n
\]
and for each index \(1\le i\le n\) we have for the projection \(\pi_i\) that \(\pi_i(A)=A_i\). In other words, a subdirect product "uses each component completely", but may be smaller than the full product.

A trivial circumstance is that \(\pi_i:A\to A_i\) is an isomorphism for some \(i\). The remaining components would then be superfluous. If an algebra \(A\) has the property than any way of representing it as a subdirect product is trivial in this sense, we say that \(A\) is "subdirectly irreducible".

Subdirectly irreducible algebras generalize simple algebras. Subdirectly irreducible groups include all simple groups, as well as the cyclic \(p\)-groups \(\mathbb{Z}_{p^n}\) and the Prüfer groups \(\mathbb{Z}_{p^\infty}\).

In the case of lattices, there is no known classification of the finite subdirectly irreducible (or simple) lattices. This page (https://math.chapman.edu/~jipsen/posets/si_lattices92.html) by Peter Jipsen has diagrams showing the 92 different nontrivial subdirectly irreducible lattices of order at most 8. See any patterns?

We know that every finite subdirectly irreducible lattice can be extended to a simple lattice by adding at most two new elements (Lemma 2.3 from Grätzer's "The Congruences of a Finite Lattice", https://arxiv.org/pdf/2104.06539), so there must be oodles of finite simple lattices out there.

Artigo para o Dia (da Aproximação) Pi.

Article for Pi Day.

https://www.sulinformacao.pt/2025/03/legislar-a-matematica-ou-a-quadratura-do-circulo/

Rust Vector and Quaternion Lib — https://github.com/David-OConnor/lin-alg
#HackerNews #Rust #Vector #and #Quaternion #Lib #Rust #Programming #Linear #Algebra #Game #Development #GitHub

Me: If you're a student in my class you will do group presentations, meaning that you will organize into a subset of the class, stand in front of the room, and talk about math to the rest of the class.

Also me: Let's talk about group presentations, a completely abstract algebraic concept that have absolutely nothing to do with standing in front of the room talking about your work.

Also also me: Okay, time for group presentations about group presentations.

#Algebra #ITeachMath #GroupTheory #GroupPresentation

Geometric Algebra — https://bivector.net/
#HackerNews #Geometric #Algebra #Mathematics #AlgebraicStructures #MathEducation #Bivector

Wendy Grossman's (@wendyg -- follow her) net.wars this week is excellent as usual:
https://netwars.pelicancrossing.net/

Its trigger is the UK government's rather #stupid #demand that #Apple provide access to all of its users end-to-end #encrypted files. And it talks more generally about the problems with governments demanding back doors in encryption provided to the public, which is hugely counter-productive.

But maybe I just like it because it agrees with what I've said here a number of times:

Encryption is math.

There is no such thing as math that "the good guys" can do, but which "the bad guys" can't.

Anyone who tells you different [1] is lying.

Use strong encryption for everything, for the same reason you send your routine correspondence in envelopes rather than on the back of a postcard.

[1] Such as politicians who never got entry-level algebra telling you that encryption that only the government can break is possible, you just have to NERD HARDER.

Applying matrix diagonalisation in the classroom with #GeoGebra: parametrising the intersection of a sphere and plane

In collaboration with Bradley Welch

https://www.tandfonline.com/doi/full/10.1080/0020739X.2023.2233513

Ich bete inständigst zum Großen #Spaghettimonster, dass Elon Musks Sohn X in seinem Leben eine Person namens Y lieben und heiraten wird.

Die ganze #Algebra hätte dann endlich mal eine Entsprechung im echten Leben.

(Jaja, Mathematiker*innen, ich weiß, ich weiß , Algebra hat mit dem wirklichen Leben zu tun und ist nützlich und funktioniert - es geht hier nur um den Witz).

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Just finished my lecture #Algebra 2 for this semester.

25x 90min lectures and ~120 page PDF script.

We did Galois theory, modules over PIDs and even a bit of classification of groups of small order.

I love this lecture, but I'm also happy that it's over.

Seen in a tutoring job offer:

"I have an Algebra 2 quiz coming back soon."

Coming back? From where?

I finally wrote the next article in the series about my project of developing a framework for working with abstract representations of simple polygons over cyclotomic integer rings.

In this article we learn to intersect line segments where the endpoints are elements of a constructible cyclotomic integer ring!

https://pirogov.de/blog/intersecting-segments-without-tears/

Z[x] from elementary ring theory is very clearly a tragic hero archetype. It wanted so badly to be a PID but is ultimately overcome by its demons (the ideal (2,x)).

2025 = (1+2+3+4+5+6+7+8+9)² = 1³+2³+3³+4³+5³+6³+7³+8³+9³

Leuk toch? Meer bijzonderheden over 2025 en #Nichomachus in dit artikel geschreven door @ionica

[Artikel] 𝗪𝗮𝘁 𝟮𝟬𝟮𝟱 𝗼𝗼𝗸 𝗺𝗮𝗴 𝗯𝗿𝗲𝗻𝗴𝗲𝗻, 𝗵𝗲𝘁 𝗷𝗮𝗮𝗿𝘁𝗮𝗹 𝗶𝘀 𝘄𝗲𝗿𝗸𝗲𝗹𝗶𝗷𝗸 𝗲𝗲𝗻 𝗳𝗮𝗻𝘁𝗮𝘀𝘁𝗶𝘀𝗰𝗵 𝗴𝗲𝘁𝗮𝗹

Door Ionica Smeets

https://www.volkskrant.nl/wetenschap/wat-2025-ook-mag-brengen-het-jaartal-is-werkelijk-een-fantastisch-getal~bbf035c7/ via @volkskrant

The Algebra font is a slab serif typeface designed by Susana Carvalho and Kai Bernau for the US edition of Esquire magazine.
https://www.fontfreedownloads.com/en/algebra.font-free-download

#Algebra is such an amazing antidote to the frustrations of work.

"In fact, if we needed to make contact with an alien civilization and show them how sophisticated our civilization is, perhaps showing them Dynkin diagrams would be the best choice!"
- Pavel Etingof
#math #algebra

This took me an embarrassingly long time to figure out. #math #algebra