[ home ] [ math / cs / ai / phy / as / chem / bio / geo ] [ civ / aero / mech / ee / hdl / os / dev / web / app / sys / net / sec ] [ med / fin / psy / soc / his / lit / lin / phi / arch ] [ off / vg / jp / 2hu / tc / ts / adv / hr / meta / tex ] [ chat ] [ wiki ]

/math/ - Mathematics

Name
Email
Subject
Comment
Verification
Instructions:
  • Press the Get Captcha button to get a new captcha
  • Find the correct answer and type the key in TYPE CAPTCHA HERE
  • Press the Publish button to make a post
  • Incorrect answer to the captcha will result in an immediate ban.
File
Password (For file deletion.)
25 Dec 2021Mathchan is launched into public
Catalog Archive

File: photo_2022-03-18_17-07-07.jpg ( 48.05 KB , 1280x800 , 1662141820030.jpg )

Image
  No. 282
Reply
>>438
Hey /math/

I've been trying to understand spherical harmonics to grok an ML paper that represented points in euclidean space in a rotation-and-translation-invariant way (https://arxiv.org/pdf/1802.08219.pdf). I found a great textbook on SO(3) (https://www.diva-portal.org/smash/get/diva2:1334832/FULLTEXT01.pdf), but while I can kind of maybe sort of follow what's being done with them in this particular paper I fail to really get an intuition of what spherical harmonics are, and it feels like there's some pretty beautiful insight in there.

Do you have any advice or perspectives on how to intuitively grasp what these harmonics are and mean, beyond just group theory definitions?
>>
  No. 285
Harmonics are solutions of Laplace's equation in a given coordinate basis. Spherical harmonics are the solutions of Laplace's equation in spherical coordinates.
>>
  No. 438
>>282
https://youtu.be/Ziz7t1HHwBw
>>
  No. 893 >>983
fdsa
>>
  No. 982
fdsafas
>>
  No. 983
>>893
fdsafdsafdsa

File: 3t0kod.jpg ( 76.97 KB , 800x450 , 1675025207218.jpg )

Image
  No. 346
Reply
>>347 >>385 >>380 >>429 >>507 >>525 >>530 >>544 >>659 >>894 >>981
So, I have a cousin who wants to win medals in math competitions, especially IMO. Post resources, guides and tips for olympiads.
his prep level: he's 12yo(7th standard), has completed mathematics books upto the 10th standard level. What should be his target next? And how do I help him clear doubts? We don't have decent teachers where we live, and the internet doesn't help much
54 posts and 7 image replies omitted. Click here to view.
>>
  No. 897 >>898
>>896
in my opinion p6 seems doable
>>
  No. 898
>>897
it was one of the hardest p6s of all time
it's not "doable", as very few contestants got it right in the time limit
>>
  No. 899
>>411
Uu
>>
  No. 941
dead
>>
  No. 981
>>346
holy what

File: vector-division.png ( 12.35 KB , 1478x540 , 1726609814969.png )

Image
  No. 964
Reply
>>969
Any reason not to teach the algebra of Euclidean vectors like this? This would come after multiplication of vectors by scalars but before the scalar product of two vectors, and the target audience is students at the level of typical high school juniors or seniors.
1 post omitted. Click here to view.
>>
  No. 970
>>969
Finally somebody gets it
>>
  No. 971 >>972
>Introduce the structures mathematicians actually care about.
Which would include the structure in OP.
>>
  No. 972 >>973
>>971
Ah yes, my favorite structure of the map taking two vectors from a normed vector space, the second of which is nonzero, and outputting the unique scalar by which one is to scale the second such that it is closest to the first one. Certainly we should teach examples of this before the notion of a vector space is introduced, giving it a designated name.
>>
  No. 973 >>974
>>972
rather important in inner product spaces bro
albeit the scaled vector moreso than the scalar itself
the remainder is important too
>>
  No. 974
>>973
Yeah, it's an important example of orthogonal projections

File: 8-41-08.png ( 285.09 KB , 2220x892 , 1713077717968.png )

Image
  No. 685
Reply
>>963
I know absolutely nothing about math, my knowledge is basically stuck to 7th grade stuff at best.
That said, even I can tell those wrong captcha answers are nonsensical, to the point I can easily get around verification by simply guessing the right answer.

Just a heads-up
4 posts omitted. Click here to view.
>>
  No. 726 >>733
>>725
Why?
>>
  No. 733
>>726
This board is being flooded with useless discussion
>>
  No. 735
>>725
it's okay, all these posts will be drafted to /ret/ - retards soon
>>
  No. 963
>>685
the captcha filters me :(
>>
  No. 966
I do not know whether you see me as a part of the problem.
I just comes here to discuss something about mathematical logic. Even if you hold the opinion that logic belongs merely in the realm of philosophy or whatever, you have to admit that symbolical logic like propositional logic are teached and investigated by serious mathematicans like Gödel, Hilbert etc. Hasn't even Erdos proofed something in this field?

I know, am far away from mastery but compared to the endless discussion about 3/3 = 0,999... = 1 or something, I regard myself as a good contributer.

File: zvvi8zwTaqXgw.png ( 549.41 KB , 379x892 , 1722429433663.png )

Image
  No. 900
Reply
I'm sorry if this belongs rather to the /phil/ section. I just want to discuss this topic and I guess, it has to do with math anyway.

Some groups like the "New Atheits" and/or the so called "Intuitionists" (and the late Wittgenstein, too) think that you can make the following assumption:
"p is true" = "There is a proof for p [within a formal system]".

If it is impossible to provide a proof for p in principle, then you can claim that p is neither true nor false. Its just "undecidable".

My question is:
After the results of Tarski and Kurt Gödel, can we really still hold this assumption?

We see that "p is true" must be something different from "there is a proof for p" as there are some true statement of which the proof doesn't exist. We cannot define "truth" within a formal system and need some relation to something without the system itself. A semantic model.
In the light of this insights, the position that identified true with provability makes a lot less sense to me and many others.

Anyway, as far as I read, the critique of the inuitionists on the rule of double negation and the law of excluded middle relais a lot on the hidden premisse that "truth" and "can be proofen" is the same.
So, there viewpoint seems much less plausible anymore.

What do you think, anon?
>>
  No. 961
I agree with you, OP.

File: 1.gif ( 43.31 KB , 870x466 , 1726526778823.gif )

Image
  No. 960
Reply
What do you think, anon?
Made up Bullshit or genial insight?
Usufull or not?

File: Remarksonzetaregularizedproducts.pdf ( 269.6 KB , 1724152318480.pdf )

Image
  No. 937
Reply
Are there any other people here who researched/studied zeta regularization (products)?

File: math.png ( 791.79 KB , 847x554 , 1724105566327.png )

Image
  No. 935
Reply
>>936
I'm interested in making a game with simple 3D graphics (only consisting of simple shapes like cubes and pyramids) without using a 3D engine but I don't know the name of the specific math/geometry stuff I need to study in order to do that, can anyone orient me?
>t. don't even remember high school math and only got the captcha right by chance, but i'm good at learning things
(Please refrain from "just use an engine"-type replies)
>>
  No. 936

File: WraithlordOnMatrices.png ( 261.8 KB , 2353x1521 , 1724105723042.png )

Image
>>935
Linear algebra as well as analysis if you plan to have physics or complicated motion.

File: Screenshot_2024-08-04-20-56-51-720.jpeg ( 25.71 KB , 1200x1920 , 1723285536405.jpeg )

Image
  No. 925
Reply
>>931 >>933
Topics which are not in high school syllabus but might help in JEE Maths or Physics questions.

Book recommendations or advice for JEE Maths or Physics
>>
  No. 931 >>933
>>925
http://sheafification.com/the-fast-track/
>>
  No. 933
>>925
>>931
teri-ma-ka-rape.com

File: 9780387984032_p0_v2_s550x406.jpg ( 21.64 KB , 255x406 , 1678360940704.jpg )

Image
  No. 351
Reply
>>376 >>490 >>492 >>929
(please move to /adv/ if this belongs there)

I started with category theory a week ago with Lane's book. It's a bit hard and there are some examples (like lie groups) that I don't quite get. Related to this I've read Fraleigh's book on abstract algebra. Is this enough background or should I wait a bit before getting into category theory?

Thanks
9 posts and 4 image replies omitted. Click here to view.
>>
  No. 571 >>573

File: BasedDepartmentCalling.png ( 105.43 KB , 727x407 , 1703638548951.png )

Image
>>570
Due to the way things end up being I'd say it's not an unfair analogy to draw. However primarily I'd say they're a priori just two different languages for describing maths.
>>
  No. 573 >>575
>>568
>Not >565 but category theory comes in handy to formulate many concepts, it's a useful language to have.

And why is it better than set theory, HOL or mereology?
(Or even some kind of formal ontology in the informatics)

As far as I understand, you could easly define a predicate "x is isomorph to y" := Iso(y,x) and work with this.
Okay, I see the advantage of a graphical picture.

What I have see in categories looks suspicies like a usual powerset.

Or I'm just to simple-minded to get it at all?

>>571
Okay.

As far as I see, the central relation in set theory is the "being part of", maybe in the HOL is more "impled".
What is the categories about?
>>
  No. 575
>>573
First of all I wouldn't say it's "better" than set theory or higher order logic.
Second of all you can't just easily define a predicate "is isomorphic to", well you can, but it's useless and you're missing the point. You want to define it in a way for it to have the desirable properties and if you just define a predicate, then you have to figure out how to piece it into the rest of the theory.
Third of all higher order logic is fundamentally different from set theory or category theory, as it's part of the deductive system of your theory, not part of the actual things you talk about. So indeed I'd say yes you're being too simple minded/delusional to get it right now.

As to what category theory is "about" is I'd say morphisms, the same way set theory is abour membership, since morphisms are what ought to be defined to speak of a category and draw the beloved arrows.
>>
  No. 928

File: BecomingAMathematician.jpg ( 842.83 KB , 2128x5320 , 1723609145686.jpg )

Image
So did you end up doing category theory?
>>
  No. 929
>>351
you lack basically all motivation. read bott tu and brown's topology first. and then vaisman's book on cohomology as an intro to cats

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
| Catalog | Archive
[ home ] [ math / cs / ai / phy / as / chem / bio / geo ] [ civ / aero / mech / ee / hdl / os / dev / web / app / sys / net / sec ] [ med / fin / psy / soc / his / lit / lin / phi / arch ] [ off / vg / jp / 2hu / tc / ts / adv / hr / meta / tex ] [ chat ] [ wiki ]