Hello friends! Ask any math question, and I will do my best to answer it.

File: 35 KB, 400x423, thatguy.jpg [View same] [iqdb] [saucenao] [google]

None !JSN8X5.Us. Sun Aug 11 01:53:52 2013 No.5961201 [Reply] [Original]

Hello friends!

Ask any math question, and I will do my best to answer it.

>>	Anonymous Sun Aug 11 01:54:22 2013 No.5961203 >>5961201 Prove or disprove: N = pN

>>	Anonymous Sun Aug 11 01:55:23 2013 No.5961204 >>5961201 Prove or disprove: P = NP

>>	Anonymous Sun Aug 11 02:00:52 2013 No.5961214 <- do this

None !JSN8X5.Us. Sun Aug 11 02:01:23 2013 No.5961215

>>5961204

Hello!

I have said this on here before. I can honestly say that I don't have the understanding of the background material to even begin like I pretend to understand the complexity (heh heh), let alone have any insight on P=NP.

Sorry!

>>	Anonymous Sun Aug 11 02:03:23 2013 No.5961218 File: 4 KB, 532x240, find_it.png [View same] [iqdb] [saucenao] [google] solve this

Anonymous Sun Aug 11 02:08:23 2013 No.5961227

>>5961215
So you can't answer any of the hard problems, huh, well, okay.

Take this one:
a ^ n + b ^ n = c ^ n[/spoiler]
Assume that a, b and c are all real, positive, integer numbers and assume n is a positive, real, integer number greater than 2; find a possible solution for a, b, c, and n.

>>	None !JSN8X5.Us. Sun Aug 11 02:08:23 2013 No.5961228 >>5961218 Hello! This guy can do a much better job than I can in a 4chan response. Good luck! http://www.youtube.com/watch?v=AncVA3cX7aQ

>>	Anonymous Sun Aug 11 02:09:22 2013 No.5961234 >>5961204 >2013 >Not knowing P vs. NP problem has been solved. http://vixra.org/abs/1307.0100 http://vixra.org/abs/1304.0163

>>	None !JSN8X5.Us. Sun Aug 11 02:09:53 2013 No.5961235 >>5961227 Hello! This one I can do. I've wrote it up here: http://math.stanford.edu/~lekheng/flt/wiles.pdf Ask if you have any issues! Best!

>>	None !JSN8X5.Us. Sun Aug 11 02:10:53 2013 No.5961238 >>5961234 Hello! I am well acquainted with vixra. Make your own vixra quality paper here: http://thatsmathematics.com/mathgen/ Best!

>>	Anonymous Sun Aug 11 02:11:23 2013 No.5961241 >>5961235 Very well. Next challenge. Prove you are Andrew Wiles.

>>	None !JSN8X5.Us. Sun Aug 11 02:15:54 2013 No.5961246 >>5961241 Hello! Or you could ask a legitimate question :) Amusing though!

>>	Anonymous Sun Aug 11 02:17:54 2013 No.5961248 File: 77 KB, 937x960, 1335817197881.jpg [View same] [iqdb] [saucenao] [google] Alright genius, try this shit.

>>	None !JSN8X5.Us. Sun Aug 11 02:21:24 2013 No.5961252 >>5961248 Hello! I don't know if I could get that correct, even if it wasn't a trick question. :) Best!

>>	Anonymous Sun Aug 11 02:23:53 2013 No.5961259 File: 3 KB, 297x87, expression.png [View same] [iqdb] [saucenao] [google] What is this

>>	Anonymous Sun Aug 11 02:24:53 2013 No.5961261 >>5961259 Oh, yeah <div class="math">\mathbb{N}_+[n]={1,2,...,n}</div>

>>	None !JSN8X5.Us. Sun Aug 11 02:25:53 2013 No.5961264 >>5961259 Hello! I have no idea what N^+[n] means. Perhaps sets of cardinality n? Best!

Anonymous Sun Aug 11 02:39:23 2013 No.5961279

>>5961248
The probability of a correct answer can only be calculated based on the distribution of correct to incorrect answers and a sample size of responses.

Since this isn’t stated anywhere, we will never know. We can’t assume there is only one correct choice or that the probability is simply 50% (right or wrong).

For example:
Say you have 6 apples and 4 oranges. What is the probability you pick an apple at random from these 10 objects? This is simple to calculate because you know the distribution of objects.

Now if I gave you a bag of 10 apples and oranges, without knowing the distribution, it is impossible to tell the probability of picking an apple at random, but it is somewhere between 10 and 100%, I promise.

Similarly if I gave you a bag of 6 apples and an unknown number of oranges, you wouldn’t be able to calculate a probability because you don’t know the total number of objects in the bag.

Now if I give you a bag of apples and oranges and you don’t know how many total objects are in the bag or how many of each, it is just like asking the original question. We don’t know the distribution of the answers, so we can’t calculate a probability.

There is insufficient information to answer this question as written. It doesn’t matter what A,B,C,D represent.

Now if you make a bunch of assumptions, you may be able to narrow down to a choice of the given solutions.

>>	Anonymous Sun Aug 11 02:41:54 2013 No.5961283 Is there any geometric intuition for function spaces?

None !JSN8X5.Us. Sun Aug 11 02:43:23 2013 No.5961285

>>5961283

Hello!

Phew, I was starting to wonder if I could answer anything asked!

There is tons of intuition. Do you mind being more specific though? Rings of continuous functions on a topological space, sections of a bundle, holomorphic functions, the coordinate ring of a variety, etc?

Let me know! :)

>>	Anonymous Sun Aug 11 02:50:23 2013 No.5961292 >>5961285 Thanks for the reply! > Rings of continuous functions on a topological space This actually

>>	Anonymous Sun Aug 11 02:58:52 2013 No.5961298 How annoying. I've often got math questions that I can't answer, but at the moment have none.

>>	Anonymous Sun Aug 11 03:03:53 2013 No.5961304 What are your thoughts on finitism?

>>	Anonymous Sun Aug 11 03:09:22 2013 No.5961307 Is there a decent way to reverse a taylor series back to its original function?

>>	Anonymous Sun Aug 11 03:11:23 2013 No.5961310 How do I integrate e^-t^2?

>>	Anonymous Sun Aug 11 03:20:22 2013 No.5961316 Not a mathfag here.. What are the goals of PDE theory in general?

>>	Anonymous Sun Aug 11 03:23:52 2013 No.5961319 >>5961316 How heat evolves through a system is described through PDEs, if that helps give you a visual. Also, advanced weather patterns.

>>	Anonymous Sun Aug 11 03:27:54 2013 No.5961322 >>5961319 I mean not the applications part. I mean what are the goals for the mathematician (things like uniqueness, existence, stability, etc)

None !JSN8X5.Us. Sun Aug 11 03:28:54 2013 No.5961323

>>5961292

Hello!

Ok, so I probably should have asked you one further question: do you want to know the geometric intuition of what the ring of continuous functions tells you about the space they are defined on, or what is the geometric intuition fro the topology on function spaces?

I am relatively sure you meant the first, so let me just jump into this.

In absolute generality, whenever you study the set of functions from one object to another, you gain information about both objects involved. This is a tenet of modern mathematics (see Yoneda's lemma for more information). Thus, one can immediately say that the ring of continuous functions should tell us something.

Now, if you're asking me specifically, give me an honest to god example of how the ring C(X,R) gives me geometric information about X--that's a little tougher. An example of how studying C(X,R) can tell you specific information are things along the lines of the following:

1. If X is a metric space, then X is compact if and only if every element of C(X,R) is bounded.

2. X is connected if and only if every locally constant element of C(X,R) is constant, etc.

the list goes on. Basically, think about examining C(X,R) like viewing the shadow of X formed by a light shining on R. You are "throwing" X against a specific space, and seeing what pops off--hopefully telling us something. It should remind you of being at CERN--you're smashing partcicles (spaces) together, and trying to understand the particles by the reaction.

Now, if you were more interested in the algebraic properties of C(X,R), then your best bet is to restrict yourself to looking at compact Hausdorff spaces. Then, C(X,R) actually completely determines X! In particular, you can identify X with MaxSpec(C(X,R)) (the space of maximal ideals)!

That was a very poorly worded response--I faltered. If there is an aspect of what I said that you'd like explained more, or I missed something (maybe your whole question!) please let me know!

>>	None !JSN8X5.Us. Sun Aug 11 03:29:53 2013 No.5961326 >>5961298 Hello! Think real hard--I'm sure you've got one! Best!

None !JSN8X5.Us. Sun Aug 11 03:32:23 2013 No.5961330

>>5961304

Hello!

To be frank with you, I don't have many. It's actually been a rare occurrence in my time in academia to encounter working mathematicians talking of philosophy of math.

That said, at the risk of putting me out of a (future) job, I would have to reject the hypothesis. I think it's a logical idea, considering how the human mind processes the world, but it just doesn't actually have much bearing on my day-to-day life.

Sorry I couldn't give a better answer!

>>	Anonymous Sun Aug 11 03:32:24 2013 No.5961331 >>5961323 Topology seems relatively easy compared to some other disciplines.

None !JSN8X5.Us. Sun Aug 11 03:34:53 2013 No.5961335

>>5961322

Hello!

Let me preface this by saying that I am an amateur PDE theorist at absolute best (I had to learn a bit for a complex geometry course). With that being said, you have hit the nail on the head. Simply put, existence and uniqueness are the most important concepts to a working mathematician. A lot of the methods to achieve these goals attempt to find "bad" solutions to "more general" problems, and then try to show that secretly you've found a "good" solution to your actual problem.

I feel as though I may not have answered your question entirely. If so, please let me know!

None !JSN8X5.Us. Sun Aug 11 03:36:53 2013 No.5961336

>>5961331

Hello!

Absolutely not true! Modern algebraic topology is some of the most brutal, abstract, soul-wrenching mathematics that there is. Try googling homotopy theory for a start :)

That said, Point-set topology, which is what most people are exposed to as an undergraduate is relatively easy. It's a lot of definitions, and a lot of pathologies--but you get the hang of it pretty quick. It's an indispensable language for a working mathematician though, so its ease might be an illusion propagated by the shear number of people who are comfortable with it--because they have to be!

Best!

Anonymous Sun Aug 11 03:41:53 2013 No.5961342

>>5961336

My mind works different from a lot of mathematicians, though. I used to struggle with math, and I made myself master it and now I'm about to finish up my undergrad in mathematics with option in finance. I've developed a unique, if sometimes flawed approach to math out of necessity.

Praticing my GRE so I can get into colombia financial engineering at the moment.

>>	None !JSN8X5.Us. Sun Aug 11 03:44:53 2013 No.5961345 >>5961342 Hello! That may be true. But, if you are able to study modern topology, then I think you're calling might not be in finance. Best!

>>	None !JSN8X5.Us. Sun Aug 11 03:45:52 2013 No.5961346 >>5961345 Your* :)

>>	Anonymous Sun Aug 11 03:48:53 2013 No.5961350 >>5961345 Thanks :) It's not typical finance, though. It's basically just throwing as much mathematics at financial patterns and doing one's best to predict behavior and alter it.

>>	None !JSN8X5.Us. Sun Aug 11 03:51:53 2013 No.5961352 >>5961350 Hello! I have no understanding of finance, so I'll just have to take your word for it! Good luck getting into Colombia!

>>	Anonymous Sun Aug 11 03:53:53 2013 No.5961355 >>5961252 Great Scott, you're an idiot! Are you kindergarten arithmetic teacher? There's self reference, which makes it nonsensical.

>>	Anonymous Sun Aug 11 03:57:23 2013 No.5961359 >>5961323 thank you so much!

>>	None !JSN8X5.Us. Sun Aug 11 03:57:53 2013 No.5961360 >>5961355 Hello! Yes, that sounds about right! Best!

>>	None !JSN8X5.Us. Sun Aug 11 03:58:53 2013 No.5961361 >>5961359 Hello! You're very welcome! Don't hesitate to ask any other questions!

>>	Anonymous Sun Aug 11 03:59:22 2013 No.5961362 Say we have some graphic on x-metric system. And we want to know it's function. So there should be at least some theory, that works on such problems, right?

>>	Anonymous Sun Aug 11 04:00:54 2013 No.5961363 >>5961201 What do you think will be the next big discovery found by maths that will be applied to a current unknown?

>>	Anonymous Sun Aug 11 04:01:23 2013 No.5961364 Is every abelian group the additive group of some ring?

None !JSN8X5.Us. Sun Aug 11 04:03:23 2013 No.5961367

>>5961304

Hello!

Hmm, this is a tricky question. I assume you mean, "if someone gave you a taylor series, is there an easy way to recognize it as a combination of elementary functions"? I feel like when phrased that way, it's basically a matter of memorizing the Taylor series for your favorite functions, and trying to match yours to derivatives/substitutions/integrations/powers there of.

So, to sum up--no, not that I know of.

Sorry!

None !JSN8X5.Us. Sun Aug 11 04:06:24 2013 No.5961371

>>5961364

Hello!

Fantastic question! The answer is no. Commutative unital rings are nothing more than commutative Z-algebras. The coproduct in the category of Z-algebras is tensoring over Z. In particuluar, if R is any ring, then R tensored with itself over R (with Z coefficients) should be nonzero. Thinking differently, the multiplication map of the ring is a Z-bilinear map RxR-->R, and so there should be at least one nonzero such map, and so R tensored with itself with Z-coefficients should be nonzero. That said, since Q/Z is both divisible and totally torsion over Z, it's not hard to see that (Q/Z) tensored with itself with Z-oefficients is zero. So, the abelian group structure on Q/Z does not appear as the underlying group structure of any commutative unital ring.

I hope that helps!

>>	None !JSN8X5.Us. Sun Aug 11 04:07:24 2013 No.5961372 >>5961362 Hello! I am not entirely sure what you mean. What is a graphic and what is a x-metric system? Thanks!

Anonymous Sun Aug 11 04:07:52 2013 No.5961373

>>5961330
Actually I was wondering about the relevance of mathematical philosophy in contemporary mathematics. I'm going to be studying more applied mathematics in grad school but I find myself drawn to things like mathematical logic. It seems to me that most people treat it as something that has been mostly worked out in the past and not to be worried about anymore. How true is this? And why did my algebraic topology prof call category theory a non-theory? I think it's pretty elegant. Am I doomed to study branches of math which are seen as irrelevant by 90% of mathematicians?

>>	None !JSN8X5.Us. Sun Aug 11 04:08:22 2013 No.5961374 >>5961363 Hello! I am not entirely sure what you mean here? Do you mean for me to speculate as to what the next big application of math might be--maybe the application of a subject that right now seems inapplicable? Thanks!

>>	Anonymous Sun Aug 11 04:09:23 2013 No.5961375 >>5961371 Damn, you really know your stuff. Are you a grad student / above?

>>	Anonymous Sun Aug 11 04:11:52 2013 No.5961378 >>5961372 Graph of the function and system of x axes. Like Cartesian coordinate system, except in x dimensions. X is real.

None !JSN8X5.Us. Sun Aug 11 04:12:53 2013 No.5961379

>>5961373

Hello!

Interesting question! I think the right analogy is this: physicists (stereotypically!) don't care about rigor in mathematics, because that is not their aim. They know what they want to do, and they use the tools that help them do that, not needing to know how the tools were built. I think it's the same with mathematics and mathematical philosophy (mind you, mathematical logic is not the same thing--model theory, for example, is a super in vogue thing right now, and is logic).

I don't know why your professor would call category theory a "non-theory". If I had to guess, it's because, a lot like set-theory, category theory is something that most people use as a tool, not wanting to ever study it in its own right. People generally learn just as much as they need to know, and no more. Of course, there is a rich and beautiful subject of category theory, and knowing more always helps you, but I think that it's just gotten that brand (although I think it's changing!) as being a "tool subject" instead of a "content subject".

I hope that helps!

>>	None !JSN8X5.Us. Sun Aug 11 04:13:52 2013 No.5961380 >>5961375 Hello! Thank you--I appreciate the comment! I just graduated undergrad--I will be starting graduate school this fall! Best!

>>	Anonymous Sun Aug 11 04:14:52 2013 No.5961381 >>5961374 Yes speculate, is there anything that you or your peers are working on ? Like a link between quantum mechanics and General Relativity for example.

>>	None !JSN8X5.Us. Sun Aug 11 04:15:24 2013 No.5961382 >>5961378 Hello! I deeply apologize, but I still don't understand. Do you mean things like considering the real numbers to the 3/2 power? Sorry!

None !JSN8X5.Us. Sun Aug 11 04:17:24 2013 No.5961384

>>5961381

Hello!

I am probably the last person that would know this. Firstly, I am only about to enter graduate school, so I don't have anything that I'm working on. Secondly, my interests are pretty diametrically opposed to applications.

That said, I have a topologist friend, who often talks about TQFT (see here: http://en.wikipedia.org/wiki/Topological_quantum_field_theory)) which seems very sexy, and application based. That might be old hat though.

Sorry I couldn't help more!

Anonymous Sun Aug 11 04:21:53 2013 No.5961387

>>5961382
Nah. Well, say, we have some function, equation of which we don't know, for example, using Cartisian coordinate system in three dimensions to visualize it. And is there generally a way to learn it's equation? Or at least some theory, that is working on it.

None !JSN8X5.Us. Sun Aug 11 04:23:23 2013 No.5961389

>>5961387

Hello!

Ah, ok. So, if someone gave you the graph of a function, is there a way to recover the function? The answer is definitively yes. Namely, suppose that you had a function of two variables f(x,y). Then, it's graph is just (x,y,f(x,y)). So, if I gave you the graph G={(x,y,z):f(x,y)=z} then you can recover f by setting f(x,y) to be the unique z such that (x,y,z) is in G.

I hope that helps!

>>	Anonymous Sun Aug 11 04:28:53 2013 No.5961391 >>5961384 Thats OK thank you very much for the response. Currently studying spatial sciences degree but really interested in new advancements in maths. Must be a topologist thing lol.

>>	None !JSN8X5.Us. Sun Aug 11 04:29:23 2013 No.5961392 >>5961391 Hello! Good on you! Maybe once you make an advance, you can come on here and tell us about it! Best of luck!

>>	Anonymous Sun Aug 11 04:30:24 2013 No.5961393 Basic linear algebra question that I've never had resolved: If in a vector space, you have a set of vectors which are linearly independent, does there necessarily exist an inner product structure where the vectors are mutually orthogonal?

None !JSN8X5.Us. Sun Aug 11 04:35:52 2013 No.5961397

>>5961393

Hello!

Fantastic question! The answer is definitively yes.

Suppose that <,> is any inner product on V, and let T:V-->V be in GL(V) (i.e. be an automorphism). Then, the new inner product (,) defined by (x,y)=<Tx,Ty> is still an inner product, right? So, begin by identifying V with R^n (or C^n, or whatever). Then, take your linearly independent set {v_1,...,v_m}. Extend it to a basis {v_1,...,v_n} of R^n. Then, define T by T(v_i)=e_i, where {e_1,...,e_n} is the standard basis for R^n. Let <,> be the standard inner product on R^n and consider, as before, (x,y):=<Tx,Ty>. Then, (v_i,v_j)=<e_i,e_j>=delta_{i,j}

I hope that helps!

>>	Anonymous Sun Aug 11 04:41:54 2013 No.5961403 where did you go to university? and should i be taking differential geometry before my senior year? what about set theory?

>>	Anonymous Sun Aug 11 04:42:22 2013 No.5961404 >>5961397 Thanks for the response! Just to make sure, similar reasoning applies for infinite dimensional vector spaces, right?

None !JSN8X5.Us. Sun Aug 11 04:47:23 2013 No.5961406

>>5961403

Hello!

I would prefer not to say :)

It all depends on what you're ultimate goals/interests are/what differential geometry means. If the course is just on curves and surfaces, it's probably not bad to take, but you can probably learn that on your own. What you really want to take, if you're very serious about math, is some kind of differential geometry/manifolds course that uses any of the books of John M Lee.

As for set theory, it once again depends on what your goals/interests are. My gut reaction is to say no. Set theory is really just a tool, and if you're a mathematician working in any of the more standard fields, you'll pick up anything you'll need along the way. For example, if you wanted to learn enough set theory to be 99.9% sure you'll know everything you'll need to, you'd probably get away with reading the first chapter of Munkres, and these following expositions of Pete L clark:

http://math.uga.edu/~pete/settheorypart1.pdf

http://math.uga.edu/~pete/settheorypart2.pdf

http://math.uga.edu/~pete/settheorypart3.pdf

http://math.uga.edu/~pete/settheorypart4.pdf

Once again though, I might be able to respond more intelligently if you give me some background: interests, goals, and content of courses.

Best!

None !JSN8X5.Us. Sun Aug 11 04:50:22 2013 No.5961407

>>5961404

Hello!

Haha, oh god, I was worrying you were going to ask this. I am fairly sure that you can extend this to countable dimensional spaces over R by working in l^2, but for uncountable dimension: ehhh. I am not sure. I'd have to think about it more.

Sorry I wasn't able to answer better!

Anonymous Sun Aug 11 04:52:53 2013 No.5961408

>>5961406
i'm doing an undergrad math/physics double major and i'm planning out my courses. they don't offer much about the course, but it seems to be mostly curves and surfaces. so far i've only been up to calc 3 which i'm retaking when i enter uni, and i don't think i could learn all that on my own

>>	Anonymous Sun Aug 11 04:54:22 2013 No.5961409 >>5961406 >uga >math UGA didn't even have an engineering department like 3 years ago

None !JSN8X5.Us. Sun Aug 11 04:55:22 2013 No.5961411

>>5961408

Hello!

Where are YOU going to school? :)

With what you've told me, taking diff geo actually sounds like a good idea. You'll need to take the more serious version, if you go to the higher levels of either math or physics, but learning the basics first always helps! Set theory, I would shy away from now.

Best!

>>	Anonymous Sun Aug 11 04:55:22 2013 No.5961412 >>5961409 But now is has. And that's only thing that matters.

>>	None !JSN8X5.Us. Sun Aug 11 04:56:22 2013 No.5961414 >>5961409 >http://math.uga.edu/~pete/settheorypart1.pdf Hello! Yeah, UGA really isn't on my radar mathematically ,save Pete L Clark. He's pretty fantastic. Best!

>>	Anonymous Sun Aug 11 05:02:23 2013 No.5961416 >>5961411 NJIT it was my safety but life happens and it's cheap at least thanks for the info

>>	Anonymous Sun Aug 11 05:04:52 2013 No.5961418 Heh. I like you. You seem so upbeat and polite.

>>	None !JSN8X5.Us. Sun Aug 11 05:05:23 2013 No.5961420 >>5961416 Hello! I'm sure you'll do great :) Best of luck!

>>	None !JSN8X5.Us. Sun Aug 11 05:06:52 2013 No.5961421 >>5961418 Hello! Thanks! I just like talking about math :) Best!

>>	Anonymous Sun Aug 11 05:09:53 2013 No.5961423 who are you?

>>	None !JSN8X5.Us. Sun Aug 11 05:10:53 2013 No.5961424 >>5961423 Hello! Just some guy! Best!

>>	Anonymous Sun Aug 11 05:14:54 2013 No.5961428 >>5961248 >>5961279 While all you're saying is true it's not really relevant. The answer is simple: All the answers are wrong. You can pretty easily check if any given answer would fit the requirements of the question and none of them do.

>>	Anonymous Sun Aug 11 05:56:52 2013 No.5961446 Whats the most general method to solve deferential equations? There has to be a better method that what you learn in 2nd year.

>>	Anonymous Sun Aug 11 06:20:23 2013 No.5961463 >>5961201 What's the simplest equation for calculating the area of a triangle marked out on the surface of a sphere.

>>	Anonymous Sun Aug 11 06:41:53 2013 No.5961479 That's not QUITE about mathematics, but, uhm, are you a virgin? If not, calculate please the quantity of your coital mates.

Anonymous Sun Aug 11 06:42:53 2013 No.5961480

I'm taking the GRE Subject test in mathematics soon to apply for graduate school in math. What is the best way to prepare for this exam? I've completed a bachelors degree in mathematics, and I'm well experienced with most of the topics that the exams covers (with the exception of probability).

>>	Anonymous Sun Aug 11 07:30:47 2013 No.5961509 I heard there are numerical systems in which 0.999... doesn't equal 1. Doesn't that violate the rules of math? I thought 0.999... = 1 was one of the fundamental axioms. Please explain.

>>	Anonymous Sun Aug 11 07:45:48 2013 No.5961521 >>5961509 You heard wrong. With any base there are no numbers like 0.xyz(9), only 0.xy[z+1]. It's an important property of <span class="math">a_pq^p \le a_pq^p + q^p[/spoiler]. Now go where you were headed, stalker.

>>	Anonymous Sun Aug 11 07:51:49 2013 No.5961530 >>5961521 What about p-adics? Does 0.999... converge in the p-adics and what is its limit?

>>	Anonymous Sun Aug 11 08:07:48 2013 No.5961544 >>5961530 The 10-adics (which are not p-adic as 10 is not prime) do not contain an element 0.999... They do contain ...999, though, which is -1. For 3-adics, see: http://upload.wikimedia.org/wikipedia/commons/5/59/4adic_333.svg

>>	Anonymous Sun Aug 11 08:09:48 2013 No.5961548 why the fuck are you doing this?

>>	Anonymous Sun Aug 11 08:31:47 2013 No.5961570 File: 103 KB, 1200x960, 1355847643301.jpg [View same] [iqdb] [saucenao] [google] You should be able to solve this. Well, /jp/ did.

>>	Anonymous Sun Aug 11 08:59:18 2013 No.5961590 >>5961570 i got 25.6cm2

>>	Anonymous Sun Aug 11 09:03:48 2013 No.5961594 >>5961570 28

>>	Anonymous Sun Aug 11 09:04:19 2013 No.5961596 Sup, OP. Will RSA/discrete log be cracked within the year? Is elliptical curve crypto safe from quantum computers?

>>	Anonymous Sun Aug 11 09:15:17 2013 No.5961605 >>5961570 >/jp/ did Really? Link to the archive?

>>	Anonymous Sun Aug 11 09:25:49 2013 No.5961610 File: 78 KB, 720x960, huehuehue.jpg [View same] [iqdb] [saucenao] [google] >>5961570 32+16-20 duh

Anonymous Sun Aug 11 09:38:49 2013 No.5961622

For my graduate degree in mathematics, the college i'm planning to go to offers various career paths like algebra/set theory, geometry, analysis, applied math, etc...

I was wandering: is geometry the best curriculum to go into mathematical physics and the study of stuff like QFT, QG, GR, etc... ?

>>	Anonymous Sun Aug 11 09:46:17 2013 No.5961623 >>5961622 (Differential) Geometry will definitely be helpful with General Relativity. For the others, you should also consider Group Theory and Algebra.

None !JSN8X5.Us. Sun Aug 11 13:39:18 2013 No.5961927

>>5961446

Hello!

Let me preface this by saying that I am not the person that would know--I know very little of differential equations, and what I do know, one could call "theoretical PDEs".

That said, I don't actually think that's true. As far as I know, when it really gets right down to it, we don't know how to solve differential equations in any reasonable, algorithmic way. I doubt that if you asked someone who was a PhD in ODEs and a relatively talented undergrad who has just taken the course, there would be much difference in practical solving ability. This is all speculation though!

Best!

None !JSN8X5.Us. Sun Aug 11 13:49:47 2013 No.5961950

>>5961480

Hello!

This is a fantastic question! To be honest with you, I am not sure. I took the subject exam twice, both times not really studying beforehand. I got an OK score the first time, and a relatively good score the second time. The unfortunate thing about the subject GRE is that your score is not really a function of your mathematical knowledge. No, much like the SATs the subject GRE is often times a function of how much of the test have you learned. The subject GRE has a certain cadence, and style, that if one learns one is much more likely to succeed. So, if you wanted to make sure to get a good score I would suggest the following three things:

1. Practice the exams many times. Buy the practice books, download past exams offline, etc. Always practice in simulated test environments.

2. When you have done this, fill in any gaps that you may have. For example, there are very popular questions that are asked on the subject GRE many years, but you may have forgotten the formula. For example, the quickest way to, say, find the distance from a point to a line. How to do Lagrange multipliers. For me, honestly, it was the calculus and probability that killed me. The algebra, topology, and analysis were trivial.

3. Take it multiple times. Seriously. If you only take it once, there is a good chance that you'll get a subpar score. Even though it makes no sense, this score will factor greatly into your admission into some schools. I had many interesting discussions with the graduated chair of my undergraduate institution [a friend] about the intricacies and quirks of graduate admission. There are many schools that use the GREs as the SATs--they sort you into initial piles based on your scores. To guarantee that you GRE score will not be a hinderance to you (I'm literally just saying neutral, not positive) you would probably want to score around an 800. This varies year to year, and school to school to.

Anyways, good luck! I hated, the GRE, but it's worth it :)

None !JSN8X5.Us. Sun Aug 11 13:52:18 2013 No.5961955

>>5961622

Hello!

Once again, as I have said multiple times in this thread, I am probably far from the most qualified person to answer this question. I know almost nothing of physics (I barely got an A in Physics 1 in college!). That said, if you are interested in hardcore theoretical physics, then I would say: probably. Geometry seems to be the language of modern physics (and mathematics for that matter!). That said, having a healthy knowledge of advanced analysis topics is obviously indispensable.

I would talk to your graduate advisors!

Best!

>>	None !JSN8X5.Us. Sun Aug 11 13:54:17 2013 No.5961963 >>5961463 Hello! Interesting question. See here: http://mathworld.wolfram.com/SphericalTriangle.html I hope that helps!

>>	Anonymous Sun Aug 11 13:55:47 2013 No.5961966 > Hello > I don't know > Hope that helps > > Hello > I'm not sure > Best of luck > > Hello > I'm not a specialist in field, but... > Sorry I'd like to have at least some PhD in diffeqs on /sci.

>>	Anonymous Sun Aug 11 13:56:48 2013 No.5961969 engineering here; i failed my physics but did really good in my mathematics exam. it was horrible and i might as well not have sat the exam for physics. how do i into physics??

>>	None !JSN8X5.Us. Sun Aug 11 13:56:48 2013 No.5961970 >>5961548 Hello! What do you mean? Why wouldn't I do this? Best!

None !JSN8X5.Us. Sun Aug 11 13:58:17 2013 No.5961973

>>5961966

Hello!

Yes, that would be nice! Differential equations and probability theory are the two areas of math that I feel most lacking, and they are two of the most common topics that people want to know about. I wish I could help more!

Sorry!

>>	Anonymous Sun Aug 11 14:01:48 2013 No.5961985 >>5961970 what do you gain from it? is it just for fun?

None !JSN8X5.Us. Sun Aug 11 14:01:49 2013 No.5961987

>>5961596

Hello!

I know someone that knows a bit about this stuff. My impression from what they said, is that the answer would be no. That while, in theory, quantum computers have the ability to do insane things, the actual sophistication of quantum computers in this day-and-age is really quite low. That said, I really don't know.

Take a look at this thread, it looks promising:

http://stackoverflow.com/questions/2768807/quantum-computing-and-encryption-breaking

Best!

Anonymous Sun Aug 11 14:02:18 2013 No.5961990

>>5961201
Hello knowledgable friend.
Wanted to ask you, is there any specific rational reason why non-standard analysis is still "non-standard"? I mean, infinitesimals and infinity are so intuitive to all of us and so, with the transfer principle and the consistency of the hyper reals, is there even a reason to not use it? There is a reason why Euler, Leibniz and all the others before Cauchy used infinitesimals with no hesitation and still found marvelous results. That was a hint of its consistency and of its power and its appeal to our intuition.
So, in short, why not make non-standard analysis standard and have better applied and pure mathematicians for the future?

None !JSN8X5.Us. Sun Aug 11 14:04:18 2013 No.5961992

>>5961985

Hello!

I guess that's a valid question. Yes, I do it for fun. I also do it because I legitimately like answering people about math, and getting (hopefully!) them somewhat excited about the subject. When I was just starting math I would have loved to have someone (even someone as lowly as a recent bachelors graduate) to ask questions to, about intuition, etc. In fact, I was able to meet some people at my school that were able to fulfill this. In some way, this is my electronic way of paying it forward.

Best!

>>	Anonymous Sun Aug 11 14:05:48 2013 No.5961994 >>5961992 I'm the guy above you. I love you for this. Thanks for the selfless generous act.

None !JSN8X5.Us. Sun Aug 11 14:11:47 2013 No.5962006

>>5961990

Hello!

Super interesting question! I do believe that there are others, like you, who are in disbelief that non-standard analysis is not more prevalent in undergraduate mathematics (Terry Tao comes to mind--you're in good company!).

If I had to guess, I would say that perhaps the lagging would be due to the two following things:

1. Tradition. Academics is very rigidly routed in its past, at least when it comes to the teaching of its core subjects like calculus and analysis. It would take a herculean effort to convince schools that they should switch from the standard techniques of analysis to that of non-standard analysis. In particular, I think you'd have to go all the way to the high school level (I don't think colleges would be willing to teach something in direct contrast to what kids learned in high school). I don't think this is ever likely to happen, purely for the reason that not many high school teachers are familiar with the material.

2. When it gets right down to it, to make non-standard analysis rigorous, one needs some serious machinery of point-set topology (ultrafilters, etc.). It just seems like while the idea of the hyperreals are intuitive, and it makes sense that, say, f'(x)=(f(x+e)-f(x))/e, that the actual rigorization of these ideas actually makes the final product less intuitive/harder to work with than any of the standard limit based curricula.

I hope that helps!

>>	None !JSN8X5.Us. Sun Aug 11 14:13:47 2013 No.5962009 >>5961994 Hello! Thank you for those kind words! As I said before, it's not entirely selfless--I really do enjoy doing this. Best

>>	Anonymous Sun Aug 11 14:16:47 2013 No.5962013 >>5961992 well that's really nice of you then

Anonymous Sun Aug 11 14:21:48 2013 No.5962021

This is more of a software question. But it could be a math question.

Say I'm using excell. I have several hundred boards of random lengths. I want to put these boards end to end and have them reach as close to a certain length as possible.

Do you know how I could figure out which boards to use with some excell function?

Anonymous Sun Aug 11 14:23:49 2013 No.5962024

Do you think we'll crack diffeqs this lifetime? I mean, come on, we created algorithms for LOTS of equation types, and all of them were considered "unalgorithmable" at some point. Would that be a big contribution to science (specifically quantum field theories and quantum computer sciences)?

>>	None !JSN8X5.Us. Sun Aug 11 14:27:17 2013 No.5962027 >>5962021 Hello! I am not quite sure I understand you. The boards are random, but you are deciding the boards? Sorry I don't understand!

Anonymous Sun Aug 11 14:28:17 2013 No.5962030

>>5962006
Thanks a lot for the answer.
Second and last question, now.
Is complex analysis the best we can do in analysis? I mean, isn't there a larger metric space containing C that has greater potential for things like analytic number theory and really, just analysis in general? I do know about quaternions, but they just don't seem to have the same potential with their lack of commutativity. Also, if not, is there a reason for that like maybe the fundamental theorem of algebra shows that they're all we'll ever really need?
Thanks in advance, once again. :)

None !JSN8X5.Us. Sun Aug 11 14:28:49 2013 No.5962031

>>5962024

Hello!

The problem is that finding exact solutions to differential equations is not anything an algorithm, or at least not a numerical algorithm could do. It seems plausible that with the power of future computing, and the endless work in the field, that we may be able to come up with a fairly impressive numerical algorithm to approximate the solutions to large classes of differential equations. But, as to your actual question, no, I don't think so.

Best!

Anonymous Sun Aug 11 14:34:05 2013 No.5962038

>>5961201
Based on information from Harper's Index, 37 out of 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of 100 adult Americans who did attend college, 47 claim that they believe in extraterrestrials. Does this indicate the proportion of adult Americans that attended college and believe in extraterrestrials is higher than the proportion that did not attend college? (probability of a type 1 error=0.01)

None !JSN8X5.Us. Sun Aug 11 14:37:36 2013 No.5962042

>>5962030

Hello!

This is a fantastic question!

The answer is, at least in one interpretation of your question, no. Namely, what makes the complex numbers such a fruitful place to carry out analysis in a way that mimics that on R, is the fact that C is both a finite-dimensional R-space (so inherits nice topological properties of R) and is at the same time a field (in a compatible way). I don't know how much algebra you know, but C is an algebraic closure of R, and so up to isomorphism all finite extensions of R sit between R and C. But, since [C:R]=2, any intermediate extension must be R or C itself. Thus, said differently, if we want to mimic analysis in R, then we're pretty much stuck with R or C. Even if we wanted to drop a condition. Perhaps we want a finite-dimensional R-space which is just a division ring (no commutativity), or even just a non-associative division algebra (not commutative or associative) it turns out (somewhat amazingly) that our choices are still limited. Up to isomorphism, the only finite dimensional division algebras over R are R itself, C, the quaternions, and the octonions. Only the first two of these, for obvious reasons, are fit to do analysis over R.

I'm not entirely sure if the fundamental theorem of algebra really shows that it's all we ever need. That said, from the above there is reasonable reason to believe that we are stuck with it. And, all things considered, it's not so bad! It's one of the nicest fields imaginable (characteristic zero and algebraically closed), and so its algebraic properties, along with the compatibility these algebraic properties have with their nice topological properties, make them a very nice space to work in.

I hope that helps!

Anonymous Sun Aug 11 14:38:35 2013 No.5962044

could you answer 2 questions?

1. how do i actually learn maths? there are times when im reading it i spend 10 to 20 minutes on 1 page, it feels like im doing it wrong.

2. could you explain adjoints of operator? im confused by them, why someone would even bother defining them.

None !JSN8X5.Us. Sun Aug 11 14:59:06 2013 No.5962068

>>5962044

Hello!

Great question, and of course I can (try and) answer them!

1. This, of course, is the million dollar question. Different things work for different people. For me, what works best is to try and approach everything like it's a challenge. I will often times try to skim the contents of a chapter in a book, and then try to develop the ideas and proofs on my own. I will always try to rephrase proofs, definitions, etc. in my own words. Not only do I become more comfortable with "my" definitions, but the personal touch forces you to think critically, which in turn helps you understand the material more. Also, talking about math. The more you talk about math, the better you get. Math is, above all, a language, and like any language, you can never become comfortable until you spend time in the company of those fluent. Go online, read about the material from different sources, try to talk/teach it to others, do problems that interest you, etc.

2. The adjoint of an operator is actually a pretty natural object. Namely, when one discusses the adjoint of an operator, we've implicitly fixed an inner product space (V,<-,->) as well as the operator T in End(V). Then, put simply the adjoint of T, let's call it T*, is just another operator in End(V) that "plays nicely" with respect to both T and the inner product <-,->. To give a simple example to motivate why one might want this nice property, consider the following annoying situation: you want to calculate <Tx,y>+<x,v>. Now, I don't know about you, but I have the most obsessive desire to want to use the bilinearity of <-,-> and "add the x's" in the left entry. Unfortunately though, I don't have two x's, I have an x and a T. But, if there was some kind of way to "shift" T over to the other entry, I could be golden.

None !JSN8X5.Us. Sun Aug 11 15:00:07 2013 No.5962071

>>5962070

(cont.)

Let me last say, that a very common trick in linear algebra is to try and prove results using an inner product. For example, suppose that you wanted to prove the following property: if A is a Hermitian matrix such that A^2x=0, then A^x=0. This looks hard a priori, no (well, if you didn't know the spectral theorem!). That said, if we phrase this in terms of inner products its trivial.

Ax=0 if and only if <Ax,Ax>=0 which is true if and only if <x,A*Ax>=0. But, A*=A, so that A*A=A^2, So, <x,A*Ax>=<x,A^2x>=<x,0>=0.

I hope this gives you a flavor of the idea!

None !JSN8X5.Us. Sun Aug 11 15:00:36 2013 No.5962070

>>5962068

(cont.)

For example, if <Tx,y>=<x,Ty> held, I'd be extremely happy. Of course, this isn't true in general. But, what we might hope is that there is some operator S such that <Tx,y>=<x,Sy> for all x,y in V. This operator will allow one to play patty-cake with the inner product, switching the acted on entry any time one wants. This S, the unique operator (which always does exist [in finite dimensions!]) such that

<Tx,y>=<x,Sy>

for all x,y is the adjoint of T. Namely, S=T*.

Often times, the importance of T* is when it relates in some particularly nice way to T itself. For example, when T=T*, we call T Hermitian, when T=-T* we call T skew-hermitian, and if T*=T^(-1) we call T unitary. All of these properties say that T has a particularly close relationship with an operator that governs how T works with the inner product structure of V, and so it's likely that T will satisfy some nice properties. For example, unitary operators are precisely the isometries of the space: distance preserving maps: those that satisfy ||Tx||=||x|| for all x. Indeed, note that |Tx||=<Tx,Tx> and by definition of the adjoint <Tx,Tx> is equal to <x,T*Tx>. But, T*T=I, so this is equal to <x,x>=||x||. In fact, all of the above examples of operators are special cases of something called normal operators. An operator is normal if it commutes with its adjoint (i.e. T and T* commute). Normal operators satisfy something called the spectral theorem, which says that they are unitarily diagonalizable--a very strong, desirable property. Thus, we see that when an operator does play nicely with its adjoint, it has extraordinarily desirable properties, and so a common technique to prove an operator is nice, is to prove that it relates to its adjoint.

Anonymous Sun Aug 11 15:03:38 2013 No.5962073
File: 424 KB, 450x624, red-dress-red-hair-blue-eyes.png [View same] [iqdb] [saucenao] [google]

I asked the question yesterday about the uses of p-adic numbers in physics, and was relating Q_p to modular arithmetic. Does somebody have this thread at hand, I can't find it.

Also, are the reals and the p-adics somehow the only extensions from the rationals which are (I don't know what the exact condition is) algebraically closed?

@OP: Very great thread!

Every set becomes a ring with symmetric difference as multiplication etc. Is every ring of this form? (probably not.) Which rings are, and then how to find said set.

Calling TQFT an area related to applicatons is stretching the term very much.

Are you interested in random matrices?
Or topological entropy?

Do your function come as tuple with their codomain or what?

>>5961323
>Now, if you were more interested in the algebraic properties of C(X,R), then your best bet is to restrict yourself to looking at compact Hausdorff spaces. Then, C(X,R) actually completely determines X!
No, check out my easy way:
>f \in C(X,R) \implies dom(f)=X
hrhr.

>>5961927
What are your personal favorite heuristics and methods when faces with a differential equation in one variable?

What is your favorite way to view the Fourier transform. It has many extensions in different settings, may they be, for example, groupie or algebraic. What is your canonical way to think about them?

I see lots of people using Melling transforms now to solve problems, but not necessarily in books. Has it always been like this or has that thechnique become hip in the last ten years?

None !JSN8X5.Us. Sun Aug 11 15:20:06 2013 No.5962094

>>5962073

Hello!

Was that the thread I explained the intuition for why one might consider Q_p (the local global principle)?

I think you mean completely valued fields! Well, in some sense they are the only ones. Namely, we obtain the p-adics and the reals by completing Q with respect to a certain set of valuations (the p-adic valuation, and the infinite place). It turns out that these are the ONLY valuations on Q, and so, in a sense, they are the only extensions obtainable by those means.

Every ring is not of that form. All of those rings are Boolean rings, for every x one has that x^2=x. In particular, any non-trivial integral domain will not be of that form. I the converse is not true. But, if you are willing to instead ask the slightly different question "what rings occur as subrings of power sets with symmetric difference and intersection" then the answer is, in fact, Boolean rings. This is the content, in part, of Stone's representation theorem (see here: http://en.wikipedia.org/wiki/Stone's_representation_theorem_for_Boolean_algebras))

I am not interested in either random matrices or topological entropy. That said, I have done neither and so really can't say for sure.

I have no favorite heuristics or methods, to be honest. I have never taken a course in ODEs, and have never had any need to solve an actual ODE in my life!

I think of the Fourier transform much the same way I think of convolution. It is a smoothing technique, meant to transform ill-behaved things into better behaved ones.

When I think of the Mellin transform, I think of like late 1800's analytic number theory (Riemann). I didn't eve know it was a hip thing now. Do you have examples?

Best!

Anonymous Sun Aug 11 15:30:36 2013 No.5962098

I made a thread about it few days ago, nobody solved it yet. I believe noone ever even succeded.
Find expression for this constant in terms of pi, e, gamma, glaisher-kinkelin etc.

\prod\limits_{n=0}^{\infty}\left ( 1+ \frac{1}{n!} \right ) = 7.364308272[/spoiler]

>>	Anonymous Sun Aug 11 15:36:05 2013 No.5962105 >>5962073 Hello! Please, deliver some more pics with this whore. Hope you'll help me!

>>	Anonymous Sun Aug 11 15:37:38 2013 No.5962108 What's your favorite part of math?

Anonymous Sun Aug 11 15:38:06 2013 No.5962112

>Stone's representation theorem
thx.

>I have never taken a course in ODEs, and have never had any need to solve an actual ODE in my life!
Weird. My Master thesis essentially soley consisted of solving one.

If you use forcing to show the independence of a theorem from the axioms, I think what you do is copy and deform the standard model into another model which is constructed so the statement is true/false.
But I don't really get this - if you're not able to proof or disproof the theorem from the standard semantics, wouldn't you have to construct -two- new models to show it's legal that it's true and false and hence independent?

Also, do you even lift?

>>5961330
>To be frank with you, I don't have many. It's actually been a rare occurrence in my time in academia to encounter working mathematicians talking of philosophy of math.
then why study math at all? :P

>>5961990
>I mean, infinitesimals and infinity are so intuitive to all of us
:/

>I didn't eve know it was a hip thing now. Do you have examples?
Just QA forums where people need integrals of number stuff solved. And when I encountered in a modern book on QFTs, I got suspicious.

>>	Anonymous Sun Aug 11 15:38:35 2013 No.5962110 >>5962108 "ath".

>>	Anonymous Sun Aug 11 15:38:35 2013 No.5962111 Can you explain how stacks work? I'm trying to learn modern algebraic geometry, and the jump from schemes to stacks is giving me a bit of a hard time.

>>	None !JSN8X5.Us. Sun Aug 11 15:39:35 2013 No.5962113 >>5962105 Hello! I guess this is what tripcodes are for :) Best!

Anonymous Sun Aug 11 15:39:35 2013 No.5962114

>>5961389
I'm not sure if you're still here, and I'm not the guy that asked the question, but I don't see how this will get you the original function. Or maybe I'm not looking at this question correctly. What exactly do you mean by "recover" the function?

None !JSN8X5.Us. Sun Aug 11 15:41:37 2013 No.5962117

>>5962111

Hello!

Haha! You and me both brother. Do you want to explain stacks to me? :) It's a goal of mine to try and understand them in this upcoming year. I've been trying to read this article:
http://www.cgtp.duke.edu/~drm/PCMI2001/fantechi-stacks.pdf

Sorry I couldn't have been of more help!

Anonymous Sun Aug 11 15:56:06 2013 No.5962126

>>5961201

Hello.

I have apprehension regarding the study of maths. I feel like one could spend many lifetimes learning maths irrelevant to what one might practically be able to put to use given a particular set of research interests.

What mathematics would advise me to have a strong grasp on if I wish to be a proficient pharmacologist. My research areas of interest include epidemiology, drug discovery and its computation approach.

>>	Anonymous Sun Aug 11 15:56:35 2013 No.5962125 >>5962117 Thanks for the reference at least. I will add that to my eternally growing reading list.

>>	Anonymous Sun Aug 11 16:10:36 2013 No.5962138 >>5962113 Have you even considered that it's just a coincidence that we have similar writing styles? What, you think I'm pretending to be you? My god, this guy has Everest level of ego. You mathgeeks are all alike.

Anonymous Sun Aug 11 16:15:06 2013 No.5962147

>>5962114
Yeah, I thought about what it means for a while myself. I guess what he's trying to say is that you just take 2 independent variables (in this case) and search for a formula which will use both of these variables and give you z, that is in respective ordered set with these x and y. Though I still don't get HOW you can do this. Just picking random functions you think should fit and then somehow adjusting them?..

Anonymous Sun Aug 11 16:19:05 2013 No.5962154

>>5961218
Place the line from it's symmetric form to parametric form and label by L(t).
L(t)=(-3,5,1)+t(3,-3,1).
Choose two points (-3,5,1) and (0,2,2) by evaluating L(0) and L(1) respectively.
The other point in the plane is (1,0,2) so we now have three determined points of the planes.
By taking the difference of (1,0,2) and (-3,5,1) and (0,2,2) we obtain the vectors (4,-5,1) and (3,-3,1). By taking the cross product of these two in the proper orientation we obtain the normal vector N=(-2,-1,3).
Thus the plane is represented by P: -2x-y+3z=d for some constant d. plugging in one of the points we find the constant d=4. Thus
P: -2x-y+3z=4 is the implicit form of the plane.

>>	None !JSN8X5.Us. Sun Aug 11 16:28:06 2013 No.5962164 >>5962138 Hello! :) Best!

>>	None !JSN8X5.Us. Sun Aug 11 16:29:36 2013 No.5962166 >>5962147 Hello! It's totally possible that I misunderstood the question (it seems likely since the question seemed trivial). I thought you were asking if you could recover a function f from its graph G. Was that not the case? Best!

>>	Anonymous Sun Aug 11 16:34:06 2013 No.5962170 >>5962166 Well yeah, it's just that this process of finding respective equation seems unclear.

None !JSN8X5.Us. Sun Aug 11 16:40:05 2013 No.5962176

>>5962170

Hello!

We must be having a discrepancy in our meanings. If you have the graph G, then you get the associated function merely by projecting onto the last coordinate. If you're asking "Given the list of values (x,y,f(x,y)) find an EQUATION (like f(x,y)=x^2ycos(xy)+log|xy|-1)" that is not possible, I would posit!

Best!

>>	Anonymous Sun Aug 11 16:45:06 2013 No.5962181 >>5962176 At last. That's what I meant. But is there really no way, even in speculation? Because, again, some time ago it was considered impossible to have negative numbers and then voila - we have so much stuff, that Newton would fall unconscious.

Anonymous Sun Aug 11 16:46:35 2013 No.5962182

Can you give an example of a discrete group G and a Hilbert space H with a linear isometric G-action, such that H is not a Hilbert module, i.e. there exists no Hilbert space V with an isometric linear G-embedding of H into the tensor product V\otimes l^2(G)[/spoiler]?

>>	Anonymous Sun Aug 11 16:50:36 2013 No.5962188 >>5962021 Google knapsack DP

None !JSN8X5.Us. Sun Aug 11 17:07:33 2013 No.5962203

>>5962182

Hello!

I cannot. I had to look up what a Hilbert module is. That type of representation theory is entirely new to me. The only representation theory I feel like I know ok is that of finite groups, a bit of associative algebras, and (compact and classical) Lie groups.

I apologize! W

What is that related to? The only references I could find linked it somehow with K-theory?

Best!

Anonymous Sun Aug 11 17:13:03 2013 No.5962211
File: 97 KB, 1096x310, hilbert modules.png [View same] [iqdb] [saucenao] [google]

>>5962203
Pic related is from "L2-Invariants: Theory and Applications to Geometry and K-Theory" by W. Lück. I was just wondering whether or why the definition makes sense.

>>	Anonymous Sun Aug 11 17:31:02 2013 No.5962229 Why can't the Banach–Tarski paradox be used to cure world hunger?

>>	Anonymous Sun Aug 11 17:34:02 2013 No.5962234 How can i to the power of i be a real number?

Anonymous Sun Aug 11 17:40:33 2013 No.5962239

>>5962211

Not OP here.

So you're wondering whether the definition is actually any different than just asking that V be a unitary representation of G on a Hilbert space, right?

I think that this condition is quite a bit stronger. I'm sorry I can't give an actual example off the top of my head, but the idea is that this definition restrict to representations which are contained inside sufficiently large direct sums of copies of the left-regular representation. For some groups, studying the left regular representation will tell you pretty much everything there is to know about the representation theory of G. This is the case for example if G is a locally compact (in particular discrete) abelian group, because of Pontryagin duality.

I think you can get an example where this doesn't happen by looking at any non-amenable group, so for example the free group F_2 should work. I'll try to see if I can come up with an actual example.

>>	Anonymous Sun Aug 11 17:55:32 2013 No.5962251 >>5962126 arithmetic and middleschool algebra

>>	Anonymous Sun Aug 11 18:13:06 2013 No.5962276 >>5962182 Potato.

Anonymous Sun Aug 11 23:20:03 2013 No.5962795

>>5962229
Because it involves cutting up ideal balls into very intrincate parts.
"Ideal ball" as in mathematical, not real-world objets.
This is because an ideal ball has an infinite number of points, where as real life objets have a finite number of indivisible atoms.
(Yes I know you can split atoms, but for the sake of this question, let's call the atom the smalles part of "food")
So no, you can't cure world hunger. Bceause in the real world you can't create matter from nothing.

>>	Anonymous Sun Aug 11 23:55:33 2013 No.5962829 >>5961355 This sentence has five words Self-reference does not immediately make something 'nonsensical.'

>>	Anonymous Mon Aug 12 07:19:02 2013 No.5963286 >>5962829 I don't know how to call it more precisely, but in this case it creates infinite loop, which makes it impossible to even read the whole question.

>>	Anonymous Mon Aug 12 07:39:02 2013 No.5963314 >>5961264 N^+[n] is obviously the set of positive semi-definite nxn matrices with natural numbers as entries.

>>	Anonymous Mon Aug 12 07:42:32 2013 No.5963315 What is a good book on p-adic analysis?

>>	Anonymous Mon Aug 12 07:58:27 2013 No.5963325 >>5961570 Not sure if it's actually solvable, but if it is can someone explain how to do it? I'm struggling to find an answer

>>	Anonymous Mon Aug 12 08:03:29 2013 No.5963331 File: 39 KB, 480x480, 954846_565599453496120_71230326_n.jpg [View same] [iqdb] [saucenao] [google] >>5961201 Solve this fuckhole

>>	Anonymous Mon Aug 12 09:06:52 2013 No.5963405 >>5963331 32

>>	Anonymous Mon Aug 12 09:07:53 2013 No.5963406 >>5963331 38

>>	Anonymous Mon Aug 12 09:11:52 2013 No.5963410 >>5963331 41

>>	Anonymous Mon Aug 12 09:12:56 2013 No.5963412 >>5963331 0

>>	Anonymous Mon Aug 12 09:13:56 2013 No.5963413 File: 102 KB, 480x480, 41ish.jpg [View same] [iqdb] [saucenao] [google] >>5963410 I can't find anymore than this. Then again, I'm about to fall asleep...

>>	Anonymous Mon Aug 12 09:14:23 2013 No.5963414 >>5963412 How do you figure?

>>	Anonymous Mon Aug 12 09:15:24 2013 No.5963415 File: 104 KB, 480x480, teehee.jpg [View same] [iqdb] [saucenao] [google] >>5963413 I found one more. :3

>>	Anonymous Mon Aug 12 09:20:52 2013 No.5963419 >>5963414 In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles (90-degree angles, or right angles).

>>	Anonymous Mon Aug 12 09:26:54 2013 No.5963427 >>5963419 True, and that would be the most accurate answer, but for the sake of counting near-square quadrilaterals, how many would be there?

>>	Anonymous Mon Aug 12 09:34:53 2013 No.5963439 >>5963331 32.

>>	Anonymous Mon Aug 12 09:35:22 2013 No.5963441 >>5963405 33, the image itself if 480x480

>>	Anonymous Mon Aug 12 09:40:24 2013 No.5963444 >>5963441 So, 43, if you include: >>5963415 or just 42.

>>	Anonymous Mon Aug 12 09:59:52 2013 No.5963473 How do you solve graphs like the bridge problem?

>>	Anonymous Mon Aug 12 10:16:25 2013 No.5963494 >>5961201 I have one week to learn second order differential equations, but have 0 differentiation or integration experience. Can I do it if I am very average at math?

>>	Anonymous Mon Aug 12 10:26:23 2013 No.5963497 Bump

>>	Anonymous Mon Aug 12 10:28:54 2013 No.5963501 >>5963331 The answer is clearly 0, as a square does not have 4 bent lines, with curved edges.

Anonymous Mon Aug 12 10:30:25 2013 No.5963504

>>5961201
Here's one for anyone interested.

 \sum_{n=1}^\infty \prod_{m=1}^n \frac{\lamba_{m}}{\mu_{m+1}} [\math]

What's the most general condition you can find on lambda's and mu's for this to converge? And can you find an analytical solution for this anywhere?[/spoiler]

>>	Anonymous Mon Aug 12 10:31:22 2013 No.5963505 Hi, Cal you explain me in few words what is a homology, and cohomology, what are their interests and applications in physics ? Examples aswell plz. Thanks

>>	Anonymous Mon Aug 12 10:31:52 2013 No.5963506 >>5963504 <span class="math"> \sum_{n=1}^\infty \prod_{m=1}^n \frac{\lambda_{m}}{\mu_{m+1}} [/spoiler] What's the most general condition you can find on lambda's and mu's for this to converge? And can you find an analytical solution for this anywhere?

>>	Anonymous Mon Aug 12 10:41:53 2013 No.5963520 >>5963494 Can nobody tell me if this is feasible?

>>	Anonymous Mon Aug 12 10:47:53 2013 No.5963526 >>5963520 You can if you work hard, get started immediately and you'll probably get by.

>>	Anonymous Mon Aug 12 10:49:23 2013 No.5963527 >>5963526 Right, any good resources to give extra help? Khan academy any use?

Anonymous Mon Aug 12 10:55:22 2013 No.5963531

>>5963527
Kreyseig's Advanced engineering mathematics would suffice. Its dry, but it'll teach you everything you need to know in a concise manner, and provide problems for you to solve. You'd probably find it if you were to search the pirate bay, for example.

>>	Anonymous Mon Aug 12 10:57:13 2013 No.5963532 >>5963531 Great thanks.

Anonymous Mon Aug 12 11:41:09 2013 No.5963567

>>5961234
>lmao at that obvious shit-tier "abstract" that was obviously written by somebody who is still in highschool.

im gonna go way out on a limb here and say this BS paper was never even read by anybody with a grain of understanding in mathematics, let alone peer reviewed.

>>	Anonymous Mon Aug 12 11:47:39 2013 No.5963572 is division really inverse of multiplication if x/0 is not possible? 1-x=1+(-x) is always true so subtraction is opposite of addition

>>	Anonymous Mon Aug 12 12:15:39 2013 No.5963587 It's not. It is short hand for multiplying by a fraction.

>>	Anonymous Mon Aug 12 12:15:39 2013 No.5963588 >>5961428 If all the answers are wrong, then the correct answer is C. The problem isn't that all the answers are wrong, but that the statement you end up assuming by answering the question is a contradiction.

Anonymous Mon Aug 12 12:23:40 2013 No.5963603

>>5961387
Besides recovering the "original" function, if the function is nice enough you could perhaps recall something like

https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem

If you're satisfied with an approximation like that, that might be a start.

>>	Anonymous Mon Aug 12 12:28:10 2013 No.5963609 >>5963572 It's the inverse for the multiplicative group R\{0}. It's as inverse to multiplication as it can possibly be.

>>	Anonymous Mon Aug 12 12:29:09 2013 No.5963612 Is there some tier-list of sciences and/or sections of sciences/math?

Anonymous Mon Aug 12 12:43:10 2013 No.5963635

Hey OP. First year math student here.

Already passed both first year semesters of real analysis, but I'm having a very hard time with linear algebra. It seems like a more abstract/general type of math to me and I have a lot of problems remembering the proofs.

In real analysis, with most of the proofs that aren't too difficult like L'Hopital or whatever, I can usually imagine the proof, what it's actually doing, and I can prove it easily on my own. But with linear algebra, I'm constantly struggling with even understanding what it is that I'm really trying to prove. It feels as though I'm proving things using various equalities/equivalence, but I can't really imagine these things in my head and see how they work.

I feel like I must be doing something wrong, because all my other classmates have done great in linear algebra and found real analysis much, while I seem to be the opposite. Do you have any idea if maybe I'm doing something wrong with my approach to this subject? Or is it possible to simply be worse at this type of math?

It might also just be that I don't I don't study it with as much effort as I did analysis... linear algebra just seems very annoying to me, as the notes I have for it are terrible and I constantly get stuck in proofs.

>>	Anonymous Mon Aug 12 12:56:28 2013 No.5963660 Why does Gabriel's Horn enclose a finite volume when 1/x does not have a finite area?

>>	Anonymous Mon Aug 12 12:58:42 2013 No.5963662 File: 539 KB, 591x456, math.png [View same] [iqdb] [saucenao] [google] mine comes in the form of a comicpanel

>>	Anonymous Mon Aug 12 13:07:34 2013 No.5963673 >>5963427 >>5963331 50 1x1 squares - 46 2x2 squares - 35 3x3 squares - 24 4x4 squares - 13 Sum it up, it's 50.

>>	Anonymous Mon Aug 12 13:11:47 2013 No.5963679 >>5963635 >remembering the proofs found your problem right there. try for understanding them next time, instead of rote memory.

>>	Anonymous Mon Aug 12 13:18:21 2013 No.5963688 >>5961204 i got this you gusy P=NP P/P=N N=1, P=[-infin,0] [0, infin] or P=0 N=all just call me a math wiz cuz im performin magic in hear

>>	Anonymous Mon Aug 12 13:18:58 2013 No.5963689 >>5963635 >I feel like I must be doing something wrong As the maths gets more complex this happens to everyone eventually. You just have to learn to use rigour instead of intuition.

Anonymous Mon Aug 12 13:20:42 2013 No.5963694
File: 111 KB, 207x320, thisfuckingshitrighthere.png [View same] [iqdb] [saucenao] [google]

>>5961201
Hey OP. I'm really shitty at Maclarian and Taylor expansions. I can get the non-zero terms for the basic ones (they are also given) but can't combine the rules. I use Wolfram, and it gives me an answer, but I need to know how to get there?

Help me please? For example, if I want to find the first few non-zero terms for something like ln(1+tanx) how could I do that? I can do it for tan(x) and ln(1+x), but not both combined.

>>	Anonymous Mon Aug 12 13:21:45 2013 No.5963696 >>5963331 All of those are misshapen and can not be considered squares. The only square is the image itself. So 1.

>>	Anonymous Mon Aug 12 19:06:18 2013 No.5964354 >>5963694 >Maclarian

>>	None !JSN8X5.Us. Mon Aug 12 23:18:38 2013 No.5964706 >>5963315 Hello! On p-adic ANALYSIS (I don't know how to italicize)? If you want the analytic part, you can do better than Koblitz's book. Best!

>>	None !JSN8X5.Us. Mon Aug 12 23:19:39 2013 No.5964709 >>5963473 Hello! I am not sure what you mean? Do you mean the Brigdes of Konigsberg problem? Could you elaborate? Thanks!

>>	Anonymous Mon Aug 12 23:24:38 2013 No.5964718 >>5961201 Alright, I've been dealing with this question all day: Find all values of X, -360<X<360, for which sin X = 2.5467. I don't fucking get this because sin is opposite over hypotenuse, it can't be above 1 and it MAKES ME MAD

None !JSN8X5.Us. Mon Aug 12 23:26:09 2013 No.5964721

>>5963505

Hello!

Homology and cohomology are not well-defined terms in and of themselves (at least not in the way you are probably expecting). You probably mean any of the popular homology/cohomology theories in algebraic topology.

To me it seems best to give an answer that, while it won't tell you anything about what homology or cohomology is/does, it helps you understand why anyone would care about it. Homology is a method to algebraically (meaning abstract algebra) quantify the "obstruction" of something.

An example perhaps. Suppose that I gave you a subset of the plane, and started asking you to do the following: draw a bunch of triangles, and determine which of those triangles is the boundary of a "filled in" triangle. In some subsets of of the plane, the answer is always, in others it isn't. For example, if you take the punctured plane R^2-{0}, then any triangle containing the "hole" will not be the boundary of any filled in triangle (that hole prevents you from filling it in). Thus, there is an obstruction to realizing every triangle as the boundary of a filled in triangle. How "big" is this obstruction? For example, intuitively the instruction to this process is "worse" for the doubly punctured plane R^2{0,(1,1)}. How do we actually quantify this? Well, it turns out that via homology we can actually assign groups to each of these spaces that measure this obstruction (as well as giving other pertinent information). This is the general type of situation encountered in homology--algebraically measure the obstruction to some process.

I hope that helps!

>>	None !JSN8X5.Us. Mon Aug 12 23:27:40 2013 No.5964723 >>5963567 Hello! I do not know if you are, as the kids say, trolling, but vixra.org (notice that it's arxiv backwards) is a gutter for crackpots. No one takes it seriously. Best!

None !JSN8X5.Us. Mon Aug 12 23:37:38 2013 No.5964737

>>5963635

Hello!

To be honest with you, it is most likely a problem of language. Algebra (and by this I mean all the embodiments of the term: linear algebra, abstract algebra, etc.) has a vocabulary unto itself. I don't just literally mean words, although that plays into things. The techniques, methods, and goals of algebra are something that is completely foreign to you.

When I first started doing algebra (my first installment was abstract algebra) I felt as frustrated and insecure as you. I was really good at analysis, how could I be so bad at this? I slogged through my first reading, and did "ok". I convinced myself that I was going to be an analyst. The more and more I did algebra though, the more I started to "get it", I saw it for what it truly was: a beautifully simple subject. Now, I am going to into graduate school (hoping) to focus on arithmetic geometry, about as algebraic as it comes.

Just keep going my friend. You're just inexperienced, and so likely doing things the hard way, missing 'obvious' things. Keep going, and I have no doubt that you'll be able to master linear algebra at the same level as your mastery of analysis.

Best!

>>	None !JSN8X5.Us. Mon Aug 12 23:38:08 2013 No.5964739 >>5963612 Hello! I am not sure what you mean by this. Could you explain? Best!

>>	None !JSN8X5.Us. Mon Aug 12 23:40:10 2013 No.5964742 >>5963694 Hello! Finding the Maclaurin series of a function is as simple as differentiating it. Do you know the general term of a Maclaurin series (f^{(n)}(0)/n! x^n)? Best!

>>	0011101000110011 Mon Aug 12 23:46:42 2013 No.5964751 File: 12 KB, 892x173, 10000.png [View same] [iqdb] [saucenao] [google]

>>	Anonymous Mon Aug 12 23:55:09 2013 No.5964766 >>5963588 so maths IS bullshit till proven otherwise, etc. etc. bullshit bullshit

Anonymous Mon Aug 12 23:59:39 2013 No.5964767

>>5964709
Holy Shit
you're still here?
yeah exactly that
How do solve graphs?
How do you go no those bridges aren't all passable because 3,5,3 or whatever?
How do you expand this problem to a system that has thousands of bridges?
How do solve the traveling salesman problem?
etc?

None !JSN8X5.Us. Tue Aug 13 00:05:11 2013 No.5964782

>>5964767

Hello!

I still am not sure what you mean. Do you mean how did Euler prove that there was no circuit? The wikipedia has a fantastic (illustrated) explanation, that I could not beat. Look here:

http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg

As for the travelling salesman problem, I really don't even know what that is off the top of my head. Not really my type of mathematics. :)

Best

Anonymous Tue Aug 13 00:13:39 2013 No.5964793

>>5964782
>http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg
what kind of math you into?
I think I can think of some stereometry problems
This is the traveling salesman problem, but I thought it had more graphs....
http://en.wikipedia.org/wiki/Travelling_salesman_problem
Given a bunch of cities what's the optimal way to visit each?

Anonymous Tue Aug 13 00:15:10 2013 No.5964796

>>5964793
hmm why'd i link that?
anyway the answer seems to be because " Euler's argument shows that a necessary condition for the walk of the desired form is that the graph be connected and have exactly zero or two nodes of odd degree."
but i mean you could have two not connected graphs

>>	Anonymous Tue Aug 13 00:16:10 2013 No.5964797 >>5961201 What's the formula that always outputs the nth prime where n is a real non-negative integer?

>>	Anonymous Tue Aug 13 00:20:08 2013 No.5964812 What can you do with a BS and/or Ph.D in mathematics?

>>	Anonymous Tue Aug 13 00:43:09 2013 No.5964832 Is math a creation of man or is it a construct of the universe?

>>	Anonymous Tue Aug 13 07:23:35 2013 No.5965323 What is the relationship between homology and higher homotopy groups?

>>	Anonymous Tue Aug 13 07:39:35 2013 No.5965340 >>5965323 Hello! The most comprehensive relationship I know (which isn't saying a lot, since I am far from a topologist) is Hurewicz's theorem. See here: http://en.wikipedia.org/wiki/Hurewicz_theorem I hope that helps!

>>	Anonymous Tue Aug 13 07:50:04 2013 No.5965359 >>5964797 it's unknown

>>	Anonymous Tue Aug 13 08:31:36 2013 No.5965434 ah nice, your are still around. I know there are (strong?) indications that P is not euqal to NP. But are there also (less strong) indications that P is equal to NP? (I asked already in another thread but they didn't know some ,see >>5964282).

>>	Anonymous Tue Aug 13 10:06:34 2013 No.5965613 >>5964832 construct of the universe observed and defined by man

>>	Anonymous Tue Aug 13 14:39:35 2013 No.5966122 What kind of math should chemist know?

>>	Anonymous Tue Aug 13 14:57:09 2013 No.5966171 >>5966122 all the maths

Anonymous Tue Aug 13 15:06:05 2013 No.5966192

>>5964721
>>>5963505
>Hello!
>Homology and cohomology are not well-defined terms in and of themselves (at least not in the way you are probably expecting). You probably mean any of the popular homology/cohomology theories in algebraic topology.
>To me it seems best to give an answer that, while it won't tell you anything about what homology or cohomology is/does, it helps you understand why anyone would care about it. Homology is a method to algebraically (meaning abstract algebra) quantify the "obstruction" of something.
>An example perhaps. Suppose that I gave you a subset of the plane, and started asking you to do the following: draw a bunch of triangles, and determine which of those triangles is the boundary of a "filled in" triangle. In some subsets of of the plane, the answer is always, in others it isn't. For example, if you take the punctured plane R^2-{0}, then any triangle containing the "hole" will not be the boundary of any filled in triangle (that hole prevents you from filling it in). Thus, there is an obstruction to realizing every triangle as the boundary of a filled in triangle. How "big" is this obstruction? For example, intuitively the instruction to this process is "worse" for the doubly punctured plane R^2{0,(1,1)}. How do we actually quantify this? Well, it turns out that via homology we can actually assign groups to each of these spaces that measure this obstruction (as well as giving other pertinent information). This is the general type of situation encountered in homology--algebraically measure the obstruction to some process.
>I hope that helps!
Hello,

Thanks a lot, it helps, can you give me excplicit example with such groups ? Or give a good reference?
Don't be afraid to use some advanced maths.
As a PhD student in math (but Analysis branch) I should understand.

I don't see the difference between Homology and Homotopy ? I mean both of them can "quantify" the obstruction.

Thank you very much!

Anonymous Tue Aug 13 15:08:05 2013 No.5966195

Hi, I am not sure if this would be a good question but. I am thinking about taking Calculus 2 and 3 this Fall..is this a good idea or not? I did well in Cal 1 wasn't hard at all..however I'll be taking engineering physics 1 as well so hm...dunno if I should take cal 3 now or later..thanks in advance for the advice!

>>	Anonymous Tue Aug 13 15:11:05 2013 No.5966203 >>5966192 >claims to be a PhD student >can't into freshman math top lel, you're too obvious

>>	Anonymous Tue Aug 13 15:15:05 2013 No.5966216 >>5962098 >>5962098 >>5962098 this

>>	Anonymous Tue Aug 13 15:16:05 2013 No.5966218 File: 21 KB, 400x400, 1366991951771.jpg [View same] [iqdb] [saucenao] [google] I don't know where to ask this, so I'll ask here. I need to quickly review math from really basic arithmetic to Calculus II. What website or book do you guys recommend?

>>	Anonymous Tue Aug 13 15:22:34 2013 No.5966228 >>5966171 Concretize please

Anonymous Tue Aug 13 15:25:04 2013 No.5966235

>>5966233
(cont.)

As for the difference between homotopy and homology, you bring a good point. They both measure certain types of obstructions (homotopy groups measure the non-contractibility of mappings of spheres into spaces). If you want purely intuition, you can think about homology as being an abelianized version of homotopy theory. The most explicitly obvious form of this is for the first homology group and the fundamental group. Namely, Hurewicz's theorem says that the first homology group of a space is actually just the abelianization of the fundamental group.

I hope that helps!

Anonymous Tue Aug 13 15:25:36 2013 No.5966233

>>5966192

Hello!

Being someone of an analytical bend, you may appreciate deRham cohomology the most.

Take your favorite manifold M (think about just open subsets of R^n if that's easier). Define for every p define Omega^p(M) to be the vector space of p-forms on M (e.g. for p=0 it's just smooth functions, for p=1 it's just smooth 1-forms [sections of the cotangent bundle], etc.). Then, for every p we have the differential which forms a map d^p:Omega^p(M)--->Omega^(p+1)(M). Now, you can easily check that that d^p composed with d^(p-1) is always zero (every exact (something in the image of d^p) form is closed [in the kernel of d^(p+1]). Thus, we see that the closed forms are actually a subspace of the exact forms. In a perfect world of sunshine and lollipops one would have that the converse is true. That, in fact, every closed form is exact. We can measure the obstruction to this property by considering the quotient of ker(d^p)/im(d^(p-1)) (the quotient of the closed p-forms by the exact ones). This is called the pth deRham cohomology group of M and is usually denoted H^p_{dR}(M).

The somewhat amazing fact is that H^p_{dR}(M) is actually secretly measuring just topological information of M (even though, a priori, it's taking the smooth structure of M into account, so you would think it would depend on that to). This is made precise by deRham's theorem, which says that H^p_{dR}(M) is isomorphic the singular cohomlogy groups of M (the purely topological homology groups). The isomorphism is actually by the integration pairing, which is awesome.

Anonymous Tue Aug 13 15:28:05 2013 No.5966239

>>5962098
>this

Hello!

I did see that thread. I am not entirely sure. You're equivalently asking for the sum over log(n!+1)-log(n!), which looks extremely hard. I would doubt that this has an explicit form--I actually enjoy doing infinite series/product/integral calculations, so me not being able to do this isn't worth absolutely nothing.

Sorry!

>>	Anonymous Tue Aug 13 15:29:05 2013 No.5966240 >>5966218 Hello! Paul's online course notes are always highly recommended. Best!

>>	Anonymous Tue Aug 13 15:34:05 2013 No.5966250 >>5966239 thanks just one thing, is it strange that this constant is approx. <span class="math"> \frac{e^{\pi}}{\pi}=7.36591[/spoiler]?

>>	Anonymous Tue Aug 13 15:40:35 2013 No.5966258 >>5966250 Hello! It's not actually that close, yeah? It's not hard to find relationships like that, given all the constants we know and love. Best!

>>	Anonymous Tue Aug 13 16:01:36 2013 No.5966311 Do you remember all the formulas you ever learned? Like every one of them? From trig to com(plex)an(alysis)? Including sciences, too.

>>	Anonymous Tue Aug 13 16:20:36 2013 No.5966360 >>5966311 Hello! Absolutely not. I remember the important ones, but things like trig identities, surely no. I do have a pretty good memory for theorems though. Best!

>>	Anonymous Tue Aug 13 16:35:06 2013 No.5966401 >>5966360 So you just fucking your brain with repetition of stuff just to pass exams and after that forget it and simply use sources? Exams suck.

>>	Anonymous Tue Aug 13 16:50:36 2013 No.5966431 Okay, I have a question and I have no idea where to start on this. "Let x, y be rational numbers such that

Anonymous Tue Aug 13 16:54:35 2013 No.5966437 [DELETED]

Okay, I have a question and I have no idea where to start on this.

"Let x, y be rational numbers such that x^2 + x + \sqrt{2} / y^2 + y + \sqrt{2} is also rational. Prove that either x = y or x + y = -1".

Anyone mind helping me?[/spoiler][/spoiler]

>>	Anonymous Tue Aug 13 16:55:34 2013 No.5966440 >>5966437 oops Let x, y be rational numbers such that <span class="math">x^2 + x + \sqrt{2} / y^2 + y + \sqrt{2}[/spoiler] is also rational. Prove that either <span class="math">x = y or x + y = -1[/spoiler]

>>	Anonymous Tue Aug 13 16:55:35 2013 No.5966442 >>5961201 When are you going to write another book?

>>	Anonymous Tue Aug 13 17:02:05 2013 No.5966450 >>5966401 Hello! No. I try to understand the material enough so that I can derive anything I need. It also makes for longer lasting "memory". Best!

>>	Anonymous Tue Aug 13 17:02:05 2013 No.5966452 >>5966442 Hello! As soon as you TeX up my old, typewriter font ones. Best!

>>	Anonymous Tue Aug 13 17:03:05 2013 No.5966456 >>5964782 What is your type of mathematics?

>>	Anonymous Tue Aug 13 17:05:05 2013 No.5966463 1 + 1 = ?

>>	Anonymous Tue Aug 13 17:05:35 2013 No.5966462 Hi, could you have a look here >>5964375 and give you ideas, if any ? Thanks! I'm very interested, but the thread is slowly dying...

>>	Anonymous Tue Aug 13 17:06:34 2013 No.5966464 >>5966463 it depends. What is you + ? where do you work ?

>>	Anonymous Tue Aug 13 17:07:36 2013 No.5966469 Why do we need math when we have calculators?

>>	Anonymous Tue Aug 13 17:08:35 2013 No.5966470 >>5966456 Hello! I am not entirely sure yet, but arithmetic geometry/complex geometry interest me greatly. Best!

>>	Anonymous Tue Aug 13 17:10:05 2013 No.5966477 >>5966469 because calculators do ...calculus, which is a very small part of math. They don't prove anything by themselve.

>>	Anonymous Tue Aug 13 17:10:34 2013 No.5966474 >>5966250 Hello! I should probably mention, that your best bet to hvae this be solved, if it is solvable, is to post it at the AOPS forum. Those guys are series/product hounds. Best!

>>	Anonymous Tue Aug 13 17:10:34 2013 No.5966476 File: 48 KB, 350x494, trollpi.png [View same] [iqdb] [saucenao] [google] Explain this!

>>	Anonymous Tue Aug 13 17:11:36 2013 No.5966480 >>5966462 Hello! Bleh, do I have to? I really don't enjoy problems like those (contest math). If you posted it on a forum focused on those type of things (such as the AOPS forum), you are more likely to get a better answer, than from me. Sorry!

>>	Anonymous Tue Aug 13 17:14:05 2013 No.5966484 >>5966476 Hello! This is a good example of why limiting processes can't be interchanged. See here: http://math.stackexchange.com/questions/12906/is-value-of-pi-4 Best!

>>	Anonymous Tue Aug 13 17:15:34 2013 No.5966487 >>5966480 so, you definitely saying me than /sci/ is not for real math, but for bullshit/trolls like >>5966463 >>5966476 , if I sum up ? I'm a bit disappointed...

Anonymous Tue Aug 13 17:17:05 2013 No.5966491

>>5966487

Hello!

In what way am I implying that? I don't actual understand that implication? Are you implying that problem is real mathematics, and my unwillingness to try and solve it indicates that I am just another member of your perceived "troll mathematics" community?

Best!

>>	Anonymous Tue Aug 13 17:20:04 2013 No.5966502 File: 461 KB, 350x292, 1374545700514.gif [View same] [iqdb] [saucenao] [google] >>5963696

Anonymous Tue Aug 13 17:20:34 2013 No.5966498

>>5966480
>>5966491
>can't into contest math
>dismisses it as "not real math"

Looks like we got another misplaced biologist who believes he can do math only by memorizing theorems and proofs. You're never gonna get far with that lack of creativity and talent. You might get a degree but you will never do actual research because you cannot THINK like a mathematician.

>>	Anonymous Tue Aug 13 17:20:34 2013 No.5966499 What is a (Kozcul) connection ? and the Levi-Civita connection ? I thought it was a derivation of two vector field. But I can't get an example. Can you give an exemple in a submanifold of R^n?

>>	Anonymous Tue Aug 13 17:22:35 2013 No.5966504 File: 126 KB, 493x511, ss (2013-08-13 at 04.21.34).jpg [View same] [iqdb] [saucenao] [google] >>5963415 you forgot one check out the image dimensions

Anonymous Tue Aug 13 17:23:07 2013 No.5966509

>>5966491
No.
But you seem to be a guy with some skills, and there are very few here.

I don't understand why you spend time to answer to such obvious trolls, and don't give a hand where you could be very helpful.

I'm not trying to imply anything, I just find this a little sad. And I know you are very polite and willingness, I just don't perceive your motivation for comming here.

I love the fact that you don't need to register here.
Forum are too static and boring

>>	Anonymous Tue Aug 13 17:26:07 2013 No.5966514 >>5966509 Hello! Unlike you I am not autistic. I hope that helps!

>>	Anonymous Tue Aug 13 17:30:06 2013 No.5966519 >>5966514 oh fuck. you get me :( Anonymous <> !JSN8X5.Us. You were a bait, I was a fish

>>	Anonymous Tue Aug 13 17:31:35 2013 No.5966520 >>5966498 Hello! Ok! Best!

None !JSN8X5.Us. Tue Aug 13 17:35:35 2013 No.5966531

>>5966509

Hello!

I'm sorry to sadden you, that was not at all my intention. If you notice, I give a two-second response to trolls, and lengthy responses to people that ask about real questions.

I am not unwilling to answer threads like you linked to, I just frankly am not interested in them. This is something I am doing with my free time, hopefully to help people. That said, I would rather not, if possible have to work on problems/discuss concepts that don't interest me. Moreover, I was being honest with you. With my combination of interest in that problem, and my natural proclivity for that type of math, there are much better suited people out there to help you--I gave you some suggestions.

So, once again, I apologize that I have disappointed. I hope you find a solution!

Best!

Anonymous Tue Aug 13 17:37:37 2013 No.5966535

>>5966470
Can you explain the cross product for me?

I know that the dot product is the projection of one vector on to the other. This allows us to measure how much of this vector is that direction. So
W=\mathbf{F}\cdot\mathbf{r}[/spoiler]
but what does the cross product mean?

 \frac{^Nd}{dt}\mathbf{v}={_N\boldsymbol\omega_A}\times\matbf{v}+\frac{^Ad}{dt}\mathbf{v}[/spoiler]
or
 \mathbf{M}=\mathbf{r}\times\mathbf{F}[/spoiler]
I know Hamilton didn't like this notation. He loved him some quaternions and so from him the definition of the cross product is the imaginary part of the quaternion product (and the dot product is the real part).
But what does the cross product "mean"?

>>	Anonymous Tue Aug 13 17:38:35 2013 No.5966538 File: 35 KB, 800x600, math troll.png [View same] [iqdb] [saucenao] [google] I know this is troll math and the conclusion is ridiculous. So it has to be wrong but I fail to see the error in the troll's proof. Please help!

>>	Anonymous Tue Aug 13 17:39:05 2013 No.5966540 >>5966538 He assumed part way through the 0.999... = 1.

>>	Anonymous Tue Aug 13 17:39:35 2013 No.5966542 >>5966531 Ok, then. No problem.

None !JSN8X5.Us. Tue Aug 13 17:40:04 2013 No.5966545

>>5966499

Hello!

A Kozul connection is just a connection on a vector bundle, can you be more specific?

The Levi-Civta connection is just the unique connection on a RIemannian manifold that acts the way it's supposed to: it should annihilate(preserve) the metric, and it should be torsion free. This is the proper connection to choose to study the geometric structure of a Riemannian manifold (M,g)

There is a good example for the sphere on wiki--take a look: http://en.wikipedia.org/wiki/Levi-Civita_connection#Example:_The_unit_sphere_in_R3

Best!

>>	Anonymous Tue Aug 13 17:44:04 2013 No.5966555 >>5966538 That's a reasonable proof; 9.9....-0.9....=9 isn't the most obvious thing in the world but otherwise s'all good. 0.9...=1 is true anyway- there are no real numbers between them, so they're equal.

>>	Anonymous Tue Aug 13 17:45:34 2013 No.5966559 >>5966555 >there are no real numbers between them What about their arithmetic mean?

>>	Anonymous Tue Aug 13 17:45:34 2013 No.5966561 >>5966450 But that takes time, which you don't have much at exams.

>>	None !JSN8X5.Us. Tue Aug 13 17:48:04 2013 No.5966573 >>5966561 Hello! I am a quick deriver :) Best!

>>	Anonymous Tue Aug 13 17:50:34 2013 No.5966577 As Andrew Wiles once said, the differences between exam/contest math and professional mathematics are of time and novelty. Remember, Wiles spent literally decades proving FLT

>>	Anonymous Tue Aug 13 18:04:05 2013 No.5966629 >>5966535 bumpity

Anonymous Tue Aug 13 18:22:06 2013 No.5966685
File: 2 KB, 434x227, img61.gif [View same] [iqdb] [saucenao] [google]

>>5966629
Engineer explanation :
In R^3, OC=OA x OB
OC is the vector orthogonal to the plane OAB, and its length is the area of OADB
Sense is given by the "Right-hand rule".

Interesting particular case : ||OA||=||OB||=1

>>	Anonymous Tue Aug 13 18:28:35 2013 No.5966717 >>5966685 but what's so special about the area? why can't i expand this to 4D? Two vectors still define a plane in 4D right? so a vector can be orthogonal to this plane in 4D and you can rotate and figure out that parallelogram area. right?

>>	Anonymous Tue Aug 13 18:38:06 2013 No.5966749 Does the algebraic closure of Q form a two-dimensional vector space over the algebraic closure of Q intersected with R, like how C is two-dimensional over R?

>>	Anonymous Tue Aug 13 18:43:05 2013 No.5966764 >>5966717 >Two vectors still define a plane in 4D right? No :) In 4D, you need 3 vectors (non colinear) to define a "plane" (in the sense you have in mind, https://en.wikipedia.org/wiki/Hyperplane))

>>	Anonymous Tue Aug 13 18:46:34 2013 No.5966771 >>5966764 that would make the cross product not work... still why the area?

>>	Anonymous Tue Aug 13 18:47:07 2013 No.5966772 >>5966749 Do you mean over Q? If so it forms an infinite dimensional vector space over Q

>>	Anonymous Tue Aug 13 18:48:05 2013 No.5966779 >>5966772 No, if I could TeX the bars over letters properly it'd be more clear. Let K be the algebraic closure of Q. My question is: Is K a two-dimensional vector space over the field <span class="math">K \cap \mathbb{R}[/spoiler]?

>>	Anonymous Tue Aug 13 18:48:35 2013 No.5966778 >>5966771 because absin(t) happens to be the area of parallelogram

>>	Anonymous Tue Aug 13 18:52:04 2013 No.5966788 >>5966786 <span class="math">\|\mathbf{M}\|=\|\mathbf{r}\times\mathbf{F}\|=\|\mathbf{r}\|\|\mathbf{F}\|\sin \theta[/spoiler]

>>	Anonymous Tue Aug 13 18:52:05 2013 No.5966786 >>5966778 but why is <span class="math"> \|\mathbf{M}\|=\|\mathbf{r}\times\mathbf{F}\|=\|\mathbf{r}\|\|\mathbf{F}\|\sin\theta[/spoiler]

>>	Anonymous Tue Aug 13 18:53:05 2013 No.5966793 >>5966779 Oh right. Yes, if a and b are real algebraic numbers, it is pretty trivial to show a + ib is K, from the field properties.

>>	Anonymous Tue Aug 13 18:53:05 2013 No.5966795 >>5966788 wtf

Anonymous Tue Aug 13 18:55:06 2013 No.5966801

A half-cell consisting of palladium rod dipping into a 1 M Pd(NO_3)_2[/spoiler] solution is connected with a standard hydrogen half-cell. The cell voltage is 0.99 volt and the platinum electrode in the hydrogen half-cell is the anode. Determine E^ο[/spoiler] for the reaction Pd \rightarrow Pd^{+2} + 2e[/spoiler].

Now the question is: can I find a numerical value of the needed E^ο[/spoiler], if I can't use half-cell potential of Pt^{+2}-Pt[/spoiler]?

I know that's not your speciality, but hey, you're a freaking math-MS-gonnabe - you can't possibly not know this. Anyway, help me, anyone, I don't want to create a new thread.

>>	Anonymous Tue Aug 13 18:56:35 2013 No.5966803 >>5966795 <span class="math"> \|M\|=\|r\times F\|=\|r\|\|F\|\sin \theta [/spoiler] 4chan tex sucks ;)

>>	Anonymous Tue Aug 13 18:58:34 2013 No.5966810 >>5966803 you can see it as a consequence of the more formal definition. see here for instance http://en.wikipedia.org/wiki/Triple_product

>>	Anonymous Tue Aug 13 18:58:34 2013 No.5966811 >>5966803 it is defined as such. the determinant version follows from this by linearity of the cross product

None !JSN8X5.Us. Tue Aug 13 19:01:05 2013 No.5966820

>>5966749

Hello!

Interesting question. It is a theorem that if K/F is Galois, and F'/F is any extension, then Gal(KF'/F') is isomorphic to Gal(K/(K\cap F')). Taking K=\bar{Q}, F=Q, F'=R this says that Gal(\bar{Q}R/R) is isomorphic to Gal(\bar{Q}/(\bar{Q}\cap R)). Note though that since \bar{Q} contains i, that \bar{Q}R=C. So, Gal(\bar{Q}R/R)=Gal(C/R)=2. So, [\bar{Q}:\bar{Q}\cap R]=2.

From this we can also conclude that \bar{Q}=(\bar{Q}\cap R)(i).

I hope that helps!

>>	Anonymous Tue Aug 13 19:01:05 2013 No.5966821 >>5966811 >it is defined as such No...It's defined as such when you begin univ. that's more the definition of the physicists

>>	Anonymous Tue Aug 13 19:04:04 2013 No.5966836 What do you think about the 3 different types of infinity

Anonymous Tue Aug 13 19:04:35 2013 No.5966832

>>5966793
>>5966820
Ok, so then more generally: Is there a more general notion of the "real number" field in any algebraically closed field? In other words, does there exist a field F \subset K[/spoiler] such that K is algebraically closed and [K:F] = 2? Can one do these sort of "reverse algebraic extensions" to replicate the situation for [K:F] = n, for any positive integer n?

None !JSN8X5.Us. Tue Aug 13 19:07:36 2013 No.5966847

>>5966832

Hello!

Haha! You are asking very questions. Somewhat shockingly the answer is yes and no.

There is a famous theorem of Artin and Schreier which says the following:

If K is any field such that \bar{K}/K is finite, then:

1. K is an ordered fied.

2. K has characteristic zero.

3. \bar{K}=K(i) for some squareroot i^2=-1.

4. Any one of a or -a has a squareroot in K

5. Any finite sum of nonzero squares is a square.

See here for more details: http://www.math.uconn.edu/~kconrad/blurbs/galoistheory/artinschreier.pdf

Best!

>>	Anonymous Tue Aug 13 19:08:04 2013 No.5966853 File: 106 KB, 422x346, u.png [View same] [iqdb] [saucenao] [google] >>5966836 >3 different types of infinity ? wut

>>	None !JSN8X5.Us. Tue Aug 13 19:09:36 2013 No.5966855 >>5966836 Hello! I am not exactly sure what you mean by this. There are infinitely many distinct infinte cardinals. Please elaborate!

>>	Anonymous Tue Aug 13 19:10:35 2013 No.5966858 >>5966821 It was historically, originally defined as such. Equivalent definitions exist.

>>	Anonymous Tue Aug 13 19:10:35 2013 No.5966859 >>5966847 Wow, that's an awesome theorem, and I actually know Keith Conrad too! Thanks for the article.

>>	Anonymous Tue Aug 13 19:11:07 2013 No.5966863 if i were to smoke 12 joints of maui wowi and you smoke 6 joints of pinapple express how high would we be? also mister math dude do you smoke marijuana LEGIT AND SERIOUS QUESTION

>>	None !JSN8X5.Us. Tue Aug 13 19:11:07 2013 No.5966864 >>5966859 Hello! Are you at UConn? I don't think KC does the ordered field part of my satement. For that you can see Kaplanski's book on Fields and Rings. Best!

>>	Anonymous Tue Aug 13 19:13:06 2013 No.5966873 >>5966864 Yeah I've been in one of his classes before. He knows a lot of stuff, it's incredible. Very helpful and explains well. Plus his webpage is an encyclopedia of basically everything undergraduate (and some graduate) mathematics.

>>	None !JSN8X5.Us. Tue Aug 13 19:16:05 2013 No.5966879 >>5966873 Hello! Very cool! Yeah, him and his brother (Brian, at Stanford) are extremely brilliant, as well as being good expositors. Are you trying to go to graduate school eventually? Best!

>>	Anonymous Tue Aug 13 19:17:34 2013 No.5966882 Hello friend! How do I gain an intuition for sheaves on grothendieck topologies? I have a decent intuition for sheaves on spaces, but I just have no idea what's going on in that equalizer diagram on a grothendieck topology.

None !JSN8X5.Us. Tue Aug 13 19:24:35 2013 No.5966909

>>5966882

Hello!

I, on principle, do not like to try and explain things to people that I am currently learning. I feel it is disingenuous. So, let me instead refer you to the book which I have gotten the most intuition from:

The Heart of Cohomology--Goro Kato

Intuitively though, the site is supposed to be a replacement for the notion of an open cover, and the equalizer diagram is just saying that with this notion of open cover on the category, the gluing and local determinacy properties we want presheaves F:C^op-->J to have to make them sheaves, does in fact hold.

I hope that helps!

>>	Anonymous Tue Aug 13 19:28:35 2013 No.5966924 >>5966909 I'll look into that book, thanks!

>>	Anonymous Tue Aug 13 19:29:35 2013 No.5966928 >>5966879 I hope so, eventually.

>>	Anonymous Tue Aug 13 19:36:35 2013 No.5966949 File: 230 KB, 610x458, .jpg [View same] [iqdb] [saucenao] [google] >>5966801 Fucken help me, people!

>>	None !JSN8X5.Us. Tue Aug 13 19:37:34 2013 No.5966952 >>5966928 Hello! Cool! Do you know where you might want to go yet? Best!

>>	None !JSN8X5.Us. Tue Aug 13 19:38:37 2013 No.5966954 >>5966949 Hello! I apologize, but I know way, way, way too little chemistry to even begin to help you. Have you tried here: http://chemistry.stackexchange.com/ Best!

>>	Anonymous Tue Aug 13 19:42:40 2013 No.5966979 >>5966952 Not sure. I guess whatever will take me. I'll have to discuss more with advisors and such to see where to apply.

>>	None !JSN8X5.Us. Tue Aug 13 19:44:35 2013 No.5966984 >>5966979 Hello! That seems like a good course of action. Just start looking/preparing/etc. early. The process is a little shitty. Also, try to do an REU if you can, it really does look good. Best!

>>	Anonymous Tue Aug 13 19:45:35 2013 No.5966993 >>5966858 > historically yes, that doesn't mean AT ALL that this is a good reason to continue to do so. Take sin and cos for instance. Or the definition of "limit" But OK, the important thing is the equivalence of definitions.

Anonymous Tue Aug 13 20:00:34 2013 No.5967038

I have a question! It's kind of pleb-tier, but I'm having a little trouble.

What does it look like/mean when a multivariable system of linear equations has infinitely many solutions? It can't mean they are all the same line, can it? I find this difficult to picture, is why I ask. Or does it perhaps mean that if they share a common variable, we can take that to be a parameter and in that variable/parameter at every point, all of the equations have some value at that point? If this is so, then what does it mean to only have one solution? Wouldn't any system that has at least one variable in common with all other equations always have infinitely many solutions? Any insight would be appreciated.

>>	Anonymous Tue Aug 13 20:05:35 2013 No.5967050 >>5966858 No.sorry http://gallica.bnf.fr/ark:/12148/bpt6k229222d/f663.image Deal with it 1773, Lagrange.

Anonymous Tue Aug 13 20:14:40 2013 No.5967068

>>5966954
So you're saying you don't know school level chemistry? Damn, people **are** *that* narrow-specialized. So that means I can (and, more importantly, have a logical right to) call myself _the_ man of chemistry? Talk about chem in a cocky "well, *we* in chemistry have..."-style?
Sucks, man. Well, I'm not gonna be *any* man, I will use my intellect to achieve a high level of understanding in the multiple science fields.
inb4: gl with that m8!
But yeah, you know some stuff - knowledge of different sci-related forums and socnets is pretty handy, gotta give you that.

>>	Anonymous Tue Aug 13 20:26:41 2013 No.5967105 File: 42 KB, 720x439, 1364408005839.jpg [View same] [iqdb] [saucenao] [google] >>5967068 but if you're asking for help on that question surely that means you don't know school level chemistry?

None !JSN8X5.Us. Tue Aug 13 20:33:39 2013 No.5967122

>>5967038

Hello!

Think about the solution set of a multilinear system as being an (affine) subspace of R^n. It could be a point, a line, a plane, etc. To have infinitely many solutions just means that it isn't a point (as soon as your not a point, you have infinitely many solutions). If it's a line, then yes, you can parameterize.

To intuit how one can get only one solution think about it as follows. You say to me

"anon, I want a quadruple of numbers (x,y,z,w) that satisfy 3x+5y-w=0".

I go,

"Ok anon. Here is the set of all those quadruples in R^4--it's a three-dimensional subspace. (a hyperplane)."

You then go

"oh, anon, I also forgot, I also want them to satisfy 55w-27z=0"

I then say

"Well, ok anon. Then you're looking for points that are both on the hyperplane defined by 55w-27z=0 AND x+5y-w=0. So, your solutions are exactly the intersection of those two hyperplanes. Now, you may have to think about it for a second, but how big this hyperplane is (in dimension) could be one of two things. Either they are the SAME hyperplane, in which case the intersection stays the same dimension (3) or you've reduced the dimension."

as you keep adding more and more equations, you keep having to intersect more and more hyperplanes. Now, if you're equations were chosen independtly enough, then the hope is that by adding enough equations (intersecting enough hyperplanes) you'll eventually just get one solution (one point in the intersection). Things of course can go wrong. For example, if you had kept adding in equations that defined the same hyperplane over and over again, no matter how many equations you throw in, there will always be the same hyperplane of solutions (infinitely many). See what other possibilities you can come up with!

I hope that helps!

>>	None !JSN8X5.Us. Tue Aug 13 20:35:39 2013 No.5967131 >>5967068 Hello! Are you for real? Best!

Anonymous Tue Aug 13 20:56:37 2013 No.5967183

The proof of dominated convergence theorem is "easy" to follow when you're in the area of Lebesgue integration.

But when I began math classes, we only studied inside integral using the "Riemann integral" framework, and the teacher said that the proof was too hard for us.
("Wait for Lebesgue integration" was his answer)

Can you explain me the "big steps", or provide me a link with a proof ?
Thanks

None !JSN8X5.Us. Tue Aug 13 21:09:34 2013 No.5967212

>>5967183

Hello!

The proof on Wikipedia is about as simple as it comes. There are no really big broad strokes for one simple reason--the somewhat difficult part of the theorem is not the proof (that's almost trivial) it's the definition of the Lebesgue integral itself.

Indeed, the proof would work perfectly fine in the case of Riemann integration save one fact--the limit of a dominated sequence of Riemann integrable functions is Riemann integrable. That really is the only difference. The Lebesgue integral is robust enough that it can deal with any pathologies introduced by a limiting process (in certain cases such as these). Once you know it even makes sense to ask if you can switch limits (that the limiting functions is integrable) you just prove it like you would want to. Make inequalities and apply limits.

If you read the proof on Wiki (and, necessarily, the proof of Fatou's lemma) with this in mind, and are still having difficulty, feel free to let me know.

Best!

None !JSN8X5.Us. Tue Aug 13 21:11:34 2013 No.5967217

>>5967212

Hello!

Oops, the above

"the limit of a dominated sequence of Riemann integrable functions is Riemann integrable"

should read

"the limit of a dominated sequence of Riemann integrable functions NEED NOT BE Riemann integrable"

Sorry!

Anonymous Tue Aug 13 21:21:34 2013 No.5967236

>>5967217
but they always make reference to results of measure theory, which we didn't use when we studied rieman integral (or it was "hidden").

For instance, how do you deal with
"the limit of a dominated sequence of Riemann integrable functions NEED NOT BE Riemann integrable" in epsilon/eta style ?

Because teacher used this theorem as a transition for introducing Lebesgue integral (deal with any pathologies introduced by a limiting process as you said).

Extra question : why don't we just use Henstock-Kurzweil integral, which is very "easy to use" compared to Rieman/Lebesgue ones ?

thanks

None !JSN8X5.Us. Tue Aug 13 21:29:35 2013 No.5967251

>>5967236

Hello!

The problem is that you don't deal with it. It can't be dealt with in the context of the Riemann integral, which is exactly why we trade in the Riemann integral for the Lebesgue integral.

As for your other question, if I had to guess it could be because:

a) that definition actually looks pretty annoying to deal with

or more likely

b) that is too complicated for a first-timer, and is conceptually the right idea for more advanced integration theories. Measures, in and of their own right, are extremely important in mathematics.

Those are just guesses though.

Best!

>>	Anonymous Tue Aug 13 21:35:38 2013 No.5967260 >>5967251 thxs for the replies

>>	Anonymous Wed Aug 14 01:29:11 2013 No.5967550 >>5967105 But I'm gonna. Duh. >>5967131 Why, yes, my friend, that problem really concerns me. What makes you think I'm trolling? Asked questions or my goal to be more multispecialized?

Anonymous Wed Aug 14 01:43:16 2013 No.5967567
File: 1.16 MB, 3270x2662, 1366497780953.jpg [View same] [iqdb] [saucenao] [google]

>>5967122
You're so awesome, Anon. That actually really helped. I guess I forgot that linear equations can represent more than just lines. I think the first paragraph was most helpful and then everything just fell into place.

>See what other possibilities you can come up with!
I'm not sure what you mean by that, unless you mean that if I intersect two independent hyperplanes, I'll get a plane of R^n-1 order as a result. Or a line + plane = line, plane + plane = line, etc.

Thanks helpful math anon!

None !JSN8X5.Us. Wed Aug 14 02:12:10 2013 No.5967603

>>5967550

Hello!

No, I think your desire to become knowledgable in multiple fields is awesome, and wish you the best of luck.

I was just wondering if you knew how much work and effort it takes to even get close to the knowledge/ability needed to do research in any of the sciences.

I can only speak from experience, but I can tell you that I have spent the last four years of my life devoting a huge amount of my waking, free hours to mathematics. It has gotten me far, but I still feel so, so far away from the front lines. If you think that in the clusterfuck that is trying to get to the point where you can do important, original, modern research that I have time to get more than a conversational knowledge of any of the other hard sciences, you're nuts.

Well, let me be less dramatic. With the goals I have, and with the field that I want to go into, I don't think I could have feasibly (nor would I have honestly wanted to considering the opportunity costs) put the effort into learning another subject to anywhere near the same depth that I have learned mathematics.

Once again, before the admonition starts, let me reiterate: I want, and attempt to always expand, my broad-strokes, conversational knowledge of all parts of modern academics. But, that is a far-cry from being able to answer even a semi-technical question from a beginning course.

I wish I was able to do the things I want in math, and still have time to learn in-depth other subjects, but I don't honestly.

I hope that clarifies some things!

>>	None !JSN8X5.Us. Wed Aug 14 02:14:15 2013 No.5967607 >>5967567 Hello! Thank you for the kind words! I'm glad I could help! Best!

Anonymous Wed Aug 14 02:26:15 2013 No.5967625

>>5967603
But math is different, right? I mean, there's like millions of times more math, than sciences, isn't that about right? Like, if we count only the most commonly accepted physics-chemistry theories. Besides, I'm mostly talking about university level of knowledge.

None !JSN8X5.Us. Wed Aug 14 02:45:18 2013 No.5967649

>>5967625

Hello!

I can't honestly say that I have no technical knowledge of other hard sciences, and the turn around and make a brash statement about math having more prerequisite knowledge.

Yes, but university level is hard. I took Chem 101, Physics 101, etc. That doesn't mean that I really know how to do anything in any of those fields. Think about your own field, whatever that may be. If someone said "I've taken the first course in ___" you would obviously write them off as being not knowledgable, yes?

Best!

>>	Anonymous Wed Aug 14 02:56:15 2013 No.5967670 >>5967649 Well, memory wouldn't be of a problem to me, so that's one less obstacle.

>>	Anonymous Wed Aug 14 05:30:10 2013 No.5967831 Hello, I heard that #{ irreductible fraction}/#{reductible fraction} is finite. Do you know how to prove it ? I think it's related to dzeta(2) ..

Anonymous Wed Aug 14 19:59:23 2013 No.5969209

>>5967625
>>5967603
Not OP. Physics theorist here (mathematical physics more like it). Just found this thread, which is the best thread on /sci/ in recent memory.

I specialize in analysis, PDE theory and exactly-solved models, but in undergrad I did a LOT of research in the theory of quantum dissipative systems (by a lot, I mean 3 years and 2 long-ass papers), so I think i can say something productive about physics research, even though I took more math than physics.

Anyways, I would say that mathematics research requires a good deal less knowledge on the whole, than physics theory. I've had to use stuff from de rham cohomology, stochastic processes and ergodic theory in a single paper, and that is not atypical for physics theory. In addition to all the mathematical tools, theorists tend to need to know tons about different branches of physics.

For example, once I used methods from quantum optics to solve stochastic problem, due to some clever intuition by my adviser. Mathematicians tend to have a very deep knowledge of the mathematics they work with, as opposed to physicists who mainly look up theorems when they need them, because there is just so much more to learn.

As a result, I have a huge breadth of physical and mathematical knowledge, but it is a good deal shallower than for example, OP's knowledge. I tried learning algebraic topology rigorously once, then gave up due to frustration at the time it took. Now I just have 3 algtop books to look shit up in.

Sorry for the rant, hope I gave a slightly different perspective about research.

>>5962073
I've published a paper on random matrix spectral theory. Awesome stuff.

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