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/sci/ - Science & Math

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File: 12 KB, 400x267, Thierry_Aubin.jpg [View same] [iqdb] [saucenao] [google]
11512441 No.11512441 [Reply] [Original]

Previously >>11502149
Actual pictures of mathematicians edition.

Talk maths.

>> No.11512490
File: 14 KB, 904x544, exampleSteps.png [View same] [iqdb] [saucenao] [google]

I have n convex sets in the euclidean plane, I take the first and second set, A and B respectively, and rotate and translate them over each other such that their intersection is maximized, now their UNION is a new set,let's call this new set (AB), we take the third set C and rotate and translate it such that it's intersection with set (AB) is maximized, this new set we call (ABC), we take the fourth set and do the same process with the previously generated set (ABC) to get set (ABCD), and we do this process
with all n sets, and end up with the set(ABC...n) which within itself contains all sets from A to n, the question is is the set (ABC... n) the same as the set that has minimum area but also contains all sets from a to n? PicRelated is an explicit example-

>> No.11512500

Asked in the last one.
How many irreducible reps are there of the complex Lie group/Lie algebra E6?
Is it 51840 since that's the dimension of its Weyl group?

I can't even seem to find a resource to learn the theory.

>> No.11512572

Lie groups/algebras don't have a finite set of irreducible representations. It's odd that you somehow got to asking questions about E6 without working through the representation theory of sl2 first.
Irreducible rep'ns of complex (semi)simple lie algebras are classified by the theorem of the highest weight; irreducibles are in bijection with dominant integral weights (of which there are infinitely many, since they're just N-linear combinations of a basis).

>> No.11512670
File: 9 KB, 1374x381, asd.png [View same] [iqdb] [saucenao] [google]

what an ugly problem
the answer is probably not
try pic related

>> No.11512698

I'm not sure what you mean, the compact complex Lie group of E6 doesn't have a finite set of irr reps? It's a finite group, so it has a finite number of conjugacy classes

>> No.11512735

What do you guys do when people ask you "what are you going to do with math?" Also how do I combat "muh when are we going to use this?"

>> No.11512745
File: 42 KB, 655x527, mZcvbSavN_ZonZcfCgsVsI8LP9Hlrc_-ENTRhY9ZvkY.jpg [View same] [iqdb] [saucenao] [google]

>It's a finite group

>> No.11512746

your picture is a valid counterexample :( , guess I'll try a new way to make the set with minimum area which contains all other sets from A to n. Got any ideas?

>> No.11512751

>is a valid counterexample
Are you sure?

>> No.11512756

Am I retarded? Then what is the atlas project doing, what would then the character table of the real split group of E8 be?

>> No.11512856 [DELETED] 
File: 39 KB, 711x620, 1553121224451.jpg [View same] [iqdb] [saucenao] [google]

>> No.11512882
File: 1.37 MB, 1140x4777, official mg curriculum.png [View same] [iqdb] [saucenao] [google]

>> No.11512891

[math]\color{#781b86}{3.}\color{#751e8a}{14}\color{#72218d}{15}\color{#702591}{92}\color{#6d2894}{65}\color{#6a2b98}{35}\color{#672e9b}{89}\color{#64329f}{79}\color{#6135a2}{32}\color{#5f38a6}{38}\color{#5c3baa}{46}\color{#593ead}{26}\color{#5642b1}{43}\color{#5345b4}{38}\color{#5048b8}{32}\color{#4e4bbb}{79}\color{#4b4fbf}{50}\color{#4852c3}{28}\color{#4555c6}{84}\color{#4258ca}{19}\color{#3f5bcd}{71}\color{#405fcd}{69}\color{#4364c9}{39}\color{#4668c4}{93}\color{#496dc0}{75}\color{#4c71bc}{10}\color{#4f76b8}{58}\color{#527ab3}{20}\color{#557faf}{97}\color{#5883ab}{49}\color{#5b88a7}{44}\color{#5e8ca2}{59}\color{#61919e}{23}\color{#64959a}{07}\color{#679a96}{81}\color{#6a9e91}{64}\color{#6da38d}{06}\color{#70a789}{28}\color{#73ac85}{62}\color{#76b080}{08}\color{#79b57c}{99}\color{#7bb779}{86}\color{#7eb777}{28}\color{#81b875}{03}\color{#83b872}{48}\color{#86b870}{25}\color{#89b96e}{34}\color{#8bb96c}{21}\color{#8eb96a}{17}\color{#91b967}{06}\color{#93ba65}{79}\color{#96ba63}{82}\color{#99ba61}{14}\color{#9cbb5f}{80}\color{#9ebb5c}{86}\color{#a1bb5a}{51}\color{#a4bc58}{32}\color{#a6bc56}{82}\color{#a9bc54}{30}\color{#acbc51}{66}\color{#aebd4f}{47}\color{#b1bd4d}{09}\color{#b3bc4c}{38}\color{#b6bb4b}{44}\color{#b8ba4a}{60}\color{#bab849}{95}\color{#bcb748}{50}\color{#bfb648}{58}\color{#c1b547}{22}\color{#c3b446}{31}\color{#c5b345}{72}\color{#c8b244}{53}\color{#cab043}{59}\color{#ccaf42}{40}\color{#ceae41}{81}\color{#d1ad40}{28}\color{#d3ac3f}{48}\color{#d5ab3f}{11}\color{#d7a93e}{17}\color{#daa83d}{45}\color{#dca73c}{02}\color{#dea63b}{84}\color{#dea03a}{10}\color{#de9938}{27}\color{#dd9337}{01}\color{#dd8c36}{93}\color{#dd8635}{85}\color{#dd7f33}{21}\color{#dd7932}{10}\color{#dc7231}{55}\color{#dc6c30}{59}\color{#dc652e}{64}\color{#dc5f2d}{46}\color{#dc582c}{22}\color{#db522b}{94}\color{#db4b29}{89}\color{#db4528}{54}\color{#db3e27}{93}\color{#db3825}{03}\color{#da3124}{81}\color{#da2b23}{96 \text{...}}[/math]

>> No.11512910
File: 7 KB, 904x544, nisamucio.png [View same] [iqdb] [saucenao] [google]

pretty sure. consider the isosceles triangle ABC inscribed in the circle, it is impossible to fully put triangle ABC inside the semicircle with diameter DB. Rotate triangle ABC around the point B so that DB and AB overlap. because C rotated on a circle with a radius larger than the semicircle, now point C lies outside the semicircle. I know this doesn't test all the possibilities but it's pretty obvious

>> No.11512943

Why do you read "character table of real split form" and see "representation of compact complex lie group"? They're very, very far from the same thing. Lie groups are manifolds; if they're finite, they're extremely uninteresting. All the usual suspects are infinite, and have infinitely many irreducibles.
The real form of a complex lie algebra is a real lie algebra that complexifies to it. "Split" means it corresponds to a noncompact real lie group, whereas the compact real form corresponds to a compact real lie group.

You can't build a literal character table for a lie group/algebra, since there are infinitely many irreducibles. What you _can_ do is find a uniform method for computing a character; the Weyl character formula does this in the complex case. Even though there are infinitely many representations of a given lie algebra, the coefficients in the formula to go from representation -> character are exactly the same for all of them, since they depend only on the Weyl group. All you have to do is compute that set of coefficients once, and you can evaluate it anywhere you want.
You should think of the "character table of split E8" as something like a monstrously complicated Weyl character formula. With split E8, not all characters can be computed with only one formula, but you can partition your irreducibles up into finitely many blocks so that every representation in each block uses the same set of coefficients. The table tells you what the coefficients in the formulas are.

Some of this may be slightly inaccurate, so take a small grain of salt here (I do not specialize in this).

>> No.11512946

Are you super duper sure the maximization for A and B doesn't look like this, or like some other shape which still admits inclusion into the disk?

>> No.11512949
File: 3 KB, 563x317, aaaaaaaaaaaaaaaaaa.png [View same] [iqdb] [saucenao] [google]

Forgot my image.

>> No.11513002
File: 34 KB, 186x146, what_did_i_mean_by_this.png [View same] [iqdb] [saucenao] [google]

I mean [math]technically[/math] up to Morita equivalence the irreps of Clifford groups are classified by their ranks up to Bott periodicity but anon obv wasn't aware of that.

>> No.11513162

Oi, piece of shit, it was my time to create the thread.

>> No.11513205

Thank you

>> No.11513241
File: 763 KB, 2478x1333, 1585477516534.jpg [View same] [iqdb] [saucenao] [google]

How much time do you guys spend on the internet? How much time do you guys spend studying?

Me: almost all day on the internet, I only get motivated to study when the tests are near, I wanna know if there are more like me here

>> No.11513256
File: 227 KB, 333x499, 90C82zP.png [View same] [iqdb] [saucenao] [google]

>How much time do you guys spend on the internet?
all day
>How much time do you guys spend studying?
not much, i do the mandatory coursework and study for exams but nothing more

>> No.11513273
File: 211 KB, 602x535, 1581217307925.png [View same] [iqdb] [saucenao] [google]

I'll wait for you to make them if you quit it with the off-topic images.
I mean, nothing wrong with memes, but at least make them topical.
Basically, I spend most of the day alternating between studying and skimping out on studying by shitposting, reading manga, watching videos on youtube and making and drinking coffee.
Sometimes I get tired and just don't study anything for a day or two.

>> No.11513283
File: 1.80 MB, 1202x910, physical maths.png [View same] [iqdb] [saucenao] [google]

Threadly reminder to work with physicists.

>> No.11513291

I study hard for maybe 2-ish hours earling in the morning. 3 on a good day.
The rest of the time I'm online, but I work some of the time I'm online too. It's not as effective, but you can still do math while watching crap on youtube.

>> No.11513325
File: 185 KB, 1217x620, Geogebra4325.png [View same] [iqdb] [saucenao] [google]

Not super duper sure, but quite sure, don't know what to try anymore, picrelated

>> No.11513337
File: 73 KB, 1024x576, 1585348757429m.jpg [View same] [iqdb] [saucenao] [google]

Ayo boys, philosophy chad here.

Are there any exercise books you guys could recommend so I can develop my algebra 1 skills? I am aware that's an embarrassing request, but my mathematics illiteracy is holding me back in my philosophy of science studies.

>> No.11513340

or Lang's Basic Mathematics if you want to get memed

>> No.11513349

Herstein's Topics in Algebra should be good, I used it for my Algebra 1 class

>> No.11513354
File: 3.44 MB, 1034x1639, file.png [View same] [iqdb] [saucenao] [google]


>> No.11513362

there is only one way to put the halfcircle into a circle (up to rotation)
there is only one way to put this triangle into a circle, up to rotation
so if you assume "set(AB) can be still covered by the circle C" you have only one degree of freedom, just rotating the triangle around
so you can just put a parameter [math]\alpha[/math] for this angle and compute the minimum of a one-variable function
finally, compare to the configuration on the left of your picture

>> No.11513366

Art of Problem Solving - Pre-Algebra (It's mostly not just pre-algebra but it's very good to read this too)

Art of Problem Solving - Introduction to Algebra

>> No.11513375

>I'll wait for you to make them if you quit it with the off-topic images.
Ok, deal, you can make the one after the next.

>> No.11513380
File: 111 KB, 1024x576, 1585090090135m.jpg [View same] [iqdb] [saucenao] [google]

Thanks, fellas. I appreciate it a lot.

>> No.11513383

Herstein is algebra II.

>> No.11513452

well yeah, but from the right picture it is pretty obvious that whichever way you rotate it it will never be as small as the tiny area on the left, and the max area included in the semicircle will be at most 3/4 of the area of the triangle. So it doesn't work I guess.

>> No.11513460
File: 5 KB, 611x659, oh no no no no.png [View same] [iqdb] [saucenao] [google]

What if it's like this tho?

>> No.11513502

the other post said there's only one way to put an that (inscribed)triangle into a circle, up to rotation. will check tomorrow

>> No.11513860
File: 117 KB, 1314x1578, ratinablanket.png [View same] [iqdb] [saucenao] [google]

I like maths, I like cute animals, I like peace and quiet. I like the quarantine.

>> No.11514045

>Have 6 girls ready to fuck
>Can't because quarantined
I fucking hate it.

>> No.11514057

R u me?

>> No.11514067

what is tropical geometry about and what is it's motivation?

>> No.11514071

elements of modern algebra by linda gilbert is a nice one

>> No.11514072

it's like algebraic geometry, but it's hot and sweaty and there's a lot of bugs

>> No.11514112

Algebraic Geometry is the european superior continent

Tropical geometry is the south american peasant


>> No.11514442

One of the required classes for my masters states:
>The student must have a solid understanding of linear algebra, calculus, ordinary differential equations, and Fourier theory...
It's an engineering analysis course. What textbooks would you recommend for preparing for this? The most math I've taken so far was calc III & diffeq like... two years ago. I would just audit a bunch of math courses, but the math department at my uni is iffy. Plus the credits would still go towards my total registered amount and I'd have to pay for them.

Thanks in advance.

t. stupid mechE student

>> No.11514610
File: 313 KB, 1024x393, 1585553870599.png [View same] [iqdb] [saucenao] [google]

/mg/pill me on topos

>> No.11514612

muh gomboc

>> No.11514616

How do I get better at forming differential equations from a paragraph of information. I was always aces at forming an algebraic formula from word problems but with differential equations the language used just confuses me.

Also, with something like
>a raindrop evaporates at a rate relative to is surface area
How tf do I get (dV/dt) = -kV^(2/3) (where k is constant)? I knew it would be dV/dt and I know the volume and surface area of a sphere, but otherwise I have no idea.

>> No.11514619

For my final year of undergraduate, I have to pick either a paper on Math Logic or Hilbert Spaces do get a math major. Which should I do and why?

>> No.11514626

What math is it? Just say physics, finance or engineering.

>> No.11514770


>> No.11514776
File: 117 KB, 1280x720, 1582985375950.jpg [View same] [iqdb] [saucenao] [google]

Go for it if you are interested in categorical logic, pointless topology or the mixture of those two. Just remember that abelian toposes are pretty much the most well-behaved categories you can have.

>> No.11514987

You're extremely fucking annoying.

>> No.11514989

Studying is for smart people, so I just waste my time some way or other.

>> No.11515014

Unvirgins are not welcome here.

>> No.11515019

Thanks for the reminder anon.
I'm trying to prove Riemann Hypothesis to distract myself from my terrible situation.

>> No.11515025

Hilbert spaces are very useful and interesting, and easy. Math logic can be immensely autistic, so if you're not sure you like the topic you should avoid it. Besides that, what do you want to do after your undergrad? If a Master's, on which area?

>> No.11515075

I've done a discrete math/math logic precursor course to the 300 level math logic course I'm considering which I really enjoyed, but can't see the use.

Im considering doing a masters in nuclear physics, quantum physics (I'm doing a double math/physic major) or math masters of some kind... Idk just where ever life takes me. I don't know much about Hilbert spaces, cant they be quite useful for quantum physics?

>> No.11515080

>I don't know much about Hilbert spaces, cant they be quite useful for quantum physics?
Kek, obvious bait.

>> No.11515146

You can probably just sit in on the lectures without registering anything, no?
Anyway, I recommend MIT OpenCourseWare 18.06SC Linear Algebra. The lecture videos are by Gilbert Strang and they're very good. Should be all you'd need.
I'm sure the most Fourier theory you'll need is to read a tiny bit about fourier series and fourier transforms, and the basic properties of each. Spend a day on each one.

>> No.11515156

It's just algebra. Your variable is volume, you want to express surface area in terms of volume. What are the formulas for surface area and volume of a sphere? Can you solve for radius in terms of volume, and then plug the result into your surface area equation?
I suppose the coefficients don't matter since it says "rate relative" instead of the exact rate.
Now why the negative sign? Cause you want evaporation, i.e. decreasing volume.

>> No.11515160

Hilbert spaces are quite literally the foundation of all quantum physics. Do that.

>> No.11515166

Don't "just spend a day on each one", anon. Spend as much as you may need.

>> No.11515173

Of course. I just meant he doesn't have to go deep into the theory of fourier series convergence, sampling theorems, poisson summation stuff, etc. All he needs is definitely "this is the definition, this is the inversion formula, this is what it does to derivatives, shifts, scaling, and products, hey look you can use it to solve the heat equation"
that's it

>> No.11515486

unrelated to math really, but I am an UG about to graduate in a semester, and at my school I can take some first year grad classes for credit. I work at a catholic school, and my principal knows im doing a graduate class, but I have reminded her multiple times that I am an UG. She seems to forget and advertises me as a graduate student in mathematics at our local university(to make me seem like a well qualified tutor for the kids) to other faculty and parents. I literally just don't feel like sending an email again to remind her cause it seems nitpicky. If I'm not lying about my academic credentials, but my boss is, can I get in trouble?

>> No.11515547

You're much more likely to fuck up your situation by ceaselessly trying to correct your boss than you are by somebody finding out you're secretly not quite a grad student.
It's quite unlikely anyone is ever going to know anyway; not even the most bored of helicopter moms are going to start calling around your department doing background checks on the tutor provided by their son's school.

>> No.11515723

Why are Eigenvectors and Eigenvalues important and why should I give a fuck about learning them?

>> No.11515741

many reasons
one of them is they let you decompose matrix into a nice form called jordan form

>> No.11515787

alright, thank you lad that makes sense.

>> No.11515792

They permit a method for calculating an nth power matrix easily

>> No.11515898

Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build with these new operations. These equations define piecewise-linear geometric objects called tropical varieties. We explore these tropical varieties in two and three dimensions, building up discrete tools for studying them and determining their geometric properties. We then discuss the relationship between tropical geometry and algebraic geometry, which considers shapes defined by usual polynomial equations.


A lot optimization,computation or math problems can be defined as Max or Min problem

>> No.11515970

the most immediate answer:

eigenvalues and eigenvectors solve the following two problems. given a linear transformation written as a matrix, how do we determine what does it do geometrically? given a linear transformation described by the geometry, how do we write it in matrix?

long answer:
just keep doing math and you will see that they appear fucking everywhere

>> No.11516188

The matrix of a linear transformation with a basis of eigenvectors is structurally revealing

>> No.11516201

cool, thanks

>> No.11516263

It seems you goofed off some of the video ID in the URL.

>> No.11516279


>> No.11516410

Could you explain a bit more where this identity comes from please?

>> No.11516556
File: 144 KB, 308x308, 1493515849631.png [View same] [iqdb] [saucenao] [google]

Just expand the polynomial.

>> No.11516558

i asked where it came from, not why is it true

>> No.11516573
File: 93 KB, 900x899, 1585530260539.jpg [View same] [iqdb] [saucenao] [google]

I'm back again.

Can one of you poindexters explain to me why -a + -a = -a


-a × -a = a

Why does multiplying two negatives get a positive?

Who invented this algebra shit anyway.

>> No.11516583

I miss middle school math.

>> No.11516594

I worked it out. I'm retarded.

>> No.11516622

Nonetheless one should learn the language of topos

>> No.11516663

You know, lad. The norm. Numberino times conjugaterino.
[math]\overline{ \omega } = \omega ^2[/math].

>> No.11516671

yes but that expression on the left is a multiplication of three terms, while when i think of norm i think of two terms

>> No.11516676

I also don't know where the first term comes from.
Second two are literally the norm, tho, since [math]\omega ^4 = \omega \times \omega^3 = \omega [/math].
Presumably just compute the norm normally and notice that stuff cancels out if you multiply by (a+b+c).

>> No.11516681

Well, but that doesn't really tell me where it comes from other than a clever identity that happened to be helpful here - I want to know if there is a more systematic way of handling that type of question. And in fact, the a+b+c term is pretty significant, since it's what gives us the "0" on the left hand side of the equation to give us the result

>> No.11516744

Is there a neat and tidy definition of category which doesn't appeal to objects?

>> No.11516851

You can do it all with just the arrows. You replace an object $C$ with a "0-arrow" $c$ such that, whenever defined, the composites $f\circ c, c\circ g$ are merely $f$ and $g$, respectively. Not a big surprise that this $c$ will turn out to be the identity of $C$.

>> No.11516853

Oops, imagine [(/)math] instead of $.

>> No.11516875

Yah, but that just tells me how to remove the objects from a given category. It doesn't give me axioms which guarantee I have a category (in the usual sense) from just the arrows.

>> No.11516936


>> No.11517047
File: 284 KB, 662x483, 1585103637525.jpg [View same] [iqdb] [saucenao] [google]

Can you guys aolve IMO problems?

Can you guys solve Putnam Problems?

I'm an average-IQ person, so I'm always insecure about whether or not I can train hard enough in order to solve them one day.

>> No.11517621
File: 195 KB, 264x503, 17H9Cyc.png [View same] [iqdb] [saucenao] [google]

my scores at the putnam have varied between 40 and 80
not sure if that qualifies as "being able to solve them"

>> No.11517665
File: 755 KB, 2460x1364, Bildschirmfoto 2020-03-31 um 12.07.13.png [View same] [iqdb] [saucenao] [google]


>> No.11517766

>I vary between top 5% and top .5% dunno how good I am tho xp
kill yourself animenigger

>> No.11517793

>tfw can't get past the drawing a tropical curve step
"just draw your triangles differently bro lmao"

>> No.11517944

Can someone please explain to me how you actually calculate global and local truncation error of a finite difference method? I'm not asking for an explanation of the terms, I'm asking how to *calculate* global and local truncation error for a specific FD method, as in what is the general procedure.

>> No.11518278

That works, thanks.

>> No.11518476

partial monoid

>> No.11518498
File: 103 KB, 461x600, Leonhard_Euler (1).jpg [View same] [iqdb] [saucenao] [google]

>partial monoid
The one defined here?

Do the axioms actually guarantee that it's the morphisms of some category?
Specifically, can you prove that, if [math]ab \neq *[/math] and [math]ac \neq *[/math], then [math]db \neq *[/math] if and only if [math]dc \neq *[/math], which roughly translates to the possibility of tracing back a codomain for [math]b[/math] and [math]c[/math]?

>> No.11518504
File: 917 KB, 1080x1847, Screenshot_20200331-182330_Firefox Preview.jpg [View same] [iqdb] [saucenao] [google]

I'm an undergrad in math and it worries me that I literally don't understand wtf is being discussed on mathoverflow. Does this mean math isn't for me?

>> No.11518511

Why do you expect that you should be able as an undergrad to understand a question so complicated that one of the best mathematicians in the world couldn't figure it out and decided to ask for help?

>> No.11518538

Yes, this is basic symplectic geometry. I learned it in the second year of my undergrad.
Go read Hofer's book on Symplectic Capacities or something.

>> No.11518543

I'm too lazy at the moment to think about it, but I've found this overflow question

>> No.11518631


>> No.11518646

yeah I don't know what 1+1 is guys please help. It's for homework.

>> No.11518656

all day on the internet here and only study near exams. If i were to rate possibly 7/10 since the internet was my tool for everything and because I hate that I study before an exam

>> No.11518671

How would you write a polynomial whose variables are a function and it's partial derivatives up to an order using multi-index notation?

>> No.11518673

20 years old and want to be proficient at math again. Started on Khan academy to revise on known concepts and to be 100% clear on them but is it a good start to do so?

Would like to know what sort of roadmap I should have since I'd like to be able to know more than what I had learnt about maths, potentially university level topics (i know there is a img general for books related), as well as, higher tiered concepts not relatively close to univeristy maths, as a means of a test of understanding. It really is one of my favourite subjects but due to bad life choices and silly mistakes, I have figured that this year onwards is my only chance at redemption.

>> No.11518687

it's the most beautiful equation in maths and involves euler's constant. 1 + 1 = e - (e-2) + 1 + i^2

>> No.11518692
File: 415 KB, 1100x1000, __kirisame_marisa_touhou_drawn_by_yomoi_nui__04fb8127b850df3ad7c2b5c62e384713.png [View same] [iqdb] [saucenao] [google]

Like this [math]\Sigma _{i, ~ \alpha} a_{i, ~ \alpha} ( D^{ \alpha} f )^i[/math]?

>> No.11518703
File: 647 KB, 910x800, __yakumo_yukari_persona_and_touhou_drawn_by_mazeran__42fa044c97f06b10c6cedb8bf59d4592.png [View same] [iqdb] [saucenao] [google]

>mfw I see people use \Sigma for summation
Also we perhaps don't want the [math]i[/math] index there since then [math]\sum_\alpha a_\alpha(x)D^\alpha[/math] ceases to be a linear operator on [math]f[/math], whence much of diff top/OA no longer apply. In particular I don't know how one would define the symbol of such an operator.

>> No.11518704

>tfw there's people far ahead of you by their second year of undergrad
But it's about how much you yourself progress, r-right guys? Haha, I mean, it's crazy to compare myself to this guy haha. S-Surely I don't have to think too much of it.

>> No.11518742

That would be nice, but he said that the variables are the function and the derivatives, so we unfortunately probably aren't working with the polynomial ring of differential operators.

>> No.11518745

You might be right, but that is definitely weird since not much can be done for those objects.

>> No.11518749

nothing is comfier than waking up at noon with the rest of the day ahead of you to write proofs and explore mathematics.

>> No.11518871

he's memeing, many mathematicians won't even know what is symplectic geometry if it doesn't intersect with their research interests

>> No.11518964

the absolute state of this board gentlemen

>> No.11518981

>implying that matters
Behold a poll truly capable of gauging this board's quality.

>> No.11519095

why are there so many chimps on this board? every other thread is 86iq garbage

is /sci/ not moderated?

>> No.11519100
File: 633 KB, 1600x1281, __nonomura_ryuutarou_and_yakumo_yukari_touhou_drawn_by_koissa__81e4edf30bac3c7e4c38ee6918383f70.jpg [View same] [iqdb] [saucenao] [google]

>no Kahler nor hyperKahler
Won't be voting

>> No.11519154

>no anon, you need to spend the entire week adding in web geometry, systolic geometry, Bieberbach groups and whatever specific object it is I like instead of hoping I can place it in a broad subfield myself
Just vote for complex geometry, symplectic geometry or Riemannian geometry lmao.

>> No.11519245

You don't even know what a kähler manifold is you pseud

>> No.11519261

You forgot hyperbolic geometry, algebraic geometry and arithmetic geometry

>> No.11519298

Why are pure maths people so fixated on one-upping each other in terms of wanting to seem like the smartest person in any given maths conversation? It's like they get off on explaining something in the most abstruse and useless way possible. The worst part is after they've formulated their point in the most abstract and obscure form possible, they'll claim that that's the most natural way to think about it for them, which of course is a lie meant to impress their equally insecure mathematician friends. You can visibly see them cum in the pants when they do this.

Why do so many mathematicians do this? Is it because they're insecure about maths being the only facet of their life in which they're able to express competence? It's like jocks trying to out-alpha each other.

I know this of course doesn't apply to everyone, but I would argue this is the case for a lot of mathematicians.

>> No.11519340
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I am taking Trigonometry and this week we are discussing Lissajous figures. I have to write a 500-word summary along with graphs, and for the research, I have to find two interesting facts about them. Apart from searching online and finding the usual answers (which I still have to source), I figured I would come to /sci/ and see if there are any unique perspectives in regards to Lissajous that are not online. I looked through the sticky and couldn’t find anything related.

>> No.11519342

I'm pretty sure it's a general human trait, much independent of the subject.

>> No.11519364

reminds me of

>> No.11519384

not all math people are like this, but a lot are
sadly I am guilty of doing this too although I taught to stop myself mostly
>Is it because they're insecure about maths being the only facet of their life in which they're able to express competence?

>> No.11519385

That's pretty amazing from what I watched. Thank you, Anon.

>> No.11519445
File: 57 KB, 960x720, CAST system.jpg [View same] [iqdb] [saucenao] [google]

When converting complex numbers from rectangular to polar form, do you need to change the angle only when the form is not contained in the first quadrant?

>> No.11519462

>change angle

where I'm sure there's a nice formula for arg, involving arctan or whatnot

>> No.11519480

What I mean is, say I have the polar form of:
r = -5
theta = -45
-5<-45 degrees

Do I leave it as that, or do I do 180 + (-45) = 135 and rewrite it as
because it is contained originally in the third quadrant.

>> No.11519501

is r the radius?

just take a positive radius and add 360 to the angle in case it's not in the range [0, 360)

>> No.11519610


If you care about results over prestige, use Schaums, and Dummies books are surprisingly good too. I personally after being out of high school for years wanted quick and dirty results for algebra used this book:

Practical Algebra: A Self-Teaching Guide, Second Edition 2nd Edition by Peter H. Selby (Author)

And it was fucking awesome. Low brow books, books for "idiots" are great learning sources because they ironically DONT spoonfeed you generalizations like the "smart people" books do, so YOU have to generalize from the concrete examples and exercises they give you BY YOURSELF. Always amuses me when I think about it but yeah. Have at it. Experiment, have fun, solve problems.


Set theory is pretentious cancer and you are sensible for being immediately repelled by it. Set theoretic notation literally adds ZERO new/novel information to whatever you are trying to say. It is completely redundant. How do I know this? ZFC is literally just predicate logic with membership "operator", i.e. set theory just forces you to talk about math in terms of predicate logic with a membership operator. That's it. It doesn't help you solve problems, it doesn't give you any extra intuition ABOUT how to solve a problem, it literally is just extra notational weight to add on for the illusion of rigor. If anything it decreases one's intuition and makes solving problems harder because you become more focused on description and making your notation look neat and pretty than actually figuring out how to solve the fucking problem. It's high order faggotry for people who are bad at math but want to sound good at it. All the "great" set theorists were essentially lawyers and logicians- verbally oriented faggots. It's the reason why physicists in the past 70 years have become better mathematicians than most math majors, and why the only good mathematicians coming out of math departments these days are students who study operations research.

>> No.11519622
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I made an argument that proves mathematically the existence of a God.

>Proposition I: Mathematics is the structure of the universe
This is true because mathematics is essentially the language in which physics amd chemistry use to explain the processes of the universe
>Proposition II: All mathematics stems from theorems, which must be proven either valid or invalid
This is, again, an intrinsic aspect of mathematics itself
>Proposition III: All proofs must have beginnings, those beginnings are the axioms, which can't be proven, just accepted as true
So, essentially, all math stems from axioms, it didn't come out of nowhere, all math came from a set of axioms which gave birth to several theorems and so on

Proof for the existence of a God:
From proposition I we can assume that mathematics is everything in the universe, if mathematics is everything then math was also the beginning, but from proposition III we know that all math begins with a set of axioms, but axioms are just absolute truths, therefore the beginning of the universe is an absolute truth, therefore the beginning of the universe can't be something like proposition III, therefore the beginning must be something that is absolute, a being that can't be from the universe itself, since the universe is just a case of proposition II, therefore there is a being, a god, who always existed and created everything, an axiom who started everything.

>> No.11519625

>Set theory is pretentious cancer

>> No.11519633

Ah yes, a rewording of the watchmaker argument
>not science or math

>> No.11519634

>therefore the beginning of the universe can't be something like proposition III
I meant proposition II

>> No.11519783
File: 87 KB, 322x302, B5EF74FC-292E-42A4-ABAA-F565ADDF0885.png [View same] [iqdb] [saucenao] [google]

Can anyone give me a hint on this proof? I am trying to prove that the sum of all the terms of the nth row of Pascal’s triangle is equal to [math]2^{n}[/math]. I wrote a proof using the binomial theorem and considering 2 as [math](1+1)^{n}[/math], but I get the feeling that there is probably a good way to prove it using induction and I wanted to practice that, but I am not able to figure it out.

>> No.11519791
File: 139 KB, 462x444, __fujiwara_no_mokou_touhou_drawn_by_shangguan_feiying__900a07ac968440ae9fb0c700e567ddfb.jpg [View same] [iqdb] [saucenao] [google]

>dude how many subsets does a set with n elements have
Literally that simple.
>inb4 how do I count subsets
Consider functions [math]S \rightarrow \{ 0, 1 \}[/math] or whatever.

>> No.11520045

Induction is a kind of aids way to do this (either the binomial theorem or the direct combinatorial argument is much better) but if you really wanted to you'd use pascal's identity:

[eqn]\sum_{k=0}^{n+1}{n+1\choose k} = 1 + (\sum_{k=1}^{n}{n \choose k}+{n \choose k-1})+1[/eqn]

>> No.11520053


That's it? Wow great comeback.

>> No.11520092 [DELETED] 

First try to prove:

[math]\binom{n+1}{k} =(1 +\frac{k}{n+1-k})\binom{n}{k}[/math]

>> No.11520108

First prove that


>> No.11520649

axioms are strings of symbol that a computing machine parses to output theorems. they are not "true", just accepted by some machine. yes, mathematics and its axioms are structures of the universe existing in thought or symbol, but it is not physics itself, we are just matching up symbols with observations. if you take two objects and stack them, they are not "adding." you are describing them additively. for a thought experiment, you could pour one glass of water into another, and you could either say youve added the volumes or that 1+1=1, where two solo cups return to one when mixed. a physical system is describable in any way, as long as our mind can perceive a connection between a description and the system

>> No.11520877
File: 8 KB, 721x169, limexp.png [View same] [iqdb] [saucenao] [google]

Hey guys, how's it going? What did my professor mean by this and what does this tell us about disease spreading?

>> No.11520893
File: 20 KB, 205x246, 1515668151539.jpg [View same] [iqdb] [saucenao] [google]

I know this is a difficult time but can we please keep /mg/ and /sqt/ math related! Thanks.
The virus is nothing to worry about!

>> No.11520900

please stay isolated in your threads don't spread the virus!

>> No.11520927
File: 132 KB, 1050x902, gigachad2.jpg [View same] [iqdb] [saucenao] [google]


>> No.11521287

The negative of a number is such that you get 0 when you add it. -x is defined by

x + -x = 0

What is -(-x) then? It would be the number such that

-x + -(-x) = 0

but we already know that -x + x = 0, so therefore -(-x) = x.

>> No.11521294

>I don't know much about Hilbert spaces, cant they be quite useful for quantum physics?
funny anon

>> No.11521307

I don't solve problems. I don't care. Why? Because I'm not a mathematician.

>> No.11521314 [DELETED] 

M always comes before D

its 1

8 / 2(2+2)
8/ 2(4)
8 / 8

>> No.11521315

Almost no one knows symplectic geometry. That said there are definitely people far ahead of you so don't get too relaxed.

>> No.11521329

All people are like this. You're singling out math for whatever reason.
>It's like jocks trying to out-alpha each other
Yes exactly. It seems you know the answer already.

>> No.11521335

>That's it? Wow great comeback.

>> No.11521352

isn't this circular?

>> No.11521353

>philosophy chad

Lel just switch to math. It has more actual results about transcendental ideals than philosophy and you will discover that philosophers suck dick at careful arguments.

>> No.11521361

No. Think about it. How would you define a negative of a number? It's the number you have to add to get 0. Then it's clear why the negative of a negative is a positive, because what you have to add to the negative to get 0 is just the positive.

>> No.11521381

couldn't you just say if x + -x = 0 then multiply by -1
-x + -(-x) = 0 so
-(-x) = x

>> No.11521402

You should learn CT instead, it's philosophy with cute symbols!

>> No.11521412

That works too if you use -1 * x = -x. You can prove this using the definition I gave with the distributive property of addition x + -1 * x = (1 + -1) x = 0 x = 0 so -1 * x = -x.

>> No.11521500

very cool!

>> No.11521546

take natural numbers with addition (which we take for granted) and multiplication defined as repeated addition. this naive arithmetic satisfies some properties such as the distributive law. now you make this into integers by introducing additive inverses. then you make this into rationals by adding multiplicative inverses. but each time you add new numbers, you need to say how does the addition and multiplication work for them. you can define -7 + 2 =: 100 for all I care. BUT there's always only ONE way to do this so that you stay consistent with the rules of the naive arithmetics that you started with.

>> No.11521596

>This is true because mathematics is essentially the language in which physics amd chemistry use to explain the processes of the universe
There is no chemical or physical law that is known to be true. In fact historically every single physics theory turned out to be false (see e.g. Newton's laws, various models of atoms, etc.). There simply is no evidence for this claim.

>This is, again, an intrinsic aspect of mathematics itself
False. In fact, this is provably false. See CH as an example.

>So, essentially, all math stems from axioms, it didn't come out of nowhere, all math came from a set of axioms which gave birth to several theorems and so on

So 2/3 of your propositions are either false or without evidence...

>> No.11521609

e=mc2 + 2 - 3 = COOOOF COOF COOOF COOOF!!!

>> No.11521639

>So 2/3 of your propositions are either false or without evidence...
That's how it goes with religions.

>> No.11521647

>That's how it goes with religions.
Or with nearly anything else, like science.

>> No.11521670

What are the most autistic fields of maths? I already know about categories, sheaves, topoï, etc... I want something as autistic as that if possible.

>> No.11521691

How about the topopluralogy which is the study of the plural of "topos"?

>> No.11521907

set theory/formal logic is as autistic as it gets
the autism value of heavily abstract categorical shit like topoi isn't bad, but it's offset by the pretentiousness.
logic is pure distilled autism without anything to dilute it

>> No.11521912

model theory

>> No.11521914

you don't seem so well anon. are you sure you don't want to take the day off ?

>> No.11521991

how are you coping with the virus guys

>> No.11522003

Have we found out already how it's contracted?
If I were to write a simulation, I guess it's just sticking and writing in threads with infected guys

>> No.11522063

model theory is just algebraic geometry with extra steps tho

>> No.11522126

Is there a way to prove the formula [math]\int_0^t x^n= \frac{t^{n+1}}{n+1}[/math] in general without appealing to the FTOC or Bernoulli numbers? Specifically using Riemann/Darboux integration.

I've tried it and eventually reached the point where one gets [eqn]\lim_{m\to\infty} \frac{t^{n+1}}{m^{n+1}}\sum^m_{i=1}i^n[/eqn]

Evaluating for small [math]n[/math] gives the expected answer using the known formulas for sums of powers, but is there a more clever way?

>> No.11522216

You can do an induction, but for that you would need a product rule, I think, which of course involves the Fundamental theorem of calculus...

>> No.11522280

Oh dear. /mg/ appears to be flying close to the sun today.

>> No.11522282 [DELETED] 


>> No.11522283 [DELETED] 


/pol/ has a huge cure thread, from what I've seen they have a script to prevent infection.

>> No.11522284

I don't care anymore, I just want to surrender.

>> No.11522304 [DELETED] 
File: 229 KB, 687x768, 1578705591436.png [View same] [iqdb] [saucenao] [google]

15 minutes have now passed since this clean post, noting observations.

>> No.11522305 [DELETED] 

Infected fucking shits please stay 6ft away from me.

>> No.11522306

Have you tried using different approximations of the area, i.e. trapezoidal?
Ultimately, you just need to figure out how to make shit cancel out.

>> No.11522319

>most autistic
Anything with "derived" in the name.

>> No.11522322

>that picrel
is it that guy from "blues brothers"

>> No.11522433 [DELETED] 

I wonder if there's a factor where you can only transmit it if you don't show symptoms.
Maybe people with the quarantine symbol are sick, but can't get others sick

>> No.11522434

Can you provide an example please?

>> No.11522474

Derived differential geometry.

>> No.11522520

You don't need to know anything about Bernoulli numbers here; every term with a Bernoulli number in front of it has degree less than n+1 and is just going to die in the limit anyway. All you need to prove is that [math]\sum_{i=1}^mi^n = \frac{m^{n+1}}{n+1}+(lower degree stuff)[/math]

and this you prove this inductively by expanding out [math](m+1)^{n+1} = \sum_{i=1}^m(i+1)^{n+1}-\sum_{i=1}^mi^{n+1}[/math]

>> No.11522525

jesus christ, is there any reason to do differential geometry like that besides autism ? I mean, does this acomplish anything, does it lead to interesting results which would be hard or impossible to prove in less abstract setting ?

>> No.11522541

Dude replacing 200 pages of math with 1100 pages of commutative diagrams is the Right Way To Think About It™ who cares if it accomplishes anything new

>> No.11522577

There are usually three reasons to abstract things further:
>there are interesting constructions you can do on set of objects which doesn't return an element of your set of objects, but still returns an object that shares many features with it, so you abstract things until your categories close off and your functors become endofunctors
>the new object is genuinely simpler to define and intuit than the previous one
>genuine autism
I'm pretty sure DDG is a case of the last one.
But sometimes, cases of the last one become cases of the first one, so you might want to check back on it in a few decades.

>> No.11522747

Higher Topos Theory

>> No.11522758


>> No.11523006

I'd say set theory, logic, model theory just like the other anones said.
although my opinion on CT is that it isn't autistic - but just too pretensions for its own good

>> No.11523155

We meet again
I recommend A-plus notes for Algebra, it covers everything you'd need to know plus more

Also you said eastern metaphysicians didn't understand that base realtiy is pain, does the Buddha not realize this?

>> No.11523493
File: 111 KB, 1200x1940, Angle_axis_vector.svg.png [View same] [iqdb] [saucenao] [google]

Rotations - logarithm edition


>> No.11523998

Is there an elegant way to generate list {x, f[x], g[x], f[f[x]], f[g[x]], g[f[x]], g[g[x]], f[f[f[x]]],...,g[g[g[x]]]} in Mathematica?

>> No.11524332

True, but you would need to know a priori what that sum looks like

>> No.11524502
File: 143 KB, 1440x1080, 0.jpg [View same] [iqdb] [saucenao] [google]

yo nikolaj why doesn't ron maimon ever hang out with us

>> No.11524980

If you do a solid course in real analysis (in R^n) and algebra by your junior year/start of senior and get in one or two graduate classes for senior year you are doing just fine.

You aren't on your way to starting a harvard Phd, but you can reasonably apply for phds or masters at state schools.

>> No.11524985

>axioms are strings of symbol that a computing machine parses to output theorems

No. This just one formalization to reason about them.

Every predicate is true or false, unless you don't believe in excluded middle. Any predicate which you can accept as a starting point for deduction is an axiom.

>> No.11525013


IDK how to do math on chan.

integral of f over rectangular region is described
by nested sums of i and j. The base of a piece has area 1/n^2 and a height of f(i/n, j/n).
Plug into exp. Exp(a + b) = (exp a)(exp b).
So sums become products. Apply an exp definition to get the right form.

>> No.11525020

Press the tex button on the top left of the reply box

>> No.11525025

I fucked you're Touhou

>> No.11525031


>> No.11525243

Look up the book by VI Arnold "Mathematical Methods of Classical Mechanics". He has a great chapter on lissajous figures!

>> No.11525329

Is there any prime number [math]p[/math] larger than 3 so that [math]p^p+2[/math] is also a prime number? I got stuck on this problem.

>> No.11525340

No. Use Fermat.

>> No.11525341
File: 116 KB, 1280x720, njwdesu.jpg [View same] [iqdb] [saucenao] [google]

Was watching a NJW video recently and he said the Fundamental Theorem of Arithmetic doesn't work for big numbers since we can't write down there prime factorizations. In fact it seems to me he's claiming most basic number theoretic properties break down on really big numbers. Is this true or is he just being a crackpot?

>> No.11525348

Brainfart. Forget.

>> No.11525354
File: 175 KB, 736x1186, 1585743674239.jpg [View same] [iqdb] [saucenao] [google]

I'm learning topology and I don't understand one thing.

Let [math]V[/math] be a normed space for simplicity, and let [math]C[/math] be some set in [math]V[/math]. For some continuous linear functional [math]f: V \to \mathbb{R}[/math], define

[math]\mu = \inf_{x \in C} f(x)[/math].

Now, this means that there is a sequence of [math]\{x_n\}[/math] in [math]C[/math] such that [math]f(x_n)[/math] converges to [math]\mu[/math]... but in what topology? Is this predetermined? Do we fix the topology at some stage? I'm lost about this.

>> No.11525358

If there is no mention of a topology on [math]\mathbb{R}[/math], then it is the usual one. Note that the convergence is happening in that space.

>> No.11525366

Right, but also [math]x_n[/math] are converging to some point in the space [math]V[/math], is that not correct? I was curious about that convergence.

>> No.11525380

Judging by your post, there is no reason to assume that. The image of that sequence converges, but that doesn't imply anything on the original one. A stupid example: [math]a_n=n[/math] but [math]f(a_n)=1[/math] for all [math]n\in\mathbb{N}[/math].

>> No.11525381

No, not necessarily.

>> No.11525387

Okay, thanks. To expand: say that the set [math]D = \{ y \in V : f(y) = \mu \}[/math] is non-empty. Can I conclude that [math]\{x_n\}[/math] converges to some [math]y \in D[/math] if [math]f(x_n)[/math] converges to [math]\mu[/math]?

>> No.11525391

No. Take the zero function.

>> No.11525395

I just meant some non-pathological example, although I'm not quite sure what that would be. Say that the closure of [math]C[/math] intersects [math]D[/math] at only one point, do we get convergence to that point?

>> No.11525431

>Say that the closure of CC intersects DD at only one point, do we get convergence to that point?
I think this is true. you can deduce that distance between x_n and D goes to zero in any case.

>> No.11525478

Does anyone know anything about the regularity of the obvious function
[math]sort: \mathbb{R}^d \longrightarrow
Is it differentiable?

>> No.11525489

Assuming you mean the function that takes in a sequence (x_1, x_2, x_3, x_4) and returns the sequence in nondecreasing order,
It's continuous.

>> No.11525496

>is it differentiable
No, consider the partial derivative along x at the point (0,0,0,0)
right limit of sort(t,0,0,0)/t= (0,0,0,1) but the left limit is (1,0,0,0)

>> No.11525504

Adding to it: the total derivative should be something like
[math] D_sort(x) = P_{\sigma(x)} [/math] where [math]\sigma(x)[/math] is the sorting permutation and [math]P_{sigma(x)}[/math] is the matrix that performs this permutation (or the inverse idk)

>> No.11525510

Adding to this, it's differentiable at and only at the points away from the closed set {(x_1, x_2, x_3, x_4): for some i!=j, x_i=x_j}. The derivative depends on which component of this open set you are. It's constant on the components and is a permutation matrix.

>> No.11525512

>Is this true or is he just being a crackpot?
It is just his view on mathematics.
He believes that if it is physically impossible to calculate something then it is meaningless to talk about it.

>In fact it seems to me he's claiming most basic number theoretic properties break down on really big numbers.
He believes the natural numbers are finite, of course that HAS to break things like prone factorizations...

>> No.11525519

I'm trying to explicitly differentiate the Steiner symmetrization as a function that takes a polygon with n points to a polygon with 2n-2 points. It involves sorting the points by their x-components.

>> No.11525531

You can rewrite the infimum as inf {f(x) | x in C}, you see that the ONLY topology that matters is the topology on R, since this is just an infimum of a subset of R.
You don't really have to consider any properties of V, it doesn't need to have any topology at all, so you can't really expect to get any knowledge on the sequence of preimages.

>> No.11525574

-a + a = -a + a
-a + - a = 0 -a - a
3 * 2 = 0 +2 + 2 + 2
3*-2 = 0 + -2 + - 2 + - 2
-3*-2 = 0 - - 2 - - 2 - - 2

>> No.11525834 [DELETED] 
File: 27 KB, 418x450, depositphotos_173773006-stock-illustration-vector-ponder-emoticon.jpg [View same] [iqdb] [saucenao] [google]

Take a norm-closed subset [math]X[/math] of a hilbert space [math]\mathcal{H}[/math]. We get a set of trace-class operators by defining [math]\{ xx^* : x \in X \rset[/math]. Is this set norm-closed in the space of trace-class operators?

>> No.11525835
File: 27 KB, 418x450, 1585835174937.jpg [View same] [iqdb] [saucenao] [google]

Take a norm-closed subset [math]X[/math] of a hilbert space [math]\mathcal{H}[/math]. We get a set of trace-class operators by defining [math]\{ xx^* : x \in X \}[/math]. Is this set norm-closed in the space of trace-class operators?

>> No.11526153
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There's various "Nest" functions, but for this one I'd generate all binary strings and then to a small loop.

I know that he was on 4chan for the truther stuff at one point, but I don't take him for a big memes consumer. Not sure.
Last time I've emailed with him was years ago - where does he currently hang out, if at all?

On a different note, Todd Trimble is going live now with a talk


>MIT Categories Seminar LIVE - Todd Trimble: Geometry of regular relational calculus

>> No.11526209

>but for this one I'd generate all binary strings
no wait, I'm stupid, what's better is probably, in pseudocode,

r = {x}; while(true): r = map(f, r) join map(g, r);

and dump the inbetweens

>> No.11526348

is "[math]\{xx^* : x \in X\}[/math] is subset of trace class operators" an assumption? what do you mean by trace class, because the way I know it the problem doesn't make sense

>> No.11526413

anons, I don't think this is correct, unless they mean an approximate.

I can get down to the products, and one could approximate exp(x) by 1 +x, but I don't see why the other terms should go away.

>> No.11526415
File: 20 KB, 704x524, exp.png [View same] [iqdb] [saucenao] [google]

pic related

>> No.11526416

Hi can you reply to this
with "this", "/thread", "agreed" and so on, thanks.

>> No.11526419


>> No.11526429

I mean, the set of projection operators [math]\{ p_x : p_x(\cdot) = \langle \cdot, x \rangle x, \; x \in X \}[/math]

>> No.11526461

>this nigga

>> No.11526521 [DELETED] 
File: 51 KB, 1149x833, intexp.png [View same] [iqdb] [saucenao] [google]

I find a bunch of formulas like this, mostly because in one dimension it relates to the Dyson formula (there the one dimension is time)
I imagine this thing pops up if you deal with field theories and you got some x's to integrate over.

Could it be that you're off by one an you get a boundary term via
[math]\int_0^1 F(x) dx = \sum_{i=0}^{n-1} G(i) = \sum_{i=1}^n G(i) + G(0) - G(n) [/math]

>> No.11526557
File: 51 KB, 1149x833, intexp.png [View same] [iqdb] [saucenao] [google]

I find a bunch of formulas in my notes, mostly because it relates to the Dyson formula
In that context, it's one dimensional with time, but for field theories in RxR^3 such integrals might pop up.

Could is be that you're off by one, leading to a canceling boundary term via
[math] \int_0^1 F(x) dx = \sum_{i=0}^{n-1} G(i) = \sum_{i=1}^n G(i) - (G(n) - G(0)) [/math]

It's interesting, can you try a simple monomial or rational function and take the limit on wolframalpha or so?

>> No.11526608 [DELETED] 

the form in the question does not have an exponential inside the double product, and it also has a +1

>> No.11526615

I can see that the exponential could be approximated by a 1+ x expression, but dont see the equality

>> No.11526646 [DELETED] 

I made following code:
RESULT = {{x}}; Table[AppendTo[RESULT, Flatten[{Map[f, RESULT[[-1]]], Map[g, RESULT[[-1]]], Map[h, RESULT[[-1]]]}]], 3];
Flatten[RESULT] gives
{x, f[x], g[x], h[x], f[f[x]], f[g[x]], f[h[x]], g[f[x]], g[g[x]], g[h[x]], h[f[x]], h[g[x]], h[h[x]], f[f[f[x]]], f[f[g[x]]], f[f[h[x]]], f[g[f[x]]], f[g[g[x]]], f[g[h[x]]], f[h[f[x]]], f[h[g[x]]], f[h[h[x]]], g[f[f[x]]], g[f[g[x]]], g[f[h[x]]], g[g[f[x]]], g[g[g[x]]], g[g[h[x]]], g[h[f[x]]], g[h[g[x]]], g[h[h[x]]], h[f[f[x]]], h[f[g[x]]], h[f[h[x]]], h[g[f[x]]], h[g[g[x]]], h[g[h[x]]], h[h[f[x]]], h[h[g[x]]], h[h[h[x]]]}

>> No.11526737

good ideas. I am not familiar with the dyson formula.

I'll try a concrete f in wolfram as you suggest.

>> No.11527555

If I’m a pretty bright guy, can I read Lang or Jacobson as my first exposure to algebra? I had to learn basic group theory for Van Kampens theorem but that was on a need to know basis.

>> No.11527588

He is mentally ill.

>> No.11527619
File: 65 KB, 1068x601, gigachad.jpg [View same] [iqdb] [saucenao] [google]

I can lift one grain of sand.
If I can lift n grains of sand, I clearly can lift n+1 grains of sand.
Thus, by induction, I can lift an entire beach.

>> No.11528391
File: 14 KB, 161x263, pls no.jpg [View same] [iqdb] [saucenao] [google]

Peano axioms BTFO!!!!!!!!!!!!

>> No.11528397

Very cruel.

>> No.11528409

I really like this. This is one of my favorite mathematical paradoxes.

>> No.11528713
File: 47 KB, 800x533, mochizuki.jpg [View same] [iqdb] [saucenao] [google]

>Nature: Mathematical proof that rocked number theory will be published

>After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in number theory, has been accepted for publication.

>Acceptance of the work in Publications of the Research Institute for Mathematical Sciences (RIMS) — a journal of which Mochizuki is chief editor, published by the institute where he works at Kyoto University — is the latest development in a long and acrimonious controversy over the mathematicians' proof.

>Two other RIMS mathematicians, Masaki Kashiwara and Akio Tamagawa, announced in Japanese the publication at a 3 April press conference in Kyoto. The paper “will have a big impact”, said Kashiwara. When asked how Mochizuki reacted to news of the paper's acceptance, Kashiwara said, “I think he was relieved."

>At the press conference, Tamagawa said the solution itself had not changed in response to Scholze and Stix's criticism. There are some comments about it that will also be published in the manuscript, but no fundamental change, said Tamagawa.

>> No.11528839

how analytics is his theory, really?

>> No.11528851

>how analytics is his theory, really?
What do you mean?

>> No.11529032

>Mochizuki is literally publishing a 600 page book in a journal where he's chief editor

>> No.11529254

a lot
i study on my own for fun pretty much all day

>> No.11529351
File: 2.69 MB, 2048x2048, Julia_Mandelbrot_Relationship.jpg [View same] [iqdb] [saucenao] [google]

Why do multiple Julia fractals look like one giant Mandelbrot fractal?

>> No.11529364

Because Mandelbrot did with computers what Julia tried to do by hand.

>> No.11529892

Would someone recommend me book about Calculus written c. 1920? (In English, German or French)

>> No.11529898

Why not Rudin?

>> No.11529903

>Why not Rudin?
Rudin is a meme.

>> No.11529906

Only if you're a moron.

>> No.11529907

it's closed: if [math]p_{x_n} \rightarrow p_x[/math] then
[math]\langle x, x_n \rangle x_n = p_{x_n}(x) \rightarrow p_x(x) = \langle x, x \rangle x[/math]
now write [math]x_n = a_n x + y_n[/math] where [math]\langle x, y_n \rangle = 0[/math] and you'll get that [math]x_n \rightarrow x[/math]

>> No.11529911

Science is a process. I'd like to see how Calculus looked like 100 years ago.

>> No.11529966

Calculus Made Easy by Thompson. Published 1910 originally. It's actually better than many modern books. Actually tells you why they call it calculus.

>> No.11529973

>Only if you're a moron.
If you're a moron or if you're not a moron.*

>> No.11529991
File: 554 KB, 743x757, 1325433879219.png [View same] [iqdb] [saucenao] [google]

When I was learning proofs, I recall my professor telling me that
[math] P(n-1) \Rightarrow P(n) [/math]
was a better or more robust or more educated way to do induction proofs than
[math] P(n) \Rightarrow P(n+1) [/math]

but I don't remember how he justified that. Can anybody provide input, re: how that might be the case?

>> No.11529995

There's no difference between the two.

>> No.11529999

Your professor was insane. Not uncommon. Many of my professors were as well.

>> No.11530013
File: 30 KB, 500x600, 328dd54ac0a1a575c21345f3034afab2.jpg [View same] [iqdb] [saucenao] [google]

Usually my natural response would also be that the former is weird, but I happened to write a Wikipedia article a few months ago where I found doing it like this helped me making a point.
I found the former makes stating some statements more natural, because you get P(n) as conclusion, but as far as the proof praxis goes, plugging in n-1 to derive at something will usually be more awkward.

>> No.11530047

your professor is an autist

>> No.11530069
File: 296 KB, 500x375, wildburger.png [View same] [iqdb] [saucenao] [google]

Hey anons, I've started what I hope is a reading-club type thread >>11530059, dedicated to field and galois theory

>> No.11530097

Physics friend here learning some set theory. I'm reading Halmos' "Naive Set Theory" and I don't entirely follow something he says:
A relation in a set is an equivalence relation if it is reflexive, symmetric, and transitive. ... the largest equivalence relation in [math]X[/math] is [math]X \times X[/math].
No matter how I think about it I don't see how [math]X \times X[/math] is an equivalence relation like this. Can anyone offer some understanding?
Thanks nerds!

>> No.11530107

Anon, a relation on [math]X[/math] is literally a subset [math]R[/math] of [math]X \times X[/math], where we write [math]aRb \leftrightarrow (a, b) \in R[/math].
Ask this shit in >>>/sci/sqt/

>> No.11530116

Kill yourself, brainlet. You will never be smart.

>> No.11530117

>I don't see how X×XX×X is an equivalence relation like this.
Everything is in relation with everything.

>> No.11530118

I understand that, what I don't get is how it's an equivalence relation

I wasn't sure about posting this in here compared to /sqt/ but I had a scan through and decided it was fine

>> No.11530124

This is literally kindergarten mathematics, moron. Gtfo of this thread.

>> No.11530130

>what I don't get is how it's an equivalence relation
The three axioms hold trivially. Literally just check them. I don't understand what there is not to get. Which one of the three axioms are you incapable of verifying?

>> No.11530152
File: 78 KB, 799x533, 9 (2).jpg [View same] [iqdb] [saucenao] [google]

[math] \color{red}{\heartsuit} [/math]

>> No.11530156

It's the relation where everything is in relation to everything. LITERALLY look at the axioms, you don't even need to think, since the conclusion holds trivially.

>> No.11530167

I dunno, probably my issue is with relations in general more than this specific example

>> No.11530169
File: 1.87 MB, 1854x2603, __fujiwara_no_mokou_touhou_drawn_by_hisha_kan_moko__b4c6e5fcb1c1d02faefd9dbb88f3f82b (1).jpg [View same] [iqdb] [saucenao] [google]

>I had a scan through and decided it was fine
Please don't depress me like that.

>> No.11530173

If your issue is not with the particular question but the subject itself then you shouldn't ask for help with the question.

This is seriously trivial and immediate from the definition.
Try re-reading the chapter and asking in /sqt/ if you don't understand something.

>> No.11530205
File: 7 KB, 270x187, Cedric Villani.jpg [View same] [iqdb] [saucenao] [google]

if you consider all the irrational numbers between 0 and 1, and presume that they are regular - in that all the 10 digits appear in their decimal expansion with equal probability, then

What's the difference between one irrational number and any other?

>> No.11530222

What the fuck is this question?

>> No.11530223

I'm pretty certain that not every irrational number is normal. (Take normal number. remove all 0s from decimal expansion.)

>> No.11530239

For me, it's the irrational number which goes n 0s, one 1, n+1 zeroes, etc.

>> No.11530394

>assume false thing
>then ask a gibberish question
great job there my lad

>> No.11531392


>> No.11531418
File: 149 KB, 640x480, 1585361399130.gif [View same] [iqdb] [saucenao] [google]


>> No.11531443

To make [math]2^{bump}[/math] write 2^{bump}.

>> No.11531597
File: 18 KB, 311x499, 41YNYb3lc2L._SX309_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google]

Has anyone here used this book before? How is one meant to learn the subject without exercises? Should I use a secondary text for exercises?

>> No.11531600

Read Ireland&Rosen

>> No.11531607

Thanks. In lock down and have nothing but time

>> No.11531805

Let [math]v_1, \dots v_k[/math] be vectors in [math]\mathbb{R}^2[/math], such that [math]||v_i|| \leq 1[/math] for each i, and [math]\sum_{i=1}^k v_i = 0[/math]. Here [math]||\cdot||[/math] denotes the Euclidean norm.
Let's define [math]f(v_1, \dots v_k) := \max_{1\leq j \leq k} ||\sum_{i=1}^j v_i||[/math].
Prove: there exists a constant [math]C > 0[/math], such that for any sequence of vectors [math]v_1, \dots v_k[/math] as above, there exists a permutation [math]v_1', \dots v_k'[/math] such that [math]f(v_1', \dots v_k') \leq C[/math].

>> No.11531812

[math] 2^{bump}[/math]

>> No.11531821
File: 2.67 MB, 3072x4096, IMG_20200404_122945486_HDR.jpg [View same] [iqdb] [saucenao] [google]

For se illegal reasons I have this book, and I think I like it, but it's just so thick. Other books on number theory jump more quickly into aspects of general theories (ring theory tools, etc.) while that on is more long wondered, I felt.
As to your question, I agree that exercises are important, but actually just trying to understand the proofs in honesty will have you occupied as well.

(bump)! for your thread

>> No.11532016

>Other books on number theory jump more quickly into aspects of general theories (ring theory tools, etc.) while that on is more long wondered, I felt.
These things are mostly just indications of the book's age. The first edition of Hardy and Wright was published in 1938; I doubt English students in the 30s would not have been expected to know very much abstract algebra, if any at all, whereas today it's just basic bedrock knowledge so authors are comfortable using it freely.

And I doubt Hardy would even have known Bourbaki existed at all yet, and their influence on writing mathematics was decades from really taking hold. Pre-Bourbaki math texts tend to be much more focused on verbal rather than symbolic explanations of things, which can make them feel wordy and rambling to people who grew up with the modern style.

>> No.11532040

Set [math]C = k[/math].
The remainder is trivial and left as an exercise to the reader.
Unless [math]C[/math] needs to be independent of k, in which case 2 probably works, but the proof sucks.

>> No.11532044

My bad, 1 works and is optimal.
Just run the whole "If the sum until k is negative, set a positive number for k+1, and if it's positive, drop a negative". Trivially the modulo is always smaller than 1, and you can show that you can in fact choose negative/positive elements from the sum being zero.

>> No.11532045

yes I wanted C to be independent of k

>> No.11532047

>if the sum is negative
we are talking about R^2 vectors dude

>> No.11532054

Irrelevant tbqh. If summing any element to the sum until k increases the norm, then the total sum cannot equal zero.

>> No.11532059

I need help for my bachelor thesis please

It's a statistics/probability question first and programming - python question second.

>> No.11532062

Take 3 unit vectors each at 120 degree angles with each other. The bound cannot be 1.

>> No.11532068

>sum two of them
>negative of the third one
>norm is trivially one
Nice counterexample.

>> No.11532071

I gave you an upvote to be at least positive.
W.r.t. the question, I'd go for a simple 2 or 3 dimensional example to validate your guess of what's going on and rule out what the formulas can't be.

There's also Math and Stats SE btw.
I don't know why you tie your question up with programming at all - seems like once you know the statistics of it, the python would be trivial to implement.

>> No.11532083

C = 1 doesn't work, try for example
[math]v_1 = v_2 = \dots = v_{10} = (\sqrt{1 - 1/400}, 1/20)[/math],
[math]v_{11} = v_{12} = \dots = v_{20} = (-\sqrt{1 - 1/400}, 1/20)[/math],
[math]v_{21} = (0, -1)[/math].

>> No.11532084

thanks for the reply, I'm a brainlet on a university for brainlets.

the problem (for me) is, the co-occurence matrix is something completely new to me that I've just copied and pasted from other stackoverflow question. as such, I don't really understand if what I'm doing with it is correct on the basic level.
thank you also for the SE maths tip, I will post it there.

>> No.11532100

Fair enough.
You do know that you could run the counterexample with only five vectors, tho, right?

>> No.11532101

What would that look like?

>> No.11532124
File: 625 KB, 1325x2048, The Night of Your Life-032.jpg [View same] [iqdb] [saucenao] [google]

I think we can all relate.

>> No.11532127

No. In fact it has been quite a long time since I had a written exam.

>> No.11532129

[eqn]v_1 = v_2 = (\sqrt{1- 1/25}, 1/5)[/eqn]
[eqn]v_3=v_4 = (- \sqrt{1-1/25}, 1/5)[/eqn]
[eqn]v_5 = (0, -1)[/eqn]

In other words, the exact same thing with 20 swapped by 5.

>> No.11532132

Wait, fuck, might have made a mistake somewhere.

>> No.11532196

I wish I could, as then I'd be a girl.

>> No.11532577