/sci/ - Science & Math

>>11861934
Every single one of those posts contained more maths than yours. Lucky for you, I'll stop here.

>>11861936
For algebra, maybe recap matrix multiplication to get a way to easily find examples of non-commutative groups and rings. If you know your partitions and equivalence relations (and how they coincide), then there's not much to do as preparation for that. If you want to look at categorical stuff, I recommend seeing the algebraic and topological examples first. For example, one would assume that in a category where the morphisms are functions of some sort, epimorphisms are the surjections. Well, if one considers the full subcategory of Hausdorff spaces, then it is not the case. If this sounds like total gibberish to you at the moment, worry not. It will make sense to you after you survive the topology course, and it is also a reason why the undergrad category theorist meme is grounded in reality. However, you will learn that stuff when you get to AT, so don't rush. I hope you get to at least the fifth stage.
>That's good to hear, be proud of your hard work
Thanks. Trying my best.

>>11861968
No problem.

Anyway, it's getting late, so /gnmg/ and a little exercise for those who need something to do:
Prove that the inclusion [math]\mathbb{Q} \to \mathbb{R}[/math] is an epimorphism in the category of Hausdorff spaces.

>>11772481
Thanks for correcting my ignorance.

/gnmg/

https://sites.google.com/view/nialltaggartmath/oats
>Kirsten Wickelgren (Duke University)
>Title: There are 160,839<1> + 160,650<-1> 3-planes in a 7-dimensional cubic hypersurface
>Abstract: The expression in the title is a bilinear form and it comes from an Euler number in A1-algebraic topology. Such Euler numbers can be constructed with Hochschild homology, self-duality of Koszul complexes, pushforwards in SL_c oriented cohomology theories, and sums of local degrees. We show an integrality result for A1-Euler numbers and apply this to the enumeration of d-planes in complete intersections. Classically such counts are valid over C and sometimes extended to the real numbers, but A1-homotopy theory allows one to perform counts over a large class of fields, and records information about the solutions in bilinear form. The example in the title then follows from work of Finashin--Kharlamov. This is joint work with Tom Bachmann.
In 15 hours.

Nighty night~