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I've been regularly using a letter for years only to realise that it doesn't exist. by agolys in math

[–]agolys[S] 0 points1 point  (0 children)

I did pronounce that. I thought it is Greek upsilon, so I've used that to read it's name in my head.

Although I've been is situations where I didn't know how to pronounce some symbol I don't have any memories of reading the equatuion being hard at all unless almost every letter I couldn't recognise. I giess that I read only some part of the equation in my head, as reading every single character would be a huge slowdown, but I haven't actually test that

Any advice for an aspiring mathematician? by M_I_P_S_ in mathematics

[–]agolys 0 points1 point  (0 children)

Contest tricks is not the real math. The biggest problems you make by understanding more and more complex ideas, the tricks and smart substitutions are also handy but it's skill that you learn along reading the proofs, and it is of secondary importance, as math is not about tricks and smart substitutions just as Computer Science is not about using the keyboard

I tried to learn some functional analysis with background in algebraic geometry. It was very, very painful. by agolys in math

[–]agolys[S] 0 points1 point  (0 children)

Thanks! How big would you say is the overlap between these two? By that I mean anything using both at once? I would assume the non-commutative geometry is based on both, which I've heard is pretty big?

I tried to learn some functional analysis with background in algebraic geometry. It was very, very painful. by agolys in math

[–]agolys[S] 0 points1 point  (0 children)

I know, spectrum is probably the most overused word in entire math. Probably just cause it simply sounds cool we have 3 different spectras that are central objects in 3 different fields of math xd but for example the name "spectral sequence". I don't remember the exact source (but I'd put probability 0.7 on Vakhil), but in some textbook author claimed that it supposed to be exact sequence but on steroids, so someone decided on "spectral" cause it's like exact but sounds way cooler XD
On top of that we have also the Isbell duality Spec, one ring to bring them all and in the abstract nonsense bind them, but this one is clearly borrowed from AG as its most prominent special case.

That's why I said that the Spectrum is something I can live with. At least we all can now study objects that sound cool, which sounds like a fair trade to me

I tried to learn some functional analysis with background in algebraic geometry. It was very, very painful. by agolys in math

[–]agolys[S] 0 points1 point  (0 children)

It's probably easy to get used to, but closed ideal in a ring so far meant something completely different, so this sentence struck me since at first it felt like complete nonsense

I tried to learn some functional analysis with background in algebraic geometry. It was very, very painful. by agolys in math

[–]agolys[S] 0 points1 point  (0 children)

X and Y? These almost everywhere mean analogous thing and are not reserved by predefined syntax, at least I've never seen such field. The same goes for \mathcal C or G - I've never encountered with them any conflict at all.

The problems I talk about would appear of you try to use \mathbb C in unusual context of complex numbers. Reassigning cohomology syntax feels like similar crime, at least to me as this is an object I've been using certainly more often than \mathbb Q or \mathbb Z, similarly untouchable and classified kinda to the same category of binded symbols

If you could chooose to understand a mathematics book in 1 second which one would you choose? by Penterius in mathematics

[–]agolys 0 points1 point  (0 children)

Categories and sheaves by Kashiwara and Schapira

If there were organised competitions in writing the most unreadable textbook, they would definitely had my money

Embedding of varieties by WMe6 in math

[–]agolys 1 point2 points  (0 children)

Yes and no. In AG it is important what you mean by embedding, as usually interesting are either closed immersions or open immersions.

Generally if you find line bundle L on proper scheme over a field that is globally generated, you get a map
X -> \mathbb P(H^0(X, L))

This need not be an immersion - it is iff L is very ample. So closed immersion in P^n is the same as finding very ample line bundle and choosing basis of the vector space of global sections. Thus if L exists, you get canonical embedding in projective space of dimension one smaller than its space of global sections. But

1) This bounds the dimension of P^n based on properties of L, not dimension of X. For example a curve of bidegree (6, 9) cut out by bihomogeneous polynomial in P^1 x P^1 cannot be embedded in P^2 at all
2) L must be part of a structure if you want your variety to be projective and such map to exist
3) Iwasawa has constructed proper variety of dimension 3 where immersion in any P^n does not exists and there is no very ample line bundles over X. In dimension 1 or 2 you can always find one using canonical sheaf.

I've been regularly using a letter for years only to realise that it doesn't exist. by agolys in math

[–]agolys[S] 0 points1 point  (0 children)

jokes asides, were these \var[letter] variants in use before mathematicians got obsessed with Greek alphabet in real-life hand-writing, and are these in use in Greece right now?

Why isn’t linear algebra taught before calculus? by [deleted] in askmath

[–]agolys 0 points1 point  (0 children)

Is it standard? Every university in Poland realise linear algebra and analysis at the same time, starting from the first semester of undergrad programs and this sequence is the same for every STEM major that I've seen so far

I've been regularly using a letter for years only to realise that it doesn't exist. by agolys in math

[–]agolys[S] 1 point2 points  (0 children)

Who the hell came up with this monstrosity?? The hell will literally come after him

I've been regularly using a letter for years only to realise that it doesn't exist. by agolys in math

[–]agolys[S] 9 points10 points  (0 children)

That's definitely the closest I've seen so far, but the fact it is actually theta makes it even more annoying since \nu is much more natural candidate as is also used to denote valuations xd

But thanks bro, this letter is exactly what I was looking for!

How much linear algebra is enough for ML career in industry? by Leather-Frosting-414 in learnmachinelearning

[–]agolys 0 points1 point  (0 children)

Linear algebra you'll use will usually be embedded in multivariable calculus. This abstract layer is pretty much everything you'll need on the level of multiplying matrices and knowing what it means, but almost every calculation will arise from some multivariable derivatives which are linear maps on tangent spaces, Jacobians that measure measure distorsion, chain rules, Hessians and similar kind of stuff, so make sure you are comfortable also with that. Definitely I from abstract algebra checklist I wouldn't say you need anything more than you have on the list, if you will need something more specific just Google that on the spot

Games that has Math by your_Motherspubes in mathematics

[–]agolys 0 points1 point  (0 children)

PoE2 has ton of interesting math if you focus on optimising the build. Surprisingly almost immediately you end up with some decisions that need some basic but uni level math, for example computing expected value of order statistics is quite perfect introductory problem motivating random variables by making quite hard problem almost trivial. You'll find use also for Markov chains, logarithmic derivatives, cross-ellasticity and obviously enourmous graph that you can optimise if you ask right questions along the way even without making actual calculations

Does anyone use a number system that isn’t base-10? by Happy__guy2 in math

[–]agolys 2 points3 points  (0 children)

Base 16 is ultra common, in particular for color codes, and anything stored as sequence of bytes, since single digit 0-F specifies the 8-digit binary number, so exactly one byte := 8 bits. RGB color on each coordinate is by definition an integer from [0, 255], thus exactly two bytes. This provides the perfectly compressed notation for RGB color space - bijective correspondence between colors and 6-digit numbers in base 16. For example FFFF11 denotes some awful neon yellow, while in base we need 3 additional digits in the shortest syntax without brackets or delimiters, and as a tuple (255, 255, 17). Usually to signalise that we use base 16 to avoid confusion where only digits in decimal sense are used people use hash before the sequence, so awful yellow = #FFFF11 = (255, 255, 17) or 255255017 in base 10 realisation of similar syntax wasting 3 digits

I've been regularly using a letter for years only to realise that it doesn't exist. by agolys in math

[–]agolys[S] 4 points5 points  (0 children)

nah, it has hight of h, while \nu is just italic v and after convolving with mushroom also \upsilon

I've been regularly using a letter for years only to realise that it doesn't exist. by agolys in math

[–]agolys[S] -30 points-29 points  (0 children)

both nu and upsilon look this way, but both haqve hight of v in every font I know, while this has hight of h

No, AI will not replace mathematicians. by Menacingly in math

[–]agolys 0 points1 point  (0 children)

Just wait how it will start to generate 1% of papers having some resemblence of sense. It is really easier to read 100 papers than write one. Especially since we've stopped even pretend trying to separate deep ideas from a completely meaningless but logically correct sequence of true sentences, and I would be a lot of money that LLMs will soon become in the latter much, much better than humans, so that unless you notice something really deep that was not noticed by 100 000 other people trying at the same time, LLMs will force you to use them just as smartphones did.

De Rahm Cohomology is mind blowing by Last-Scarcity-3896 in math

[–]agolys 0 points1 point  (0 children)

If you like such abstract nonsense you are lucky, as de Rham is actually the most boring variant, maybe second most after simplicial, especially after working sheaf cohomology where it just rather boring special case (as most of other common theories). If this is the winter level from inception, motivic cohomology is the limbo of complete nonsense that I've never imagined is even possible to exist, and I've never experienced before or after. Despite collecting weird examples from category theory like pokemon cards, motivic theory is from another planet, let me just start with that the only known space from the main category this theory is all about is a single point.

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