Advanced Mathematics Question/Answer thread.

>>8050515
Start the thread off with one?

>>8050570
If all characteristic classes of a bundle vanish, does that imply the bundle is trivial?

What is the derivative of f(x)= e^x ?

How do I find the cardinality of nonintersecting vectors within a closed frobenoid surface?

>>8051192
Do you own kneepads?

>>8050515

How can it be proven that

[math]

\displaystyle \frac{d}{dx} sin(x) = cos(x)

[/math]

?

>>8051224
maybe you should check what a derivate is

How do I prove the Birch and Swinnerton-Dyer conjecture?

>>8051224
Look at the Taylor series.

>>8051235

I've heard of derivatives, but I'm not aware of "derivates".

Say, friend, can you put the following into reduced row echelon order

[math] \displaystyle

\begin{bmatrix}

i & 2i & \pi i & 82 \\
42 & e & \sum\limits_{n=0}^{5} n & \frac{1}{10} \\
4 & 3 & 2 & 22 \\

\end{bmatrix}

[/math]

?

>>8051169
hm gee i wonder

>>8051202
Is this supposed to imply something about sucking dick?

Is the human penis an open or closed surface in topology?

>>8051224
https://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/sinx

you couldve just googled

>>8051224
Isn't it obvious given they are inverse?

File: advanced_mathematical_problem.png (23KB, 796x850px) Image search: [Google]

23KB, 796x850px

>>8051264

In what sense are these two functions "inverses" of one another?

Oh, another one. Find A.

Alright, so I've got a SICP related question:

One of the exercises in the book requires you to prove that Fib(n) is the closest integer to φn/√5, φ of course being the golden ratio (1 + √5)/ 2. To do this, the book gives you the hint that you need to prove that Fib(n) = (φn - ψn) / √5 where ψ = (1 - √5) / 2.

How would I know to do that if the book didn't give me the hint?

>>8051255
damn this is not a problem this is just boring af

>>8051255
Also i've just passed my math mock competitve exam and there was also a "recude row echelon order" over-annoying problem

>>8051273
Here is the solution.
http://www.billthelizard.com/2009/12/sicp-exercise-113-fibonacci-and-golden.html

File: Poincaréduality.png (1MB, 1334x1215px) Image search: [Google]

1MB, 1334x1215px

>>8051273
Additionally, you may find this useful:
http://www.billthelizard.com/2009/10/sicp-challenge.html

>>8051296
I'll use this as a reference after I reach a working solution to each problem to get a better understanding.

Thanks anon.

>>8051269
nvm i got cos and csc mixed up.

>>8051255

by the way , its was part of a bigger problem :
Given
u(n+3)=-u(n+2)+5u(n+1) -3u(n) ,
u0=0 u(1)=0 , u(2)=1
Find u(n)

>>8051302
Indeed, I wouldn't recommend looking at the solutions until you've put in great effort to solve them/want to check your work. No problem.

>>8051192
I'm guessing either it is countable or the same cardinality as the real line.

File: SMT.png (769KB, 1695x1486px) Image search: [Google]

769KB, 1695x1486px

Does anyone have experience with Satisfiability modulo theories?

I'm trying to decipher the notation.

I don't understand how to read

bE
bvE
mE

Can someone make sense of it?

>>8051239
and I thought /sci/ was full of smart people

c'mon

File: Screen Shot 2016-05-04 at 10.52.28 PM.png (18KB, 1248x176px) Image search: [Google]

18KB, 1248x176px

>>8050515
Idk if this is too easy for this thread or not, but I was hoping /sci/ could help me with my hw.

pic related

>>8051239
Can only be proved in special cases, what would you expect; It's a millenium prize problem.

>>8050515
TELL ME ABOUT GALOIS THEORY HOW DO I GET GUD

>>8050515
>tfw just failed a Real Analysis II class
>tfw can't graduate for another semester

Jesus Christ just end me.

>>8051269
Find the area of the whole circle. Divide by 4. Find the area of one of the 4 squares. Subtract 1/4 the area of the circle from the area of the square. Find the area of the smaller circle. Go from there.

>>8051169
too advanced

>>8051345
work harder

>>8051351
Analysis is just meme math anyway I don't give a shit anymore.

>>8051345
I recommend:
Tao Te Ching,
Littlewood's Three Principles, and
Bressoud's "A Radical Approach to Real Analysis." Peace, epsilon, convergence.

>>8050592
Nope. Take for example TS^4.

Got an analysis II final on Wednesday, been slugging and coasting by.

What's the possibility of getting an A on the final? We studied Limits, derivative, Taylor & power series, & integration chapters.

>>8051389
suppose I have a polynomial P(x) irreducible over Q and is solvable in radical
denote K as the splitting field of P(x) over Q
how can I construct an extension L over Q such that
1) Gal(L/Q) is a solvable group
2) K is a subfield of L, and K,L are distinct

yo what is a dee over dicks?

Can anyone take a stab at what this notation means >>8051315

I almost think the expression bE where E represents an expression/variable that can be replaced with: true, false, b, ~b, ~bE, bE1 or bE2 etc... but I am certainly not sure.

>>8051416
dude maths is useless in life
study cs

>>8050515
yo when am i gonna y=mx-b in my life

>>8051347

Oh okay, thank you. I see it now. How about this thing?

[math]

\displaystyle

\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} ( \sin x \cos x \tan x ) dxdydz

[/math]

?

Also what does everyone think of the notion that "p implies q" is the same thing as " 'not-p' or q"? sounds kinda dumb and counterintuitive to me. After all, if something false implies something that is true, then that defies reasonability as a true statement.

>>8051534
triple integral of the same variable??? wtf lol.
literally integrate that 3 times. I sinxcosxtanx can be rewritten as sin^2x

>>8051534
this is literally just sin^2(x) dx from 0 to 1

>>8051435
never, now go pave my driveway or fill my car with gas

>>8051550
>>8051554

Okay. How about

[math]

\displaystyle \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} ( \sin x + \cos \phi + \tan x ) d \phi dydz

[/math]

?

still need an answer on the implies thing too.

File: image:26131.jpg (403KB, 1100x3300px) Image search: [Google]

403KB, 1100x3300px

>>8050515

i understand the mechanics, but not the intuition behind tilted density sampling

anyone that did some work in statistics/sampling theory help out?

File: a06a03dfbd7ab3f902831c51f008bbd2077bb254.png (9KB, 771x368px) Image search: [Google]

9KB, 771x368px

>No Pre-Calculus, Calculus I-III, Differential Equations or elementary Linear Algebra questions allowed.

So that excludes all engineers right?

>>8051240
The Taylor series are themselves created from the derivatives though.

>>8051653

signal processing \ information theory can be breddy based

File: gorilla_623_sheilasmith.jpg (46KB, 623x446px) Image search: [Google]

46KB, 623x446px

>>8051603
for your logic question just do the logic tables m8 it is the same thing

and do you not know triple integration or something?

the answer to that integral is sin(x) - sin(1) + tan(x)

>>8050515
what is x?

>>8051354
>meme math
just stop

How do I into control theory?

>>8051790
PID controllers and state space analysis lad

>>8051780
math meme ?

>>8051808
I was asking for a book recommendation.

>>8051315
The syntax is defined in BNF notation. (possibly extended BNF) Apparently, the author assumed the reader would be familiar with it.

>>8051836
ogata - modern control engineering is what we used.

it uses MATLAB too for some bits which I like because I'm an EE and it's basically our bread and butter.

File: stokes theorem.png (192KB, 1920x1080px) Image search: [Google]

192KB, 1920x1080px

Hey guys,
Just a moron-tier engineering student here with a question regarding Stokes' Theorem:

Shouldn't the terminals of integration be 0-->a? Or have I missed something?

>>8052118
>terminals
and yup, looks like an error.

also
>no calc III

>>8052130

sorry for posting that shit-tier math problem bro, won't happen again

>>8052118
>>8052134
Why didn't you just post it in the stupid questions thread?

>>8051908
Your reply exceeded my expectations, thank you! Indeed the author makes many such assumptions, as I've never heard of BNF before.

How would you grind through the grammar?

For the Boolean expression type I'd assume you could convert the "b" in bE as follows

bE := (true)E, (false)E, bE (not sure about the b by itself?), ~bE, bE1 or bE2 and so on... and then you can replace the Es with either bE again, bvE or mE.......

is this correct?

Also, for the mE can you make sense what the lambda (x1,...,xk).bvE is?

looks like something from lambda calculus with lambda is binding x1,...,xk in the head and bvE is the argument for the formula.

Anyways, any good online resources to get some basic background in BNF or SMT?

>>8052235
BNF is a standard method to express syntax in formal language theory or computer science in general. I think wikipedia should be able to provide enough information on the format. The basic idea is that you define "tokens" (in your pic "bE", "bvE" and "mE"), for which you give a list of replacement option separated by "|". Those replacements are combinations of literals (e.g. "true") and other tokens, which allows you to construct and parse the language recursively.

I can't make much sense about the example you're giving, but the idea is to replace the entire "bE" part. Perhaps this clarifies something. If we want to create an "bE", start with that token and replace it by e.g. "bE1 v bE2". Now we can replace those new tokens (the numbers are only there to show the tokens need not have the same value) such that we get e.g. "true v false", which then is a valid instance of "bE". I think the author means that "bE" stands for boolean expression, "bvE" for bit vector expression and "mE" for memory expression. A bit clunky notation, imo.

The lambda part does seem to indicate binding from the lambda calculus. I suppose that is one way to formalise "memory".

I don't have any knowledge on the topic of SMT at all, but it looks interesting. Can you tell me where your image in >>8051315
is from?

There is a formula for a projection operator that uses a contour integral like so:

[math] P_{k} = \frac{1}{2\pi i}\oint_{|\lambda-\lambda_k|=\delta}(\lambda I-A)^{-1}d\lambda. [/math]

where A is a self-adjoint operator. For simplicity, let's work in finite dimensions. Where can I find a proof that the target subspace dimension equals the number of eigenvalues within the contour?

>>8051315
>bE ::= true | ....
bE is a boolean expression
Boolean expressions can either be true, false, a boolean variable, negations of a boolean expression, a clause of two boolean expressions, a conjunction of two boolean expressions, the equivalence of two boolean expressions, ...

bvE = bitvectorExpression which can either be a bit vector constant or a bit vector variable or ..., mE = memoryExpression ...

>>8050515

i only know the math topics listed by op, so what do i learn next?

>>8052419
complex analysis or functional analysis

There's a lot of unanswered questions in this thread, why aren't you guys posting on math.se or mathoverflow?

>>8052440
I gave up. My question didn't receive any answers there.

>>8052440
Posting on /sci/ is easier. I don't need a username.

>>8052445
Bounty/more attractive title/more popular tags?

>>8052474
Just post as an unregistered guest with a fake email.

This anon is at work. Will respond after

I want to see atom

>>8052539
I have tried everything. I'm certainly sure that there are people, who the answer, but deliberately ignore. Meanwhile, the question is well appreciated (it got 10 votes)

>>8052548
How long ago was the question posted? I mean, if someone could answer such a well appreciated question, it's basically free rep.

>>8052579
A lot. Over two weeks. After some time, questions simply fall into abyss and never get answered.

Still at work. I want to post my questions :/

>>8052741
Yeah that won't be seen again... want to give it a sneaky edit to bump it back to the top?

>>8050515
How prove?
[math]\mathbb{R} = \mathbb{Q}\sphericalangle \diamondsuit \multimap \infty [/math]

>>8051273
pretty obvious from the formula for the n-th term?

>>8052800
i have taken math classes in 3 different countries, read hundreds of papers and textbooks in various languages, and never have i seen this clusterfuck of notation

explain yourself

>>8052779
I tried. I don't think it helps

>>8052890
IUT

>>8051169
Is e transcendental or just irrational?

File: Screen+Shot+2016-04-09+at+9.04.14+PM.png (24KB, 568x74px) Image search: [Google]

24KB, 568x74px

>>8053047

>>8052165
kek

>>8052800
The proof is left to the reader

Not directly a math question, but a logistical question about synthesizing advanced math:

I spent the past six months studying a certain area of advanced mathematics, learning all the proofs through and through, even re-writing every proof from my own memory/understanding after learning them.

And now I can scarcely remember a damn thing.

It is so fucking frustrating. I feel like, relative to mathematicians, I must be downright mentally retarded with respect to memory. I don't know how I'll continue as a phd student if I can scarcely remember a single goddamn proof.

Is this common, or am I exceptionally retarded? Regardless, what do I do about this?

Thank you.

>>8053268
Just skim your notes. It will all come back quickly.

>>8053272
+1'ing this, hope someone answers this.

>>8053273 was for >>8053272; I edited a typo.

>>8053273
Thanks. I hope so.

I also regularly forget what variables stand for halfway through a proof.

I was a drug addict throughout my undergraduate years, yet somehow got into a top-tier grad program. But I almost know for a fact that I did irreparable brain damage during my drug binges. I feel like I'm riding on the coat-tails of my former intellect, and now I'm a husk of that.

You have no idea how much I hate myself all the time for this. I don't know if I'm even capable of getting a PhD anymore.

To any anon who hasn't methodically fucked up his own self and life: take a moment to be grateful.

>1+1 = 2, find x
Help pls

>>8053282
The solution set is the solution set to a system of linear equations -- namely, the empty system.

So simply put the empty matrix into row-echelon form to solve for x.

Basic linear algebra.

File: 1449434996300.jpg (38KB, 460x447px) Image search: [Google]

38KB, 460x447px

So I'm reading up on category theory on wikipedia and I found this:

"Every poset (and every preorder) may be considered as a category in which every hom-set has at most one element."

If every hom-set had at most one element, would that not just be the identity morphism for each object?

Is there something I'm missing?

>>8053297
Think about if the two objects are distinct. Can there possibly be an identity morphism between two distinct objects? No. (Though there can exist isomorphisms.)

In general, wikipedia is probably not the best place to learn about new math.

>>8053285
nice reverse bait desu

>>8051534
>"p implies q" is the same thing as " 'not-p' or q"?
This is counter-intuitive to a lot of people, but makes sense when you unpack it (coming from an LSL perspective):

p -> q means "if p, then q." this means that p is a sufficient condition for q to occur, and q is a necessary condition. Thus, you can reason that it's equivalent to say that either p doesn't happen or q does happen, *but not both* (that's the tricky part about disjunctions - that Law of the Excluded Middle). This is key, because it's saying that q, being a necessary condition, must be disjunctive with p, the sufficient condition, not happening.

Putting it into a case study:
Let p = my car has gas
Let q = my car's engine starts.

Symbolizing it, we get p -> q, because having gas is a sufficient condition for the car to start. Thus, we can derive the equivalency ~p v q because either my car does not have gas or the engine starts - but the car can't not have gas and the engine start. You could do this with any sufficient condition for the car's engine starting (having the key in the ignition, the gearshift being in park, etc.) and it would work. It's just a syntactical necessity of the grammar.

Here's the wiki on it: https://en.wikipedia.org/wiki/Material_implication_%28rule_of_inference%29

>>8053272
Revel in the fact that you have the technology of writing.

Of course you don't remember all the details - you don't have to. What you remember is how to *read* the proofs, and have acquired the technical literacy of the language of math to the degree that you can synthesize and explain the underlying concepts well enough to use the structures therein.

This problem is like a chemist worrying that they can't reproduce the periodic table from memory. Not to worry - that's why it's written down!

>>8051255
I'm browsing this thread out of curiosity - I'm not at the appropriate level, so I was just wondering, what is this sort of math used for?

>>8053371
It's a matrix. Matrices have all sorts of applications, as they are a representation of the structural correlations between elements in a set, function, or series. You can solve linear equations, for example, by placing coefficients into a matrix. The benefit of the matrix is that it creates a visual representation of the pattern of data to make manipulation of it easier.

From Wikipedia: There are numerous applications of matrices, both in mathematics and other sciences. Some of them merely take advantage of the compact representation of a set of numbers in a matrix. For example, in game theory and economics, the payoff matrix encodes the payoff for two players, depending on which out of a given (finite) set of alternatives the players choose.[71] Text mining and automated thesaurus compilation makes use of document-term matrices such as tf-idf to track frequencies of certain words in several documents.[72]

https://en.wikipedia.org/wiki/Matrix_%28mathematics%29

>>8053420
>>8053420
I'm not the person you're replying to, but maybe he meant the contents of the matrix not the matrix itself, which I'm also curious about. I've only taken an introductory course in linear algebra; are those entries like that just to make the elimination process more tedious, i.e. to test how well is the person at reducing a matrix, or does it have an actual purpose?

>>8053272
you do not remember, because you did not understand. If a proof is not trivial at some point, then you do not understand the proof.

File: Untitled.png (4KB, 230x169px) Image search: [Google]

4KB, 230x169px

If you think you're so advanced try explaining this.

Quick questions
https://proofwiki.org/wiki/Fundamental_Theorem_of_Calculus/First_Part#Proof_1

Why do you have the to prove that primatives are continuous?
And doesn't [math] \forall x\in [a,b]: F'(x) = f(x) [/math] imply that F is differentiable for the closed interval [a,b] not just (a,b)?

a modular elliptic curve is an elliptic curve that arises from the parametrization of a modular curve i.e. there is a rational mapping from the modular curve to the modular elliptic curve

what is the meaning of this? I look up wikipedia and the definition of rational mapping is too abstract and beyond my comprehension level

Bump this >>8052353

>>8054077
the modular parametrization is a surjection from the modular curve X_0(N), to the elliptic curve E, where N is the conductor of E (just an integer that keeps track of which primes your elliptic curve reduces to something undesirable)

(i think) the reason for a rational mapping is that the function might not be defined on all of X_0(N), just an open set of it

see http://wstein.org/people/goins/lario.pdf p26 onwards for some explicit parametrizations

>>8051224
Use Euler's Identity to substitute sin (x)

>>8054175
>>8054077
see https://en.wikipedia.org/wiki/Classical_modular_curve#Mappings for a good clear example

Solve the the Helium Atom without using approximations. Show your work please

how do i into math

I haven't done much math since secondary school

Whats ker[(x+iy)+i(x-iy)]?

What's the biggest number?

>>8054295
Ker={(0,y) : y in \mathbb{C}}

>>8051169
-1/12

>>8054300
-1/12

>>8053757
Do FTC proofs not count as advanced enough?

>>8054539
Considering that it's first semester...

>>8051269
`[; \frac{1}{16} \left(2 \sqrt{7}+\pi +8 \sin ^{-1}\left(\sqrt{\frac{3}{8}-\frac{\sqrt{7}}{8}}\right)-8 \tan ^{-1}\left(\frac{5 \sqrt{7}}{9}\right)\right) ;]`

>>8054552
But its analysis first semester?

>>8054571
Which is undergrad first semester.

>>8054605
But isn't calc i-iii, diff eq or lin alg :)

>>8054611
It counts as differential equations :)

File: andrew wiles.jpg (26KB, 837x160px) Image search: [Google]

26KB, 837x160px

What books do i read so i can understand the proof of FLT

any easy way to learn group cohomology and scheme? I don't need to learn everything, just the basic definitions and basic theorems that are useful when I read the proof of FLT.

Also what is the "X in a circle" sign? (see pic)

>>8054662
>X in a circle
Direct product

>>8054662
Tensor product for example. Depends on context

>>8054662
>What books do i read so i can understand the proof of FLT
There are experts in arithmetic geometry who don't understand the proof.

>>8050515
Prove that two non parallel lines, if produced, will intersect.

>>8054692
Physicists, everyone.

>>8054662
For asuperficial account of number theory in general, including a sketch of FLT, read manin's book. I don't recall what it's called, but there is a coauthor.

What does it mean for a set to be well ordered?

>>8054749
It means that for every subset of the set there is an element which is less or equal than every other element of the subset: take a set, the naturals for instance; then every subset has a least element (given that for every element of the naturals, there is only one predecessor). The definition only takes in consideration non-empty subsets, for obvious reasons.

The definition applies to every set in which an order relation is defined, and whether the lest element belongs to the subset or not is often not important.

A well order is also a total order, but the converse is false, which means that for a set to be well ordered also means for it to be totally ordered, otherwise we couldn't compare every two elements.

The fact that the naturals are well ordered is extremely important for proving many results, the most famous being the induction principle.

If you want to know more I suggest you look into order relations on a set: if you had any rigorous Analysis (or, to some extent, Topology) class you will find many clarifications about inf, sup, max, min and so on. But I figure that if you had any class about those you wouldn't be asking what a well ordered set is, so the last paragraph is pointless.

Goodbye fuck yourself.

>>8054616
Fine you got me.
I'll ask in /sqt/

Brains, I need a little help with one task. It's in polish, so I will do my best to translate the the description.

Enumerate sin(15*30') with approximation of 10^-5. Designate value of this function in Octave (our main tool) and find what's the module of difference (error value) between your calculation and the one from Octave.

First of all should I change the sin value from degrees to radians?
Should I use Maclaurin's (Taylor's) method?

If anyone would be so kind to assist I am waiting here (drawing board)
https://awwapp.com/b/ugonypyy9/

If F is a smooth mapping from of n-dimensional compact manifolds, show that if F is not surjective, then F is degree 0.

The idea I think is that if F is not surjective, then the image F(M) in N is smoothly homotopic to the constant map, which has degree 0. Just not sure how to show the image is contractible in N.

>>8054964
the point is that there is a nonempty open subset (the complement of F(M)) such that the fibre of F (= the preimage of F) is empty on this open subset. for me the definition of degree is the number of points in a generic fibre (see wikipedia's page on degree), so the claim is kind of obvious

Can someone redpill me on cohomology with non-abelian coefficients? I'm not much into homological algebra, but I want to use Cech cohomology on a principal bundle with non-abelian gauge group. Give it to me straight: How much of the comfortable features of cohomology still works when the coefficients are non-abelian? I know we lose the group structure on the cohomology sets. What else?

>>8053053
That's not true tho. Even Wildburger can agree that there are numbers that are not rational as well as numbers that are not roots of any polynomial with integer coefficients.

>>8056477
So memeberger believes in the existence of transcendentals? Does he believe in [math]e[/math] and [math]\pi[/math]?

>>8057027
Yes, why wouldn't he? Are you one of those memers that have never watched any of his videos or read anything he wrote but keep spouting
>muh [math]\mathbb R[/math]
all day?

>>8057031
I have never watched any of his videos, and though he is a meme, I am not a memer with respect to memeberger.

Can anyone explain to me about Hilbert Space?

>>8057135
What do you want to know? (in case you're not memeing)

>>8057106
At least watch this one if nothing else:
https://www.youtube.com/watch?v=lcIbCZR0HbU

>>8057031
I don't think that he does believe in e or π since there is no way to construct them that doesn't involve doing an infinite amount of work. For example using Dedekind cuts
[eqn]
e = \{ x \in \mathbb{Q} \mid x \lt 1 \}
\cup \{ x \in \mathbb{Q} \mid x \lt 1 + \tfrac{1}{2!} \}
\cup \{ x \in \mathbb{Q} \mid x \lt 1 + \tfrac{1}{2!} + \tfrac{1}{3!} \}
\cup \cdots
[/eqn]
Strictly speaking constructing the sets requires infinite work as well but you could avoid that by working with just the predicate so that gets a pass.
So you can see this idea of defining what the hell you get when you take an infinite sum has really just been replaced with the problem of constructing an infinite predicate.

>>8057167
fug. It should be 1 + 1/1! + 1/2! ....

>>8057138
Everything about it.

>>8057027
> believe

He refuses to use transcendental functions
Pretty sure transcendental numbers are a nono too

>>8056477
I don't think he likes algebraic completion.
Don't you need calc to prove fundamental theorem of algebra?
And you can't calculate roots of some of those polynomials exactly sooo yeah

>>8057207
What does the fundamental theorem of algebra have to do with anything? The only thing stopping you from calculating roots of complex polynomials exactly is being unable to calculate their real coefficients. You can do this with [math]X^2-2[/math] as well. The fundamental theorem of algebra is entirely irrelevant when you aren't acknowledging real numbers.

>>8057229
Can you show that there is a solution to x^2-2=0 without FTA?
Not being cute. I thought you needed it even for integer coefficients.

Kinda new to math, almost finished with real analysis

>>8057254
>Can you show that there is a solution to x^2-2=0 without FTA?
A solution in what? This is the key point. The algebraic closure of Q has solutions to all polynomials with rational coefficients and I can define it without any reference to analysis or real numbers.

>>8057292
Ahh I gotcha.
I think.

>>8057254
You can prove it using the Intermediate Value Theorem.

f(x)=x^2 is continuous, and f(1)<2, f(2)>2. So there's a point 1<x<2 such that f(x)=2.

You can similarily prove that all polynomials with an odd degree have a real root.

>>8053685
My advisor is literally world-renowned in his field.

When I took graduate courses from him, it was clear that all of the material was utterly obvious to him. The proof takes an hour to even write down? Trivial to him. As it should be.

When it comes to more modern research as well, 99% of the time, his brilliance and expertise are completely intimidating. Makes me wonder how I'll ever contribute.

However, I've seen even him struggle to recall a proof or work through a problem. It almost made him seem human.

>>8051534

Make a truth table of the two situations. They are identical, so the statements say and imply the same things, thus, the statements are the same.

>>8053272
Nah, don't worry, this is something that everyone has to deal with. You cannot remember every detail of everything that you learn.
Nobody can. Sure, some people have a better memory than others, but you cannot reasonably expect anyone to be able to tell you about in detail about the proof of a very hard theorem unless they happen to be working on it. But that's okay.
What is important is to have the outline in mind in order to be able to quickly remember everything.
Also keep in mind that what seems hard to you now might seem like routine once you are more familiar with it.

What is a conundrum

>>8051169
that's trivial: xe^(x-1)

>>8057167
the problem of these expression for e and pi through series is that we need classical math to obtain them, then go back to constructive math.

Any ideas on how to even begin proving the Collatz conjecture

>>8057946
induction

what math should i be exceptional at for an incoming cryptography course im about to take?
lets assume i have nothing

Does (∂ x )^ 2 =∂ xx

I am trying to prove the identity
4∂∂ ¯ =∂ xx +∂ yy
Where
∂=1/2 (∂ x −i∂ y ). Cheers math bros

>>8058001
It's practically tautological, just write out what del del bar is.

>>8057996
Depending on the flavor of the class, cyclic groups, elementary number theory (congruences), elliptic curves

>>8058010
im guessing finite fields too right

>>8058012
Yep, might end up doing some computations of F_q points over an elliptic curve at some point

See Koblitz book 'A Course in Number Theory and Cryptography'
http://users.metu.edu.tr/aldoks/478-Koblitz-2ndEd.pdf

>>8054248
>Solve the the Helium Atom
nbody problem you dipswitch

hi guys. i'm a bit of a retard with stats (doing a finance and law degree, so i've got to do some math).

if there is a skew to the high end for the population, should there be a skew to the high end for a sample of that population?
also, if you take the avg of those samples, what is the distrib of those avgs? it should all be the same value?

File: [HorribleSubs] YuruYuri S3 - 05 [1080p].mkv_snapshot_07.42_[2015.11.09_20.03.49].jpg (87KB, 1920x1080px) Image search: [Google]

87KB, 1920x1080px

>>8055388
Non-Abelian-ness of the gauge group is reflected in the Lie algebra of the structure group G, not in the cohomology. Look up Zumino and Stora's differential geometric treatment of gauge theories.
On the other hand if you want to use non-Abelian coefficients in forming your chains and cochains then there will be some duality theorems that you will have to abandon, since some of them relies on the fact that chains/cochains form dual vector spaces, but personally I don't see how using non-Abelian coefficients can get you anything.

>>8054964
>smooth mapping
>not surjective
What?

>>8052353
Use rank-nullity theorem.

>>8058135
Take your pedophile cartoons back to >>>/a/.

>>8058139
smooth just means infinitely differentiable

>>8058135
>Look up Zumino and Stora's differential geometric treatment of gauge theories.
Is it a book, or a paper or a collection of papers? I tried to search these names but couldn't find a text written by both of them.

>>8059096
They're separate authors. There are books that summarize their stuff but they've also written several papers on the topic

>>8059037
And by the inverse function theorem smooth means the map is invertible on a neighborhood. I'm probably missing something

How do you prove the absolute continuity of the Lebesgue integral?

File: Screen Shot 2016-05-08 at 6.19.48 PM.png (77KB, 662x210px) Image search: [Google]

77KB, 662x210px

>>8050515
Need /sci/ to verify for me that this is problem is trivial. It really seems like it is, but I don't know why someone would put it in a book.

>>8059461
Take the inclusion map from any open subset [math]U \subset \mathbb R[/math] to [math]\mathbb R[/math]. Yes, this is certainly locally invertible, but it will never hit anything not in U.

Any function (smooth or not) is surjective if you restrict the codomain to its image, which is essentially what you're suggesting.

>>8059868
Its trivial, indeed.

>>8059461
> smooth implies invertible locally
are you serious? the idea behind IFT is that if the derivative is nonsingular:
det(dF) =/= 0
then you can invert dF, and hence invert F locally. So you need dF to be invertible. The map taking everything in one manifold to a single point, is smooth, yet is clearly not invertible locally, or anywhere.

>>8059908
Oh ok so the map isn't globally surjective

>>8058135
>how using non-Abelian coefficients can get you anything.
you can happily define H^1(M;G) for non-abelian G, and this space is actually the moduli space of principal G-bundles over M! So for example, a path integral over this moduli space can actually be done by looking at cochains. This stuff is pretty useful in geometrical quantization.

It turns out you can also define H^2 and get some interesting results, but I don't know much about this. I think anything over degree 2 is impossible for categorical reasons.

>>8059928
>this space is actually the moduli space of principal G-bundles over M! So for example, a path integral over this moduli space can actually be done by looking at cochains

Not the guy you were responding to, but this sounds interesting. Recommend a book for learning about it?

>>8059935
the first result is basically obvious if you apply the definition of Cech cohomology to the cocycle construction of G-bundles. A good elementary reference is
http://pages.uoregon.edu/adding/notes/gstc2007.pdf
if you want the more categorical stuff, look at the nlab article on nonabelian cohomology.

I have a projective variety, let's say the zero locus of [math]xy-z^2[/math], and I want to show it's normal, i.e. the local ring [math]\mathcal O_P[/math] is integrally closed at every point. Is this general train of thought valid?

Take an affine piece containing P: so if z is nonzero for isntance, then P is in an affine piece cut out by [math]xy-1[/math]. Then the local ring is [math]\mathcal O_P = \left( k[x,y]/(xy-1) \right)_{\mathfrak m_P}[/math] where [math]\mathfrak m_P[/math] is just the maximal ideal of functions vanishing at P. Since the localization of integrally closed is integrally closed, it is enough to show [math]k[xy]/(xy-1) \cong k[x,x^{-1}][/math] is integrally closed, but this is itself a localization of [math]k[x][/math] which is integrally closed.

You would continue this through whatever necessary cases to cover the whole variety. It seems right to me, but I want to make sure I'm not missing anything subtle.

>>8059868
>>8059912

How is it trivial? Genuinely interested. Consider a simple case. Suppose f is a smooth function with compact support in the open interval (0,1). Show [math]\int_0^1 f'(x) dx = 0 [/math] directly, i.e. without using the Fundamental Theorem of Calculus. Is that any different?

>>8059928
>>8059942
That's interesting. I've seen [math]Z^1(M)[/math] used in a symplectic geometry context but never with a non-Abelian group of coefficients.

>>8060241
>>8060241
Because for a n-dimensional manifold the de Rham complex is :

[math] 0 \to {\Omega ^0}M \to \ldots \to {\Omega ^n}M \to 0[/math]

omega is defined as an n-form, so is it not a trivial fact that the integral of d(omega) is zero?

>>8060256
That makes sense, but then I think OP is right to think there is something off here... you don't need the box-shaped chart or even the integral really.

>>8060198
Since I'm thinking more about this, this should also lead to saying that a projective variety is normal iff it has an open cover by affine varieties with integrally closed coordinate rings. The fact that this sounds logical to me is assuring.

File: 1459935883068.jpg (130KB, 832x690px) Image search: [Google]

130KB, 832x690px

Prove there is a vector field F such that
FxT=T'
FxN=N'
FxB=B'

Is there some easy way of doing this? What I thought was to set F=(f_1, f_2, f_3) and plug the formula into Frenet's equations.

What are the workhorse algorithms to get a non-square matrix into block triangular or diagonal form?

All I have been able to find are great theorems that are incredibly prone to noise.

>>8061142
Is this from Barrett O'Neill's book? I vaguely remember doing that question and using that method

>>8061152
maybe. it was on my exam today. i didn't have time to solve it properly.

>>8053420
I thought we decided
>no elementary Linear Algebra
? Spoon-feeding _matrices_ to anon means that they probably need to go elsewhere (like secondary school).

What's the coolest shit you can do with algebraic geometry? I mean what are some applications to "real" geometry so to speak?

>>8061279
>I mean what are some applications to "real" geometry so to speak?
That's not really the point of algebraic geometry. We understand "real geometry" and want to use that knowledge to understand solutions to polynomials by giving the solutions some sort of geometry.

>>8051169
Not sure, although I know you need to use Barnett Integrable Functions™ to solve for it.

>>8051255
what is this meme square

>>8061149
do you mean singular value decompositions?

What's a good text for baby's first Lie groups?

>>8061439
It depends.
Do you want it purely for mathematical purposes? If so are you interested more in the Geometric or Algebraic perspective?


Do you want it for applications to physics? If so are you more interested in like the representation theory style for particle physics, or the Diff. Geom. style for pure Gauge Theory?

>>8061447
no interest in physics

>>8061450
> are you interested more in the Geometric or Algebraic perspective?

>>8061450
>>8061451
geometric

File: tvcFH.png (2KB, 241x240px) Image search: [Google]

2KB, 241x240px

>>8050515
Prove that a 1024 x 1024 chessboard can be completely and perfectly dissected into trominoes. Bonus: Generalize this.
(If you don't know what a tromino is, look at pic related. The shape formed by the green shaded squares is a tromino.)

>>8061474
This is not advanced math at all I'm afraid. Once you realize that 2 "trominos" can be combined to make one 6x2 rectangle it's over since 1024 is divisible by 6 and 2.

Get off this thread

>>8050515
What is the biggest class of structures, for which MSO is decidable? I know about the graph sets closed under minors, what about structures with more than one relation?

>>8061493
#REKT

>>8061498
By anon's rationale, we can dissect a 1x6 grid into trominoes simply because 6 is divisible by 3, but we can't.

>>8061501
That wasn't his argument at all.

>>8061501
don't be stupid, 1 isn't divisible by 6 or 2 never minds both of them.

he's right, you should be here:
>>>/sci/sqt

>>8061493
>1024 is divisible by 6
Are you retarded?

>>8061507
Problems are stupid because snarky anons deem it so. Also, 1024 is divisible by six? What the actual fuck? Are you fucking kidding me? 1024 is a perfect power of 2, for Christ's sake.

>>8061511
lol such a simplebrain

6x4 = 24
6x2x2 = 12
6/3x2x3 = 12
12/6x2x3= 12
1024/4 = 256
2/4 = 2
256x6/2x4/12x3x4 = 1024/6

brainlet

It's funny how half of /sci/ is in denial or just plain retarded.

>>8061522
Is this guy trolling? Somebody fucking screenshot this.

>>8061522
There are no fucking 3's in 1024's prime decomposition, you dumb cuntwipe.

>>8061522
If more people like you killed themselves on a daily basis, we would have cured cancer by now.

>>8061528
lol such a perpetually incredulous brainlet

cant think outside the box

you are the reason why math has taken thousands of years to get where it is today

you can only do what has be done, what people tell you to do, what people tell you is correct

>there are no 3's in 1024

1024/2 = 512
512x12 = 6144
6144/1024 = 6
6/2 = 3

try to think for yourself next time before blindly following the sheep infront of you

>>8061537
>1024/2 = 512
>512x12 = 6144
>6144/1024 = 6
>6/2 = 3
8/10, people will fall for this and feel mad, next time post a smug anime girl for full points

>>8051345
>tfw a guy in my class is taking Analysis II, while still not having passed Analysis I

He just spends most of the lecture browsing shit on his laptop too

>>8061557
>1024/2 = 512
>512x12 = 6144
>6144/1024 = 6
>6/2 = 3

what da fuq

>>8051345
Lol I just saw this, I'm this anon here >>8051370


So yeah I might not graduate. last math class and only offered in the spring, so might not graduate until Spring 2017 (JUST).

Sorry anon. I feel you

>>8051370
How the fuck is that analysis 2? That shit should be covered in regular calc classes or at most in an intro to proofs class.

>>8053281
Your brain is fine. Just look at the guy with hydrocephalus who got a math phd.

You feeling super depressed is probably harming your math the most.

>>8063107
Uh, are you retarded? it's not computation nigger. it's a proof based class

>>8063125
It should be covered in analysis 1 you stupid dumbass.

>>8063129
Different universities offer different courses, and while the subject matter as a whole in undergraduate real analysis is fairly standard, the 2-semester sequence is treated as a block and different universities divide the topics differently among the courses.

Can anyone explain if there is a nontrivial relationship between thermodynamics and fractals?