/sci/ - Science & Math

>>11152037
>another maths general thread

>>11152037
Send for based Thurston

>>11152057
Second*

>>11152037
If you were offered a job at Renaissance, would you take it? I know /mg/ is probably too pure to work for a 'greedy financial firm'.

>>11152068
go fuck yourself, idiot

BSc Computer Science + BA Math. Y/N?

Light blue is Computer Science
Dark blue is Maths.
Green and Bronze are required Gen Ed courses.

>>11150942
this stuff is pretty interesting. I hope to self-study it in depth some day. thanks.

Today I learned that the distributive property of a lattice can be defined with reference to one operation only, i.e. that it's meaningful to speak of "distributive semilattices" that agree with the usual notion on lattices.

Apparently, the standard definition is that a semilattice is distributive iff the set of its ideals (under inclusion) is distributive, but there are alternative proposals. E.g. https://arxiv.org/abs/1902.01656 argues, on intuitionistic grounds, to restrict the set to ideals satisfying a certain finite intersection property.

I personally like their suggestion, but that might just be my constructivist bias showing. Does /mg/ have any thoughts on the matter?

>>11152137
Not maths, sorry.

>>11152106
you are a faggot

Brainlet here. How do I find the characteristic polynomial of a square matrix given its kernel, without using det(f-xId)?

>>11152299
Fuck off nigger

>>11152043
>>11152096
>>11152299
I'm sorry, but you need to leave.

>>11152096
Reverse the two. Get a BSC. for math and a minor/BA for computer science. Computer science is helpful for some problems not necessarily computational.
>bronze
Intro to lit is fine, I recommend human geography over Europe history. Replace int. pol. with US gov. Macro is fine, replace jazz with philosophy unless if you really like people of color being forced down your throat.
>light blue
I would recommend learning Python and going for that minor that way you learn the basics of programming. Math majors have no trouble adjusting into software if that is what you wish, the problem is commitment to a math career.
>dark blue
You don't really need advanced math classes with a CS degree. Depends on your career path.
>light green
I recommend biology too. As a math major physics was hell because I lacked mechanical aptitude while chem is hell because I don't care about chemistry lol.

>>11152301
>Fuck off nigger
Why the racism?

>>11152299
>How do I find the characteristic polynomial of a square matrix given its kernel, without using det(f-xId)?
What have you tried?

>>11152454
would be nice if more mathfags would look into theoretical biology, the entire field is sorely lacking in rigorous thinking. physicists and mathematicians in general should consider branching out into that area since they are highly valued and it is far less competitive for them.

>>11152581
math is fundamentally racist

>>11152068
>If you were offered a job at Renaissance, would you take it?
Absolutely.

>>11152289
>faggot
Why the homophobia?

How far along is /mg/?

Threadly reminder to work with physicists.

Given a minimal bandwidth ordering of a graph, how do I convert it to the maximal bandwidth ordering? Pic related is an example for a singly connected graph, but I can't figure out how to generalize it.

>>11152849
Green is "I know this and I'm confident in my knowledge of it", and yellow is either "I know some of this stuff" or "I half remember this stuff."

>>11152454
>Get a BSC. for math and a minor/BA for computer science.
My interest and stronger skillset is the comp sci side of things. I *might* be able to stretch the Math BA into a BS if I do summer classes, but I'm not sure yet.

>bronze
My school has a weird gen ed system where you need to get credit in 13 categories (STEM, Humanities, Fine Arts, Diversity, etc) while also having a class in 8 different course categories (Fine Arts, Literature, Math, etc)

Jazz History knocks out 2 categories (Arts & Diversity) while the combination European History/International Politics knocks out 5.

>light blue
A python course was an entry level course I was able to test out of (although they don't usually allow it).

>You don't really need advanced math classes with a CS degree. Depends on your career path.
The dark blue is to get the double major. I tried to choose topics (optimization, number theory, differential equations) that seemed useful to the comp sci side of things as well.

>>11152441
hahahaha

>>11152936
huh wonder who made that last one

I have questions about Category theory, please dont meme about.

>What does it do better then set theory?
>What does it do better then abstract algebra?

As far as I can tell, It just seems to be some sort of algebra, I just dont understand what its doing better then set theory and modern algebra.

>Also what are the prerequisites?

>>11153207
Categories represent abstractions of other mathematical concepts. Many areas of mathematics can be formalised by category theory as categories. Hence category theory uses abstraction to make it possible to state and prove many intricate and subtle mathematical results in these fields in a much simpler way.
A basic example of a category is the category of sets, where the objects are sets and the arrows are functions from one set to another. However, the objects of a category need not be sets, and the arrows need not be functions. Any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category—and all the results of category theory apply to it.
The "arrows" of category theory are often said to represent a process connecting two objects, or in many cases a "structure-preserving" transformation connecting two objects. There are, however, many applications where much more abstract concepts are represented by objects and morphisms. The most important property of the arrows is that they can be "composed", in other words, arranged in a sequence to form a new arrow.

>Also what are the prerequisites?
Nothing but a bit of mathematical maturity.

>>11153207
These questions are not particularly sensical. This is like asking what group theory does better than calculus.

>>11153235
whats the main purpose of it

>>11152299
read Linear Algebra Done Right to see the determinant-free approach

>>11153310
>Linear Algebra Done Right
yikes

>>11152068
what's renaissance?

>>11153330
>what's renaissance?
https://en.m.wikipedia.org/wiki/Renaissance_Technologies

>>11153269
It was originally just a language developed by algebraic topologists to make naturality precise. Then people discovered adjoint functors, connections to type theory, etc.

What's the best way to approximate pi, better than the Chudnovsky brother's formula?

>>11153394
shoving a pinecone up your ass.

>>11153329
proof based course BAD
determinate GOOD

>>11153447
>acting like proof based course and 'determinate' are mutually exclusive
the IQ-dropping effect of linear algebra done right everyone

>>11152037
Post your favorite Thurstons

>>11152037
Mathlet here. How come I can, understand the reason or concept behind questions but not calculate them?
I know what I should do with algebra but even then, it just slips out of my mind. There was a time I had to multiply 4*4 and my mind just said 8, for some reason and I keep going from there.
I think it may be my depression kicking in or some sort of undiagnosed ADHD.
Is there a way to improve this or am I doomed to die an algebralet?

>>11153545
>Mathlet here. How come I can, understand the reason or concept behind questions but not calculate them?
Habit.
>Is there a way to improve this or am I doomed to die an algebralet?
Obtain a little sister or little brother that needs your help to do math/physics/chemistry homework.
I've found my algebra error-detection skills go up by a solid 200% when I'm looking through my sister's homework.
>>11153526
Getting good pictures of mathematicians online is hard.

>>11153384
>>11153235
>>11153228
is there no notion of cardinality" of categories? The fact that you can have a category of all category seems paradoxical. can i construct uncountable categories?

>>11153579
>cardinality
The cardinality of the set of objects is usually irrelevant to the data you want from it.
>category of all categories
That's like a class of all classes. IIRC you had a problem and needed to work over 2-classes or something.

What are the morphisms in the category of axioms?

>>11153438
Cool. So pi is finite and the last digits are

>>11153609
>>11153609
Projection.
Specifically, [math]A \wedge B \rightarrow A[/math]

>>11153619
>Projection.
>Specifically, [math]A \wedge B \rightarrow A[/math]
Interesting.

>>11152915
To clarify, I'm looking for a polynomial time reduction from one pre-solved NP-hard problem (minimum bandwidth) onto another NP-hard problem (maximum bandwidth).

Bros how do i learn stats fast, i need it for job applications

I took stat classes and got As but i feel like nothing stayed in my head and i dont want to get humilliated in a job interview

>>11153706
fuck cs faggot. go make your own thread

>mfw both algebra and analysis are awesome

PLEASE HELP
I need a function that looks like this, but is composed of elementary functions, i.e. not the cumulative distribution function. It doesn't need to be exact, I just need to make sure low values become lower, and high values become higher.

>>11154365
Logistic function ?
tanh?
x on [0,1] 1 otherwise?
some shifted sin/cos and the rest 1?

>>11154365
y = (tanh(a(x - 1/2)) + 1)/2
Let a be as big as you require.

When you forget how to make a symbol in Latex, do you lads also just go to wikipedia, click to edit the page and find the symbol written out in it or do you have any better techniques?

>>11154365
>Logistic function
Hill equation

>>11154453
http://detexify.kirelabs.org/classify.html

>>11154468
Nice, thanks.

>>11154374
Logistic function works perfectly, thanks buddy.

>>11152299
Not possible

>>11154768
why

What's the easiest way to show that Chebyshev polynomials are linearly independent?

>>11154772
Because the kernel alone does not determine the charpoly dummy
Can you determine the characteristic polynomial of a matrix knowing that it looks like this [math]\begin{pmatrix}0 & 1 \\ 0 & \star \end{pmatrix} [/math] ? It depends

>>11152037

Anyone know what a good book about network theory is?

>>11154778
>how do I show polynomials are linearly independent
>polynomials
Anon's Lemma: Let [math]p_n[/math] be a sequence of polynomials, such that [math]p_i[/math] has degree i. Then the sequence is linearly independent.
The proof is left to the reader as an exercise.

Note: anon's lemma is probably a really old result, but anon doesn't know it's name, and it's easy enough to probably not have one.

>>11154772
let A be any 2 by 2 matrix. suppose the kernel is zero. the matrix can represent rotation, shearing, scaling, whatever. do you really expect to be able to write the characteristic polynomial without further information ?

>>11153930
It's a discrete mathematics problem.

>>11152037
What's the best calculator tutorial? I can't into parenthesis when it comes to cumbersome equations.

>>11154972
>I can't into parenthesis
There is a thread exactly for people like you, where you can describe your problem and might get help.

Being unable to operate a calculator is NOT part of a discussion about mathematics.

>>11154972
if you can't operate a calculator you have bigger problems you should try to sort out.

>>11154979
Why are you so anal about this? Do you have Asperger's? Only on 4chan do you see people trying to force on-topic discussion when off-topic is completely healthy.
>>11154990
I'm talking about a ti-83. My math teacher doesn't even know how.

>>11154995
embarrassing

>>11154997
What part was "embarrassing", curious? For things out of my control, that's embarrassing to you?

>What part was "embarrassing", curious? For things out of my control, that's embarrassing to you?

>>11154995
>Only on 4chan do you see people trying to force on-topic discussion when off-topic is completely healthy.

>>11154995
>Why are you so anal about this?
Because you are annoying everybody. Nobody wants questions not only entirely unrelated to mathematics, but also by people with zero mathematical education here.

There is a thread EXACTLY for these questions try searching for "stupid" and YES this question is stupid.

>when off-topic is completely healthy
If you think that discussing how to operate a calculator, something which pretty much every eighth grader can do to a satisfying degree, is "healthy" discussion you have to be braindamaged.

You clearly are underage (and if you are not you have to be in an institution for the mentally ill), go away.

>>11155003
>What part was "embarrassing
That you have to ask how to operate a calculator, there are so many places where you can get answers to this question (have you tried reading the manual? have you tried Google?) and you post in an unrelated 4chan thread and get upset that people won't help you.

>>11154995
>I'm talking about a ti-83. My math teacher doesn't even know how.

You can use the ramp function (|x|+x) for step functions and rounding.

woah /mg/, don't go dying on me.
*flips book to random page*

Let [math]H_{\omega}[/math] be an infinite-dimensional Hilbert space, with its weak topology. Prove that the inner product is a separately continuous function on [math]H_{\omega}\times H_{\omega}[/math] which is not jointly continuous.

>>11156016
>separately continuous
That's trivial.
>not jointly continuous
That's hard.
By the by, the inner product on the product was the sum or the multiplication?

>>11156016
i dont wanna

>>11156023
Let [math]V[/math] be an [math]n[/math]-dimensional vector space, [math]B : V\times V \to \mathbb{R}[/math] an inner product and [math]e_{1},\dots e_{n}[/math] a basis of [math]V[/math] which is positively oriented and orthonormal. Show that the "volume element" [math]\text{vol} = e_{1}^{*}\land \dots \land e_{n}^{*} \in \Lambda^{n}(V^{*})[/math] is intrinsically defined, independent of the choice of basis.

>>11156021
No, wait a minute, that's fucking trivial, I'm retarded. You just pick any sequence that converges weakly to zero but not strongly and double it, the inner product just goes to the norm when it should go to zero.
>>11156038
That's also trivial.

>>11156044
would you like something not "trivial" then?

>>11156062
No, I'm just weirded out.
You usually post hard stuff.

>>11156066
trying to appeal to the brainlets. give me a second to look for something

>>11154778
Show their orthogonality by integration. [math](T_n,T_m) \propto \delta_{nm}[/math].
>>11154813
Anon meant linearly independent over [math]L^2([-1,1],d\mu)[/math] where [math]d\mu(x) = \frac{1}{\sqrt{1+x^2}}dx[/math] is the half-circle measure, not over [math]\mathbb{R}[x][/math].

>>11156091
>Anon meant linearly independent over [math] L^2([-1, 1], d \mu) [/math]
I'm pretty sure that doesn't actually matter.

>>11156151
Sure it does. Sturm-Liouville is one of the most accessible and useful ways to find ONBs and [math]N[/math]-representations for infinite-dimensional Hilbert spaces. This is worlds away from linear independence in the trivial, tiny world of polynomials.

Let [math]G[/math] be a finite subgroup of [math]GL_{2}(\mathbb{Q})[/math].
>(A)
Show that [math]GL_{2}(\mathbb{Q})[/math] does not contain an element of order [math]n[/math] for [math]n=5,7[/math] or [math]n\geq 9[/math]. Deduce that [math]|G| = 2^{a}3^{b}[/math]
>(B)
Show that the Klein [math]4[/math]-group is the only noncyclic abelian subgroup of [math]GL_{2}(\mathbb{Q})[/math]. Deduce from this and (A) that [math]|G| \text{ | } 24 [/math].
>(C)
Show that the only finite subgroups of [math]GL_{2}(\mathbb{Q})[/math] are the cyclic groups of order [math]1,2,3,4[/math] and [math]6[/math], the Klein-4 group, and the dihedral groups of order [math]6,8[/math] and [math]12[/math].

>>11156169
what's the element GL2(Q) of order 6?

>>11156169
GL_2 (Q) doesn't have an element of order 3.

>>11156251
You sure about that?

>>11156299
Yes

>>11156169
>group theory
lmaoing @ ur life

rational canonical forms

>>11156338

a/b where a is relatively prime to b

am i allowed to like math yet?

>>11152037
What is a good introductory book into real analysis for self learning and where can I find a pdf?

>>11156251
>>11156306
[math]\left( \begin{matrix}0 & -1 \\ 1 & -1\end{matrix} \right)[/math]

>>11156387
>self learning
As opposed to what?

>>11156436
BTFO

Forgive me if this is a stupid question, but what kind of preliminary knowledge do I need before starting Spivak's Calculus?
I've done single and multivariable calculus already.

>>11153451
Not him, but what would you recommend instead for a first course in proof based la?

>>11154365
Gompertz growth curve.

>>11156529
>Not him, but what would you recommend instead for a first course in proof based la?
H&K

>>11156529
>Not him, but what would you recommend instead for a first course in proof based la?
Bourbaki

>>11156491
it is a stupid question. you do not need any preliminary knowledge, you need a work ethic.
>>11156529
hoffman and kunze

>>11156454
I just want to learn analysis on my own.

Some textbooks serve more as a "container" of knowledge than as a written lecture that explains the concepts and gives some intuitions and whatnot.
I want a written lecture book, not a knowledge container book.

https://arxiv.org/abs/1902.07437

Will /mg/ tune in?

https://sites.google.com/view/vantageseminar
>In spring 2020, a new math seminar is starting: VANTAGe, a virtual seminar on open conjectures in number theory and arithmetic geometry (NT&AG). The seminar will provide open access to world class mathematics, with a focus on progress on unsolved problems in NT&AG. The purpose of the seminar is to provide a viable way for researchers to be involved with cutting-edge research in NT&AG without the expense and environmental impact of travel. Another aim of the seminar is to advance understanding on the most exciting open problems in this field. As the goal of the seminar is to build communication among researchers developing the fields of NT&AG, speakers and participants will be expected to uphold the highest standards for clear exposition and respectful interactions.

>The first topic of the seminar is CLASS GROUPS OF NUMBER FIELDS. The first talks of the seminar will focus on this survey paper.

>On a conjecture for l-torsion in class groups of number fields: from the perspective of moments - https://arxiv.org/abs/1902.02008

>Jan 21: Lillian Pierce. On some questions in number theory, from the perspective of moments

>Feb 4: Melanie Matchett-Wood. Conjectures for number field counting

>Feb18: Caroline Turnage-Butterbaugh. Moments of zeta and the vertical distribution of its zeros

>March 3: David Zureick-Brown. Moduli spaces and arithmetic statistics

>>11156924
Sounds above my level but the area is interesting so I might tune in.

>>11156151
Me too.

>>11156091
We already talked about this. Chebyshev polynomials are something which is occasionally done in a Linear algebra 1 class, Anon CLEARLY has no idea what an Lp spaces is since literally every person who knows what an Lp space is, is able to show the independence of Chebyshev polynomials by looking at them.

Stop trying to show off, you giving answers that the people asking can obviously not comprehend is just retarded.

>>11156164
All of that is irrelevant. The linear independence carries over.
They are linearly independent on your Lp space and so they are independent in the space of polynomials and since they are linearly independent in the space of polynomials they are linearly independent in your Lp space (potential integrability issues in the general case aside).
Where is the difference? The linear independence of a set of vector is independent of you making the vector space larger, or maybe I am retarded, but at least in that case I don't have crippling social unawareness.
Also none of this has to do with Sturm-Liouville, this is a Linear algebra 1 question, so don't be autistic and respond like you would respond to a first semester student.

>>11156943
http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html
http://mathworld.wolfram.com/ChebyshevDifferentialEquation.html
Just stop.

>>11156932
same

>>11156976
Did you even read what I wrote?
NOBODY who knows about Chebyshev polynomials in this generality has problems showing their independence.
The guy CLEARLY is a linear algebra 1 class (or something similar) and got the basic recursive definition on some exercise sheet.

Stop showing of, if you are unwilling to respond to people with answers they can understand, don't respond and NO this guy does NOT KNOW WHAT AN LP SPACE IS.
But at least you acknowledge that you were wrong about the linear independence of polynomials...

>>11156988
>NOBODY
>CLEARLY
Were you the original anon that asked the question? Note I didn't mention Lebesgue spaces at all when replying to him.
There is only one sense in which "linear independence" is asked [math]specifically[/math] for Chebyshev polynomials, and that's the Sturm-Liouville sense for ONBs of some[math]L^2[/math] space. Why would an elementary linear algebra class ask for linear independence for them instead of just monomials? Why add the extra fluff if they're not even relevant to the basic argument? Nameone single lin alg book that has a question like this.
It is obvious that not everyone who's taken mathematical methods class knows about Lebesgue-Hilbert spaces but that's the setting in which it is phrased. And no, in this setting the linear independence of the polynomial kind do not at all carry over to that of the [math]L^2[/math] kind.
Your post is pure and applied garbage. Please don't reply to me ever again.

>>11157007
>Note I didn't mention Lebesgue spaces at all when replying to him.
No, you just wrote down an inner product nobody who doesn't know about Lp spaces understands.

>There is only one sense in which "linear independence" is asked specifically for Chebyshev polynomials, and that's the Sturm-Liouville sense
No. If you know what Sturm-Liouville is it is trivial to see their linear independent.

>Why would an elementary linear algebra class ask for linear independence for them instead of just monomials?
Because there are followup exercises.

>It is obvious that not everyone who's taken mathematical methods class knows about Lebesgue-Hilbert spaces but that's the setting in which it is phrased.
And knows why these polynomials are linearly independent by sight.

>And no, in this setting the linear independence of the polynomial kind do not at all carry over to that of the L2 kind.
Making the space large doesn't affect linear independence of a common subset.
You are wrong.

But seriously do you not see how autistic you are? You are replying to first semester people with stuff they obviously have no clue about. If you are doing this to show off you are just an asshole getting off of being smart and if you are not, you are severely autistic and you have lost your grip on reality.

>>11156924
>Moduli spaces and arithmetic statistics
Might be interesting.

>>11157043
it might not be.

>>11157045
Also true.

>>11156091
>Anon meant linearly independent over [math]\mathrm L^2[/math]
That is meaningless

Do go straight into Analysis before doing proofs? Or should I start with abstract algebra then analysis?

>>11152915
>>11153706
>/mg/ literally doesn't know how to answer this

>>11152037
why do csfags hijack every math thread? Philosophy of maths is so much better anyways

>>11157267
"Doing proofs" as a standalone study is a total waste of time unless you're retarded. These courses exist at universities only because our admission standards have fallen so low that we're now teaching unmotivated morons who need months of forcefed practice to get them to stop fucking up obvious logic.
You will pick up how to read and write proofs well naturally by working through an actual math book.

The ordering of analysis/algebra makes no difference. You'll have to learn both of them anyway and they don't seriously rely on each other at the undergraduate level.

>>11156436
>>11156478
Tricked you into answering my question!
>have a question about maths
>confidently claim a falsehood about the question
>some autist answers your question thinking he's BTFOing you
This method never fails me.

Let [math]A \in \mathbb{C}^{n \times n}[/math] be a positive definite self-adjoint matrix, and let [math]\mu(A)[/math] be the matrix obtained by taking the diagonal part of [math]A[/math] in some fixed basis. Then [math]n \mu(A) - A[/math] is positive semidefinite.

Does the above follow from something trivial? I have a proof but it's ugly as shit and I'm just curious if I missed something here.

>>11157580
It is an application of Cauchy-Schwarz to the Hermitian form [math]\langle , \rangle_A: (X, Y) \mapsto X^* A Y[/math] defined by your matrix A.
Letting [math]A = (a_{ij})[/math], [math]X = \begin{pmatrix}x_1 \\ \vdots \\ x_n\end{pmatrix}[/math] and [math](E_i)[/math] be the canonical basis of [math]\mathbb C^n[/math], the Cauchy-Schwarz inequality yields :
[eqn]|a_{ij}x_ix_j| = |\langle x_iE_i, x_jE_j\rangle_A| \le ||x_iE_i||_A ||x_jE_j||_A = \sqrt{a_{ii}a_{jj}}|x_ix_j| \le \frac{1}{2}(a_{ii}|x_i|^2 + a_{jj}|x_j|^2)[/eqn]
and therefore:
[eqn]X^*AX = |X^*AX| \le \sum_{i=1}^n a_{ii}|x_i|^2 + \sum_{i \ne j}|a_{ij}x_ix_j| \le \sum_{i=1}^n a_{ii}|x_i|^2 + \frac{1}{2}\sum_{i \ne j}(a_{ii}|x_i|^2 + a_{jj}|x_j|^2) = n\sum_{i=1}^n a_{ii}|x_i|^2 = X^*(n\mu(A))X.[/eqn]
Dunno if this is what you had in mind or if this is still ugly

>>11157331
no one gives a shit about your computer science problem

Any anons in the workshop at Leicester Uni this week?

>>11157337
CS is math

>>11158132
>CS is math
Actually, maths is a proper subcategory of CS, so not all CS is maths.

any europoors here?

>>11158162
CS is math literally means CS is a subset of math

>>11158168
>CS is math literally means CS is a subset of math
"Actually, maths is a proper subcategory of CS, so not all CS is maths." literally means you're wrong.

>>11158165
Yes.

>>11157569
BTFO
But really anon the only person here being BTFO is you because you robbed yourself of the opportunity to improve your problem solving skills.

>>11158205
based

>>11158205
The only people who should be interested in improving their problem solving skill are those who have a lot of problems. I'm fine.

I have a problem with matrices. I dislike them. They just look so ugly and disgusting- I don't know, maybe it's a problem

>>11158299
You'll start loving matrices when you begin doing very abstract maths.

>>11158314
False, I've been doing abstract math for 5 years and I still hate matrices.

>>11158175
nice

>mfw someone integrates around my punctured disk

>>11152037
What do you guys think about Abbott's Understanding Analysis?

>>11158472
then you don't understand your linear algebra as much as you think you do

>>11157580
I feel like I am missing something obvious, but positive semidefiniteness is basis indepedent, so you can just chose the eigenbasis and make A diagonal and then its trivial, no?

>>11158793
You have to show it holds for ANY basis, not just ones that diagonalize.

>>11152037
I'm torn between low dimensional Topology and hardcore analysis and PDEs. I'm about to finish my MS, and will have done a significant amount of course work in both, dabbling in some 3-manifolds/knots type stuff. Any anons recommend one way over the other for PhD?

>>11158799
Stat with A in an arbitrary basis. Construct mu(A).
Look at nmu(A)-A. To check if its positive semidefinite, you can look at nmu(A)-A in any basis you want, so chose the one than makes A diagonal. Basis change is linear, so mu(A) and A both become diagonal and you are done (A become diagonal by definition, mu(A) becomes diagonal becaus you need to get the same result as if you started with an eigenbasis of A). I aint the sharpest tool in the shed, so I am worrying that I am wrong, but the argument looks correct to me.

>>11152068

>>11153330
It's medallion fund for zoomers. They just renamed.

>>11158168
>>11158170

It's a different type of axiomatic(formal) science.

>>11158966
AXIOMATIC FORMAL SCIENCE TIER LIST:
1. Scholastic theology.
2. Maths.
3. Microeconomics.
4. Law.
5. Aristotelian science.
6. Islamic theology.
7. Analytic philosophy.
8. Semantics.
9. Board games.
10. Computer science.

>>11158998
>not doing all at once

>>11158866
FYI PDEs gets more publications than any other field of math, if you're concerned about getting a postdoc after graduation (as you should be).

>>11158660
>I don't like X
>Well you just don't get it
Where have I heard this before...

>>11159037
This is true, but knots/3-manifolds is what I'm currently able to do research in. I'm taking a one to three year Gap off between MS and PhD. In that time I'll be teaching part time at CCs and publishing papers in knots/three-manifolds. I have to take time off due to finances and family circumstances, but my prof from MS is still willing to get results with me

>>11159037
Also a post-doc isn't super necessary, I'd be ok working part time (wife makes 6-figure) although I'd want to become a professor but I can do part time work and part time research, just means less money

Have a fun integral
[eqn]\int_1^2 {\ln x \over 2 - 2x + x^2}dx[/eqn]

>>11158998
You forgot physics sweetie.
>>11158866
That's a pretty wide dichotomy thee. Which do you like best? Inequality chasing or invariant chasing?

>>11159154
>wife supports you with 6-figure salary so you can go all in on your favorite field without caring whether a university will hire you on for it
How do I get a woman like this?

>>11159261
Physics is neither axiomatic, nor formal, nor a science. See >>>/toy/.

>>11159261
A lot of the invariants that I'll be working on will be inequality chasing. My profs most famous result, width is not additive came from this.

Tbh, I'm probably gonna go with whomever I get along with the most

>>11159273
Find a woman CS major that's talented and beautiful

>>11159353
Oh like finding bounds on invariants like monopole /Heegaard-Floer or Lusternik-Schnirelmann? That stuff is quite hard, too, though these results do sometimes see quite surprising applications in PDEs as well. The two fields may not be as disjoint as I first implied.

>>11152037
What do you guys think about understanding analysis by Abbott?

Can someone help me intuitively understand this proposition?
I grok what it means but I can't really visualize it not reason through it.
Thank you!

>>11159409
Remember mean value theorem from calculus 1? This is the higher dimensional version of that. I think MVT from calc 1 is even used to prove this version, actually.

The way this theorem is stated in Folland is a little different, so I'm not even sure that there are enough hypotheses in the proposition to ensure that what it wishes to show always holds. Nevertheless, the intuition here is the same as it is in the case in which n=1. If n=1, and if is differentiable in a neighborhood of x, you pick can point xh sufficiently close to it and calculate the slope of the line connecting both x and that point; there will be a new point between x and and x+h, say z, such that we will have f(x+h) - f(x) = f '(z)(h).

>>11158882
If you change the basis, then mu(A) will not remain diagonal in general.
I don’t understand your argument for why it might be so.
Also, even if it were true, it would not yield the result

>>11159409
What it tells you is that you can understand how the function varies through its derivatives, and gives you a precise relation. Having information about the behaviour (sign, variations etc.) of the derivatives tells you how the function varies.
That’s it. MVT in dimension 1 is what allows you to relate monotonicity of a function and sign of the derivative for example.
Now for this exact statement, idk what to say exactly. I have never seen this before. It involves partial derivatives at various points and does not seem like a very exploitable statement.
It seems more like a gratuitous generalization of the one-dimensional MVT by induction, because why not

>>11159408
the guy was a genius, simply that, flatland was the best book ever to be written

Can't wait to get into some meme french institution and bang their hairy undergrad hotties.

>>11160096

C'est là qu'on s'est connu

Moi qui criait famine

Et toi qui posais nue

>>11160109
>Moi qui criait

>>11160096
kys normalfag

>>11160117
Seething incel

>>11159045
I don't know anon-kun, where have you ?

>>11159409
literally mean value theorem along the line passing through x with direction h

>>11159915
mu(A) remains diagonal because nmu(A)-A after basis change must be equal to nmu(A)-A with eigenbasis from the start.
And why would it not yield the result?

What do you think is pedagogically the best textbook for analysis? I'm considering Tao's ones

>>11161777
Abbott

>>11160096
>Meme french institution
nice, big recommend
>Bang French girls
Never done that, lemme know how that goes for you

On the topic of french unis, I was looking through our library for math books to study, and I found three introductory topology books. Which would you guys recommend? One was a joke so I ignored it, the other two were Kasier or Croom. I've done intro to real analysis and I'm finishing multivar calc rn, and I just want to get my feet wet.

>Professor decides to use a textbook a colleague and of his is working on for graduate level class
>emails pdf to class
>Turns out it's horrible, many of the definitions are just plain wrong, and many examples are not done correctly
>We receive an updated PDF nearly twice a week with the errors corrected, only for more errors to crop up
Why do professors do this shit? Just tell us to get the canonical textbook and spare us your friend's shitty attempt at trying to write a textbook that has a snowball's chance in hell at being accepted as a decent textbook

>>11162030
/mg/, don't do this to me

>>11162030
>>11162425
In my opinion learning pointset topology by itself is stupid. It's pretty dry without motivation.
The way it is taught at my uni is that in analysis they mention the topological versions of things and encourage topological proofs where possible. Then in later courses (algebraic topology, algebraic geometry) if more topology is required then you are expected to learn it yourself.

With measure theoretic probability there are scenarios where are a particular event has probability zero but can still occur (picking a rational number from a uniform distribution for example). How do we distinguish this scenario from events that cannot actually occur (for example picking -1 from the uniform distribution on [math] [0,1] [/math])?

>>11159409
>grok
leave and never come back

>>11162488
set membership you fucking moron

>>11162527
I guess what I'm saying is think of the second example as a distribution over [math] [-1,1] [/math] where the density function of negative values is zero.

/sci/, it's 3 AM here and I'm wracking my brain over the most insignificant shit.
I've been trying to find the volume of a tetrahedron with vertices (1,0,0), (0,1,0), (0,0,1), and (0,0,0) for reasons that are my own. I cracked open my calc three textbook to the section on triple integrals in cartesian coordinates, and the book happened to have this exact problem:
[math]
\int_0^1 \int_0^{1-x} \int_0^{1-x-y} z dV = \frac{1}{24}
[/math]
This didn't seem right to me, so I went to wikipedia, where the answer could be found to be 1/6. I then ran 10*10^7 simulations of the problem in python and got almost exactly 1/6. Why was the integration wrong?

>>11161808
Why?

>>11162488
You cannot distinguish them with probability alone.
As this anon >>11162527 says, you need to look at the actual sets and see that one is empty whereas the other is just negligible

>>11162565
because

>>11162524
>leave and never come back
Oh Hi Scar

>>11158646
Very good book if you are younger mathematically and can't appreciate going straight into abstract metric spaces. Highly recommend if you have done 0 analysis and don't have a course or two in algebra or topology. If not just read Apostol or rudin.

I found a new equation to represent the Heaviside step function:
[math](|x|+x)^{(|x|-x)}[/math]
In discrete form it would be:
[math]\left\{\begin{matrix} 0, x < 0
\\0, x \geq 0

\end{matrix}\right.[/math]

>>11163237
Oops, meant
[math]\left\{\begin{matrix} 0, x < 0
\\1, x \geq 0

\end{matrix}\right.[/math]

>>11162475
Intro to topology is a mandatory course in undergrad here

>>11162556
>zdV
>z

>>11163252
Intro to topology is mandatory in every place that isn't an unsalvageable shithole.

>>11163237
>>11163243
nobody cares

>>11163259
Nobody appreciates the power of absolute value. add a constant n and you can essentially transform any discrete form into an equation.

>>11162538
the set containing just 1/2 is then just as much of a null set as the set containing the negative numbers.
you can look at the support of the measure if you'd like.

>>11163264
Can it be used to model material continuity as a negative temperature?

>>11163325
I've reread the measure support definition to be sure, and apparently it depends on the topology.
The issue is I can use the Dirichlet function as a probability distribution to induce a measure on the unit interval and the rationals are in the support.
An idea like anon's should be independent of the topology.

>>11163368
without a topology, there's no way to distinguish between 1/2 and -1 in R with a measure which is only nonzero on sets in [0,1]. they're the same with respect to the measure.
measures dont give a shit about where you mean to define something, any null set is as good as any other
>b-but 1/2 is close to sets with nonempty measure, and -1 isn't...
oh. you mean close in a FUCKING TOPOLOGY?

>>11162762
Why would it be superior to the alternatives?

Is theoretical CS belong to math? Things like proving NP-hardness, approximation and shit.

>>11163951
Yes but /mg/ will get butthurt if you try to talk about it.

>>11163951
Sure

>>11163937
because

>>11163951
it is, but no one here will be able to understand you because the people who frequent here are either: highschoolers, arrogant undergrads, or autistic specialized grad/post-grad students

>>11163951
No, if we're going to consider theoretical CS we might as well consider 90% of physics, 80% of finance and half of economics to be maths.

>>11164002
And?

>>11164002
what exactly do you mean by "maths"?

>>11164002
If you think 90% of physics is theoretical physics then it's time to actually talk to someone in the physics department.

>>11163951
No, it is computer science, because it is the application of mathematics to the theory of computation.
Is psychology, or quantitative social science mathematics because it uses statistics?

>>11163993
>>11163957
>>11163951
all the cs bugmen have crawled out of the woodwork

>>11164099
enjoy being unemployable?

>>11164101
enjoy working with trannies? enjoy living a shallower life? enjoy always being envious of mathfags?

>>11164106
lol the fucking cope. i study pure math and cs you sperg. enjoy being subpar.

>>11164125
>t. wont get a job in academia.

>>11164127
projection

>>11164106
>enjoy always being envious of mathfags?
please don't tell me that mathfags actually believe that people doing "lesser" stuff like cs or engineering are envious of mathfags

>>11164144
of course not, for the same reason why a monkey isnt envious of a human. They lack the capacity to even understand what they should be envious of.

>>11164144
its no delusion. all the cs fags in my department wont shut up about how much overlap there is with cs and math. it logically follows that even though they are stupid cs bugmen, they realize that math is the purest and most difficult field out there.

Suppose [math]A[/math] is a closed subspace [math]C(S)[/math], where [math]S[/math] is a compact Hausdorff space; suppose [math]\mu[/math] is an extreme point of the unit ball of [math]A^{\perp}[/math]; and suppose [math]f\in C(S)[/math] is a real function such that [math]\displaystyle \int_{S}gf d\mu =0[/math] for every [math]g\in A[/math]. Prove that [math]f[/math] is constant on the support of [math]\mu[/math]. Show, by an example, that the conclusion is false if the word "real" is omitted from the hypotheses.

Suppose [math]L[/math] is an elliptic linear operator in some open set [math]\Omega \subset \mathbb{R}^{n}[/math], and suppose that the order of [math]L[/math] is odd.
>(A)
Prove that then [math]n=1[/math] or [math]n=2[/math].
>(B)
If [math]n=2[/math], prove that the coefficients of the characteristic polynomial of [math]L[/math] cannot all be real.

Let [math]ABC[/math] be a triangle in a Euclidean affine plane [math]\mathbb{A}[/math] and let [math]P[/math] be any point of [math]\mathbb{A}[/math]. Prove that the three straight lines through [math]P[/math] perpendicular, respectively, to the straight lines [math]AB[/math], [math]AC[/math], and the median corresponding to the vertex [math]A[/math] (the straight line determined by [math]A[/math] and the midpoint [math]M[/math] of [math]BC[/math]) cut the altitude through vertex [math]A[/math] in equal line segments.

Let [math]f:\mathbb{R}\to\mathbb{R}[/math] be an [math]\mathcal{L}[/math]-measurable and integrable function and define the function [math]F:\mathbb{R}\to\mathbb{R}[/math] by:
[eqn]
F(t) = \begin{cases}
\int _{\chi_{[0,t]}} d\lambda & \text{ if } t\geq 0 \\
-\int _{\chi_{[0,t]}} d\lambda & \text{ if } t<0
\end{cases}
[/eqn]
Show that for any compactly supported smooth function [math]g\in C_{c}^{\infty}(\mathbb{R})[/math] we have [math]\displaystyle \int fg d\lambda = -\int Fg^{\prime} d\lambda[/math]

>>11164244
Lemme see if I correctly understood what the problem is asking you to do, youre asking me to prove that the 2 lenghts i mark on picrel are equal right?

(Srry friends, english is not my native language and im not used to reading problems in english)

i'm not fixing it, you can read it just fine

>>11164291
Pls fix, it fucks how the page displays on my phone's browser

>>11163237
This is discontinous at 0 whilst [math] 1(t) [/math] isn't. Its also 1 for every negative value of x

>>11164301
just hide it dumb phoneposter

>>11164319
Shit is 0^0 for every negative value, not 1.
Which means the function doesnt exist of every x \leq 0, whilst 1(t) is well defined over all of R

>>11164321
But I wanna hide it AND look at problem

>>11164125
you'll never be worth anything to anyone with even the least bit of mathematical inclination

can somebody post the rant about algebraic geometr or topologists thatt ook some dudes conjecture or even proof and used their techniques to prove it way faster and more "elegeant" than he did?

>>11158922
and this is why most sane professors confront students with categories after a topology&riemann surface/algebraic geometry course
so you can actually use the tools and make connections

>>11163951
yes

>>11164336

>>11164160
>>11164227
>>11164244
what's the point of these exercises? more generally, what's the point of olympiad mathematics? It's just a waste of time it's serves the fucking same purpose as those "how to do proofs" books. It's like trying to teach a kid how to do induction by trying them to solve a medium hard problem like "given a finite graph with n vertices every turn the set of its vertices is partioned into two 2 subsets and vertices from the opposite subsets are being joined togerher with edges. What's the minimal amout of steps needed to make the graph complete?". If you want to pick up techniques in some topic just do the main proofs from that topic straight by yourself.
So either you frogposter start posting good problems involving some new techniques or ideas or I'm going to shoot your family.

>>11164371
>what's the point of these exercises?
to get people talking math in the math thread
> what's the point of olympiad mathematics?
these aren't olylmpiad problems, they are from pretty standard textbooks. the point of olympiad problems is to find new ways to solve things / new ways of thinking of problems that are either known or unknown.

>>11154365
y = 1 - e^(-x)

>>11164366
nice, thank you a bunch!

I give up. This math shit is to hard

>>11164464
and what exactly is that supposed to be?

>>11164471
My college algebra class

>>11164476
>scam class
my condolences. but I can't read anything you just posted so how about telling me what the problem is.

>>11164483
We're learning about squares

>>11164495
like, exponents? or the actual geometrical thing

>>11164464
You are either 4 years old or mentally retarded

>>11164483
>>11164502
stop being rude

>>11164495
I saw there's also a 36^(-3/2), are you beyond just squares? Which part are you stuck on

>>11164517
how am I being rude? I'm trying to figure out what the fuck he posted so I can help the fuck.

>>11164517
Stop encouraging him.
>>11164520
Stop trying to help him.

>>11164527
Shut the fuck up. You're the worst poster in the general by far you autistic faggot.

>>11164030
Newton's laws were cutting edge theoretical physics at one point.

>>11164529
I fucking wish I was.

>>11164520
i dont know it was your tone of voice

>>11164527
trial by fire?

>>11164502
>>11164483
>>11164517
We're expected to memorize all the squares and cubes and cube roots and all this other shit that is just impossible

>>11164539
why dont you try calculating them each individually? try it by drawing squares, if you want 7x7 draw a square of 7 blocks by 7 blocks, and count em up. or, if you dont wanna be that primtive, try counting by 7, 7 steps, 7, 14, 21, 28, 35, 42, 49. just do the actual math yourself, and itll stick in your mind better

if your test is tomorrow though just use flash cards and try to do a lil of actual computation

>>11164539
hahahah retard. how does itfeel to be aretard.

>>11164546
The test is in a month I don't see how about could learn all this by then

>>11164548
i bet you're a retard anon. i bet you're struggling with calc 3 homework right now.

>>11164551
no. im in gradschool at the moment and im doing research on non-commutative algebra

>>11164549
oh, a month? you should be able to learn it in two weeks if you try hard. listen, just memorize them all first, that way when you do problems in your head you have a database to check your work with. memorization cant be too hard? its just like a phone number, everyone had to do that back in the day

>>11164539
Raising things to powers at the end of the day is just repeated multiplication. At the very least, you can work them out by hand, but it's really convenient to know them by heart.

For simplifying radicals the procedure is the same for any root. Ex: [math]\sqrt{72}[/math] . You want to try and write the number as a product containing perfect squares. For instance, [math]72=36\cdot 2[/math]. So [math]\sqrt{72} = \sqrt{36\cdot 2} = \sqrt{36}\sqrt{2} = 6\sqrt{2}[/math]

>>11164552
I like algebra. I'm studying linear algebra right now and in a proof the book said "replace term Vj with U1+W2.." after proving their equivalence, in order to prove that the term Vj was removable. It was kind of a mindfuck on the relationship between algebra and geometry. Treating the term for a vector in an equation like an actual object, then replacing it by calling into mind its equivalencies.

>>11154365
It's called a sigmoid
Google it

Geometry is for brainlets.

What does it mean when a vector spans a space? A column? A row?

>>11164571
A single vector's span is the set of vectors given by the multiplication of each scalar Ai,j.. with the vector v, or (Aiv, Ajv..), where Ai,j.. are bijected with elements of a field that has an operation set containing the operations of the Reals.

>>11164571
you should probably start learning linear algebra from the beginning

>>11164570
How come? Why is algebra better?

take the algebraic geometry pill.

>>11164593
What is algebraic geometry? Post the axiomatic concepts?

>>11164594
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the curve and relations between the curves given by different equations.

Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

>>11164593
>>11164594
Geometry is just the algebra of shapes, aka algebra for retards

>>11164587
Thabks

>>11164600
so its not shapes? its polynomial functions?

>>11164600
wow that last paragraph sounds cool but why are polynomials so important? they seem like relatively boring equations, i just dont get how theyre a good vessel for all that depth

also im curious does kindergarten style geometry ever reappear in higher math, like shapes? i just think shapes are really cute and fun

>>11164738
Technically a shape that is the set of zeroes of a polynomial.

>>11164748
somehow this reminds me of graph theory

what does someone with a phd in algebra do for a living if they don't go into academia? only guy i've met was a data scientist. are there algebra heavy industry applications?

>>11164600
you had me til the end when you started jerking yourself off

>>11164593
give me 4 textbooks to read to master it

This is cool and all, but does someone have an answer to my question?

>>11162030

>>11164601
me like triangool

>>11152037
Hey anons, I'm trying to make friends with people in grad school but I'm failing miserably. Any advice? I try going to bars to hang out with them, but I fucking hate bars. I try hanging out in the lobby, but I just find it difficult to mesh. I try talking math, but it seems most people are either interested in other things, or I have yet to really dig into the material they're are interested in.

>>11165442
how can they be against talking math if theyre in grad school for it? I think math is just a very intimate topic, they have to feel comfortable with you first. dont worry anon, stand in the hallway till they begin to acknowledge you and eventually come to appreciate you

>>11165008
maybe cryptography

>>11165445
Thanks for the encouragement anon. Yeah, I don't think it's that they dislike talking about math, more that they have more niche interests. A lot of them seem to like algebra, which is fine and all, I like it too, but there are other pieces of interesting math and for the most part they just seem to enjoy talking about either homework assignments, things covered in class, or material related to things in class, like which proofs of the fundamental group of the circle are their favorite or maybe some category theory and algebraic geometry. Which is rather unfortunate because I haven't really spent too much time with either field, so I can't really discuss much, and I tend to do homework and such alone.

>>11165008
Seconding cryptography. My country's government research agency shills pretty hard in our maths department for people to do crypto.

I want to learn R. I'd like to do stats and data analysis with it. How do I start learning?

>>11165745
what kinds of data are you analyzing?

>>11165442
>or I have yet to really dig into the material they're are interested in.
That's not a problem. Just let them talk about it. People love to ramble about what they're interested in, especially the obsessive autists that end up in math departments.

>>11152037
I study computer science but I am not that good at math (for example I participate on Codeforces round as I am trying to get better at solving those problems). How can I improve my maths and intuition to solve problems and see small hints ? I am talking mostly about discrete math

>>11165008
Tropical geometry, algebraic graph theory, Polytope optimization or Topological computation (homology computation, Topological data analysis, persistence homology) aka Algebraic topology on computers

>>11166476
did you even read the question

Hello, in lab they gave us the mass of and object saying it's mass was of 0,5g

Now, considering it's not a measured weight what would the uncertainty be?

I think it should be of 0,01g but my partner says 0,01%

>>11166503
>>11159921

>>11165014
jokes on you, i just copy and pasted that from wikipedia LOOOOOOOOOOOOOOOOOOOL

>>11164746
>why are polynomials so important
Answer one: all you need to define a polynomial is a concept of addition and multiplication, so you can define polynomials over any ring (https://en.wikipedia.org/wiki/Ring_(mathematics)).. Other functions (exponentials, sine/cosine, etc) depend on the specific topology of the real numbers and so don't usually make sense in this broader context.

Answer 2: Polynomials are fairly well behaved (particularly over algebraicly closed fields). We have a hope of describing how their solution sets behave. More general functions can be intractable to work with. In some sense algebraic geometry is the continuation of linear algebra in the sense that it is the next easiest problem to tackle (this doesn't mean it's easy though).

>>11164570
Visual processing is the most g loaded component of general intelligence, so it would seem that your aversion to it is indicative of misunderstanding of differences in cognitive function or simply low intelligence.

>>11156491
High iq

>>11166644
>>11166644
new
>>11166644
>>11166644

>>11166645
>post 310 was the new thread post
FUCK NEW THREAD POSTER AND FUCK HIS AUTISM

>>11166631
>Other functions (exponentials, sine/cosine, etc) depend on the specific topology of the real numbers and so don't usually make sense in this broader context.
Can you elaborate on this?

>>11166906
Sine and cosine are functions of an angle: they take an angle and give the height/length of the triangle created by the line segment at that angle intersecting the unit circle. The reason this even makes sense is that we have a geometric interpretation of the real plane [math]\mathbb{R}^2 [/math] by which we can talk about the angle between two vectors.
In general a ring doesn't have to have *any* geometric interpretation. As a really simple example, consider the ring with two element, 0 and 1, where for instance [math] 1+1 = 0 [/math] (you can work out how addition and multiplication works for any combination of 0 and 1 from the definition of a ring). This ring doesn't really admit a useful geometric interpretation. All we can really say about the geometry is that the points are distinct (this is called the discrete topology and is basically useless).
We can still define a unit circle as the points [math] (x,y) [/math] satisfying [math] x^2 + y^2 = 1 [/math]. Unlike the real case, where there are infinitely many points on the circle, there will be only two (can you work them out?). However, there is no obvious way to describe an angle in this plane.
By contrast, we can still make sense of (and ask questions about polynomials in our ring). For example the polynomial [math] x^2 + x [/math] has two roots, 0 and 1, whereas the polynomial [math] x^2+x+1 [/math] has no roots.