/sci/ - Science & Math » Thread #10960172

485KiB, 616x1000, DB6DD209-EC5B-464F-9751-5C1A5F2C988D.jpg

View Same Google iqdb SauceNAO

/mg/ - maths general

Anonymous Mon 09 Sep 23:54:10 2019 No.10960172 View Reply Original Report

Quoted By: >>10960195 >>10961156 >>10968678

Previously >>10946255

4 pests campaign, hundred flowers campaign, back to the country side campaign edition

Anonymous

Anonymous Mon 09 Sep 2019 23:54:59 No.10960175 Report

Quoted By: >>10960189

What's math?

Anonymous

Anonymous Mon 09 Sep 2019 23:55:43 No.10960177 Report

Quoted By: >>10960257

What’s your favourite math conundrum bros?

Anonymous

Anonymous Tue 10 Sep 2019 00:01:15 No.10960189 Report

Quoted By:

>>10960175
BABY DON'T HURT ME

Anonymous

Anonymous Tue 10 Sep 2019 00:03:27 No.10960195 Report

Quoted By:

>>10960172
Someone redill me on Alex Eskin and the Magic Wand Theorem. Is it just a meme?

Anonymous

View Same Google iqdb SauceNAO physical maths.png, 2MiB, 1202x910

Anonymous Tue 10 Sep 2019 00:05:32 No.10960203 Report

Quoted By: >>10960933 >>10968306

Threadly reminder to work with physicists.

Anonymous

Anonymous Tue 10 Sep 2019 00:24:43 No.10960257 Report

Quoted By:

>>10960177
>What’s your favourite math conundrum bros?
Monty Hall

Anonymous

View Same Google iqdb SauceNAO desu.png, 251KiB, 1626x1109

Anonymous Tue 10 Sep 2019 03:01:09 No.10960662 Report

Quoted By: >>10960675 >>10960678 >>10964309

Why is this wrong?

Anonymous

Anonymous Tue 10 Sep 2019 03:05:48 No.10960675 Report

Quoted By:

>>10960662
Try putting amplitude 4 in there and see if you get it right. Don't know what else could be wrong.

Anonymous

Anonymous Tue 10 Sep 2019 03:07:05 No.10960678 Report

Quoted By: >>10960686

>>10960662
Oh, you've used t as the variable. Try x.

Anonymous

Anonymous Tue 10 Sep 2019 03:09:39 No.10960686 Report

Quoted By: >>10960697

>>10960678
Wow, thanks! I really should've used the variable from the graph but I never thought of that.

Anonymous

View Same Google iqdb SauceNAO 1561172934285.jpg, 774KiB, 1080x1080

Anonymous Tue 10 Sep 2019 03:12:00 No.10960697 Report

Quoted By: >>10960708

>>10960686
Also, confused anime girls should always have question marks nearby. So you get -1 point for that too.

Anonymous

View Same Google iqdb SauceNAO ouchy.gif, 1013KiB, 500x281

Anonymous Tue 10 Sep 2019 03:15:19 No.10960708 Report

Quoted By:

>>10960697
I'll do better next time.

Anonymous

View Same Google iqdb SauceNAO numberofposs.png, 46KiB, 1105x570

Anonymous Tue 10 Sep 2019 03:50:21 No.10960805 Report

Quoted By:

How many possible ways one can reach yes and one can reach no?

Anonymous

View Same Google iqdb SauceNAO yukari_sneer.png, 1MiB, 1366x768

Anonymous Tue 10 Sep 2019 04:54:40 No.10960933 Report

Quoted By: >>10961067 >>10962138 >>10969724

>>10960203
https://arxiv.org/abs/1105.0805

Anonymous

Anonymous Tue 10 Sep 2019 05:33:59 No.10961000 Report

Quoted By: >>10961019 >>10961187 >>10962127 >>10971982

How do I dedicate myself to Mathematics?

Anonymous

Anonymous Tue 10 Sep 2019 05:42:15 No.10961019 Report

Quoted By: >>10961024

>>10961000
>How do I dedicate myself to Mathematics?
What have you tried?

Anonymous

Anonymous Tue 10 Sep 2019 05:45:25 No.10961024 Report

Quoted By:

>>10961019
Reading, researching, attending lectures, doing lots of math. Because it's all I have.

Anonymous

Anonymous Tue 10 Sep 2019 06:04:12 No.10961067 Report

Quoted By: >>10961072

>>10960933
When are we getting sushi?

Anonymous

View Same Google iqdb SauceNAO yukari_smile1.png, 266KiB, 428x556

Anonymous Tue 10 Sep 2019 06:12:35 No.10961072 Report

Quoted By: >>10961320 >>10967042

>>10961067
>sushi
That's no way to refer to a lady's private parts, is it?

Anonymous

Anonymous Tue 10 Sep 2019 07:26:54 No.10961156 Report

Quoted By:

>>10960172
>CCP Communist programs
>KMT Nationalist animu
Stick to bean counting senpai

Anonymous

Anonymous Tue 10 Sep 2019 08:08:25 No.10961187 Report

Quoted By:

>>10961000
Which part of math?

Anonymous

Anonymous Tue 10 Sep 2019 09:55:07 No.10961261 Report

Quoted By: >>10961411

Can algebraic topology have a non-self contractory set of Abelian groups?

Anonymous

Anonymous Tue 10 Sep 2019 10:52:29 No.10961320 Report

Quoted By: >>10961422

>>10961072
what did he mean by this

Anonymous

Anonymous Tue 10 Sep 2019 12:05:08 No.10961411 Report

Quoted By:

>>10961261
wut?

Anonymous

Anonymous Tue 10 Sep 2019 12:12:52 No.10961422 Report

Quoted By: >>10961454 >>10964038 >>10967042

>>10961320
>what did he mean by this
I'm not a "he".

Anonymous

Anonymous Tue 10 Sep 2019 12:41:25 No.10961454 Report

Quoted By:

>>10961422
It's ok anon, we're all girls here.

Anonymous

View Same Google iqdb SauceNAO 776.jpg, 53KiB, 648x838

Anonymous Tue 10 Sep 2019 12:43:37 No.10961457 Report

Quoted By: >>10961458 >>10961573 >>10962317

Why does this pos calculator give me shit values like this?

Anonymous

View Same Google iqdb SauceNAO 65656.jpg, 6KiB, 211x148

Anonymous Tue 10 Sep 2019 12:44:37 No.10961458 Report

Quoted By: >>10961573 >>10962317

>>10961457
Instead of this.

Anonymous

Anonymous Tue 10 Sep 2019 14:31:02 No.10961573 Report

Quoted By: >>10961608

>>10961457
>>10961458
I don't see what the difference is. You dislike precision?

Anonymous

View Same Google iqdb SauceNAO 56565.jpg, 41KiB, 743x778

Anonymous Tue 10 Sep 2019 14:54:50 No.10961608 Report

Quoted By: >>10961630 >>10962317

>>10961573
The real issue is that my calculator keeps screwing up long decimals while dealing with integrals. Just trying to come up with some kind of a workaround.

Anonymous

Anonymous Tue 10 Sep 2019 14:57:09 No.10961613 Report

Quoted By:

Can someone post the chronological math order you should study meme pic so I can choose my next topic to study, thanks

Anonymous

Anonymous Tue 10 Sep 2019 15:07:28 No.10961630 Report

Quoted By: >>10962336

>>10961608
Your calculator integrates numerically, just like literally any computer system. The only situation in which it will calculate an integral precisely is for a line (no error). Otherewise, whether it's visible in the amount of digits or not, there will always be some error.
Keep in mind that the error is ridiculously small compared to the size of your answer.

Anonymous

View Same Google iqdb SauceNAO 9780387967875_200x_basic-mathema (...).jpg, 5KiB, 199x300

Anonymous Tue 10 Sep 2019 15:13:20 No.10961640 Report

Quoted By: >>10961656 >>10962334 >>10962506 >>10966998

Thoughts on this for an anon who has worked 6 years after failing highschool with deep regret and wants to go back into studying?

Anonymous

Anonymous Tue 10 Sep 2019 15:21:03 No.10961656 Report

Quoted By: >>10961666

>>10961640
Lang is a meme.
Probably a good idea though.

Anonymous

Anonymous Tue 10 Sep 2019 15:27:49 No.10961666 Report

Quoted By: >>10961675

>>10961656
Fags who say this are a meme and should not be taken seriously.

Anonymous

Anonymous Tue 10 Sep 2019 15:32:24 No.10961675 Report

Quoted By: >>10961695 >>10971535

>>10961666
Hi Lang. How's the AIDS denial life treating you these days?

Anonymous

Anonymous Tue 10 Sep 2019 15:40:39 No.10961695 Report

Quoted By: >>10971535

>>10961675
Gee i may be a Aids denier but whats that got to do with mathematics.
Tell me based senpai.

Anonymous

Anonymous Tue 10 Sep 2019 19:32:58 No.10962127 Report

Quoted By:

>>10961000
don't lmao

Anonymous

View Same Google iqdb SauceNAO JUST_Theranos.png, 323KiB, 503x481

Anonymous Tue 10 Sep 2019 19:38:12 No.10962138 Report

Quoted By: >>10962147

>>10960933
what does Higgs mean to them, in this general context?

Anonymous

View Same Google iqdb SauceNAO yukari_lick.png, 214KiB, 471x577

Anonymous Tue 10 Sep 2019 19:43:16 No.10962147 Report

Quoted By: >>10962211

>>10962138
The section of a Hermitian line bundle $V$ .

Anonymous

Anonymous Tue 10 Sep 2019 20:09:25 No.10962211 Report

Quoted By: >>10962233

>>10962147
What makes it "Higgs"?

Anonymous

Anonymous Tue 10 Sep 2019 20:16:14 No.10962233 Report

Quoted By:

>>10962211
Connection 1-forms of the tensor bundle $P\otimes V$ enter the action just like how Higgs couple to the gauge field strength.

Anonymous

View Same Google iqdb SauceNAO 10BB7CBA0B9A4703A9687332B384F8D7.jpg, 101KiB, 1920x1080

Anonymous Tue 10 Sep 2019 20:42:59 No.10962283 Report

Quoted By: >>10962312 >>10962321

Terry Tao announced today that he has new partial results toward proving the Collatz conjecture!
https://terrytao.wordpress.com/2019/09/10/almost-all-collatz-orbits-attain-almost-bounded-values/
we're almost there

Anonymous

View Same Google iqdb SauceNAO ashton_C_cups.png, 697KiB, 532x536

Anonymous Tue 10 Sep 2019 20:55:51 No.10962312 Report

Quoted By:

>>10962283
>Theorem 2 Let {f: {\bf N}+1 \rightarrow {\bf R}} be any function with {\lim_{N \rightarrow \infty} f(N) = +\infty}. Then we have {\mathrm{Col}_{\min}(N) < f(N)} for almost all {N} (in the sense of logarithmic density). ,
Almost there, and yet infinitely far away

Anonymous

Anonymous Tue 10 Sep 2019 20:59:08 No.10962317 Report

Quoted By:

>>10961608
>>10961458
>>10961457
The nature of floating point calculations makes errors inevitable.

If you want exact results you need to consult a computer algebra system, if you want more accurate results you need to use variable precision arithmetic or if you want a mathematically verified bound you might have to dive deep into interval arithmetic.
All of that comes at a computational cost unsuited for a pocket calculator, I recommend that you use an appropriate software package on a desktop computer for anything more then the basic numeric integration your calculator does.

Anonymous

Anonymous Tue 10 Sep 2019 21:00:26 No.10962321 Report

Quoted By:

>>10962283
>Little brain Riemann hypothesis
>Normal brain Navier Stokes
>Big brain Goldbach conjeture
>Galaxy brain Collatz conjeture

Anonymous

View Same Google iqdb SauceNAO jpqodmc83ia21.jpg, 126KiB, 683x767

Anonymous Tue 10 Sep 2019 21:02:45 No.10962325 Report

Quoted By: >>10963391

Can someone explain this one thing to me?
Say I have a space of bounded functions $B\left ( U,V \right )$, where $U$ is a normed vector space and $V$ is a complete vector space. Then one can prove that the $B\left ( U,V \right )$ is complete w.r.t. the sup norm by arguing that a Cauchy sequence of functions $\left \{ f_{n} \right \}$ in $B\left ( U,V \right )$ converges to a bounded function $f$, where $f$ is defined pointwise by setting $f(x)=\lim_{n \to \infty }f_{n}(x)$. But for each $x\in U$ one has to choose $N_{x}$ which may depend on $x$ such that for a given $\varepsilon$ one has $\left \| f_{n}(x)-f(x) \right \|<\varepsilon $. But what guarantees uniform convergence then, if the choice of $N$ cannot be made to suit all $x$ in the domain? Can someone clarify this for me? Here's a cute cat photo in return.

Anonymous

View Same Google iqdb SauceNAO Unbenannt.png, 61KiB, 953x825

Anonymous Tue 10 Sep 2019 21:05:37 No.10962333 Report

Quoted By:

Terry is into abstract art now

Anonymous

Anonymous Tue 10 Sep 2019 21:06:19 No.10962334 Report

Quoted By: >>10962438 >>10962458

>>10961640
Check Khan Academy too desu

Anonymous

Anonymous Tue 10 Sep 2019 21:06:24 No.10962336 Report

Quoted By:

>>10961630
>just like literally any computer system.
This is false.

>The only situation in which it will calculate an integral precisely is for a line
This is most likely false, as even basic numerical integration routines exactly calculate polynomials of certain degrees.
See eg. https://en.m.wikipedia.org/wiki/Simpson%27s_rule

>Otherewise, whether it's visible in the amount of digits or not, there will always be some error.
Also false. There might be no error due to you being lucky and depending on the display and calculator internals the error might very well be always visible.

>Keep in mind that the error is ridiculously small compared to the size of your answer.
This is generally false.
Numerical approximations can and do fail in many situations. Even very basic calculations can through elimination produce enormous errors.

Anonymous

Anonymous Tue 10 Sep 2019 21:09:40 No.10962342 Report

Quoted By: >>10962344 >>10962352

I just took the constructivist redpill. Don't think I can go back to seeing math the way I used to. I hope you guys enjoy your fantasy land. It's not for me anymore.

Anonymous

Anonymous Tue 10 Sep 2019 21:10:20 No.10962344 Report

Quoted By:

>>10962342
learn agda fag

Anonymous

Anonymous Tue 10 Sep 2019 21:12:39 No.10962352 Report

Quoted By: >>10966563 >>10971544

>>10962342
https://xenaproject.wordpress.com/
https://wwwf.imperial.ac.uk/~buzzard/one_off_lectures/msr.pdf

Anonymous

View Same Google iqdb SauceNAO 1427414066660.jpg, 12KiB, 255x217

Anonymous Tue 10 Sep 2019 21:15:31 No.10962360 Report

Quoted By: >>10963563 >>10963878

Say I have three bits of information:
the apple is red (1), round (2), and not rotten(3).

it can be written as 110 in terms of information where each bit represents a resolution of a yes or no "question" "is it red", "is it rotten" etc.

Is there a generalized Mathematical term for these "questions"?

Anonymous

View Same Google iqdb SauceNAO 1024px-George_Richmond_self-port (...).jpg, 131KiB, 1024x1024

Anonymous Tue 10 Sep 2019 21:52:23 No.10962438 Report

Quoted By: >>10962458

>>10962334
I have tried Khan academy but I got to be honest I really hate his voice and watching his vidfeos are boring as hell compared to reading

Also having to answer the questions in non-latex plain text is just not as nice to me as writing down and checking answer in the back of the book

Maybe I'm just too fucking gay and demanding but I really prefer books

Anonymous

Anonymous Tue 10 Sep 2019 22:00:53 No.10962458 Report

Quoted By:

>>10962438
>>10962334
I know what you mean I prefer books too, but I like KA because sometimes videos present the material in a different making it easier to understand. I think it is also a good way to grind exercises, before applying your knowledge to problems.

Anonymous

Anonymous Tue 10 Sep 2019 22:15:53 No.10962506 Report

Quoted By: >>10962526

>>10961640
Precalculus by Sheldon Axler is best

Anonymous

Anonymous Tue 10 Sep 2019 22:30:19 No.10962526 Report

Quoted By: >>10962574 >>10962622

>>10962506
What do you like in it ? I've ordered Precalculus in a Nutshell, it seems more straightforward.

Anonymous

Anonymous Tue 10 Sep 2019 22:53:46 No.10962574 Report

Quoted By: >>10962586

>>10962526
>why do you like it
Because he wrote it.
Axler has been shilling his linear algebra and the Springer GTM series for years now.

Anonymous

Anonymous Tue 10 Sep 2019 22:59:55 No.10962586 Report

Quoted By:

>>10962574
You just like the book because Axler wrote it ? Nothing more ?

Anonymous

Anonymous Tue 10 Sep 2019 23:09:03 No.10962606 Report

Quoted By:

I'm investigating vibration analysis with eigenvalues and eigenvectors. Can someone refer me examples of a spring-mass system in 2 dimensions? By 2 dimensions I mean the assume the masses are positioned in a plane, not a line and not in 3 dimensions.

Anonymous

Anonymous Tue 10 Sep 2019 23:15:52 No.10962622 Report

Quoted By:

>>10962526
Precalculus in a Nutshell is also a great book, but too brief, it's more like a quick review of the most important topics than a textbook that teaches everything you need to know from the ground up the way that Axler's book does. Still, Axler's book is half the number of pages of most precalc textbooks, and still does a great job of explaining everything. You can find both books on Libgen

Anonymous

View Same Google iqdb SauceNAO 3f403742b9272bf52b2c7abbcdfc91d5.jpg, 27KiB, 506x556

Anonymous Wed 11 Sep 2019 04:12:53 No.10963196 Report

Quoted By: >>10963350

>Wall-crossing

Anonymous

View Same Google iqdb SauceNAO 1501333971240.png, 162KiB, 500x464

Anonymous Wed 11 Sep 2019 05:51:27 No.10963350 Report

Quoted By: >>10963359

>>10963196
Dumb squidposter

Anonymous

Anonymous Wed 11 Sep 2019 05:54:59 No.10963359 Report

Quoted By:

>>10963350
>cohomogy

Anonymous

Anonymous Wed 11 Sep 2019 06:14:42 No.10963391 Report

Quoted By: >>10963564

>>10962325
Well. since you're considering the space of bounded functions, you know that the maximum pointwise difference between two functions must always be bounded. Using this, coupled with the fact that V is a complete vector space, you should be able to argue that the sup of this maximum variation must go to zero as n goes to infinity. At this point, you can just apply this maximum difference as a crude estimate that applies independent of x, but still goes to zero as n goes to infinity.

Anonymous

Anonymous Wed 11 Sep 2019 09:13:13 No.10963563 Report

Quoted By:

>>10962360
CS

Anonymous

View Same Google iqdb SauceNAO wnjo243usdg.jpg, 75KiB, 500x333

Anonymous Wed 11 Sep 2019 09:14:25 No.10963564 Report

Quoted By: >>10963645

>>10963391
I think I sort of get what you're saying, but still I could use some further clarification. What I'm trying to do is basically translate the claim regarding convergence in $B\left ( U,V \right )$ to a basic claim regarding uniform convergence. So now that $f$ has been defined as a pointwise limit of a Cauchy sequence, I'm trying to find $N$ s.t. $n>N$ implies $\left \| f_{n}(x)-f(x) \right \|<\varepsilon$ for a given $\varepsilon$ . Which $N$ would work here? What confuses me is that the inequality $\left \| f_{n}(x)-f(x) \right \|<\varepsilon$ holds whenever $n>N$ , but that $N$ may very well depend on the $x$ in question.
Here's another cat for you and anyone else willing to help.

Anonymous

Anonymous Wed 11 Sep 2019 10:33:27 No.10963645 Report

Quoted By: >>10963656

>>10963564
Well at one point, you do need to use the fact that $(f_n)$ is Cauchy with respect to the sup norm.
So far, you have only used the fact that it is pointwise Cauchy, but being sup-Cauchy is actually much stronger.
So start with $\varepsilon > 0$ , and let $N > 0$ such that, for each $m, n \ge N$ , $||f_m - f_n|| \le \varepsilon$ .
Now, for each x in U and all $m,n \ge N$ , we have $|f_m(x) - f_n(x)| \le \varepsilon$ .
Letting m go to infinity, we then get $|f(x) - f_n(x)| \le \varepsilon$ , for all x in U and $n \ge N$ .

Anonymous

View Same Google iqdb SauceNAO jfas12gas.jpg, 83KiB, 1024x834

Anonymous Wed 11 Sep 2019 10:51:58 No.10963656 Report

Quoted By:

>>10963645
That helped. Thanks anon, here's a cat for you.

Anonymous

View Same Google iqdb SauceNAO 1495439679013.jpg, 47KiB, 645x968

Anonymous Wed 11 Sep 2019 12:36:08 No.10963791 Report

Quoted By: >>10964144

53^1326 (mod 97)

Fermats little theorem:
53^96 = 1 (mod 97)

1326 = 96 x 13 + 78

53^1326 = 53^96x13 x 53^78 = (53^96)^13 x 53^78 mod 97

53^78 mod 97

now what? If I repeat the same theorem thing it just becomes 53^78 again(?)

Anonymous

Anonymous Wed 11 Sep 2019 13:24:08 No.10963876 Report

Quoted By: >>10963885 >>10963898 >>10963900 >>10964007 >>10964083 >>10965745

How do I prove that if a real sequence (Xn)_n has two limits, a and b, then a = b?

Anonymous

Anonymous Wed 11 Sep 2019 13:25:03 No.10963878 Report

Quoted By: >>10964395

>>10962360
The term in set theory and other such logical platforms is "proposition". In naive set theory at least, a set can be constructed from a proposition by taking all elements for which the proposition is true, and then one could do this for each proposition and then take the intersection of the sets. There are generally more restrictions on valid propositions and creating sets in non-naive set theories.

Anonymous

Anonymous Wed 11 Sep 2019 13:29:35 No.10963885 Report

Quoted By: >>10963914

>>10963876
I'm not a mathematician but that sounds like something that would follow from the axioms of the space/number system you are working with. Unless "real sequence" is one of those weird category theory things.

Anonymous

Anonymous Wed 11 Sep 2019 13:35:48 No.10963898 Report

Quoted By: >>10963900

>>10963876
specifically, well-ordering axioms possibly...

Anonymous

Anonymous Wed 11 Sep 2019 13:37:00 No.10963900 Report

Quoted By: >>10963935 >>10964015 >>10964050

>>10963876
Suppose $a \neq b$ are such that $x_n \to a, x_n \to b$ when $n \to \infty$ . Let $\varepsilon = \frac{|a - b|}{3}$ , and let $K_a, K_b \in \mathbb{N}$ be such that $|x_n - a| < \varepsilon$ when $n > K_a$ , and $|x_n - b| < \varepsilon$ when $n > K_b$ . Now, let $K$ be the larger of those threshold indices. What happens when $n > K$ ?

>>10963898
Separation axioms.

Anonymous

Anonymous Wed 11 Sep 2019 13:42:05 No.10963914 Report

Quoted By: >>10963942

>>10963885
Real sequence should just be than n -> R I think. My idea is to use delta-epsilon to find a limit for each one-hand side and somehow show that they the limits are equal to another

Anonymous

Anonymous Wed 11 Sep 2019 13:50:09 No.10963935 Report

Quoted By: >>10963950 >>10963988 >>10965751

>>10963900
I'm stupid so I have some questions. Why did you make epsilon = (|a-b|)/3, and what is K_a and K_b? And why make them elements of the natural numbers?

Anonymous

Anonymous Wed 11 Sep 2019 13:55:57 No.10963942 Report

Quoted By:

>>10963914
Follow the advice of the anon above and also note that if $\left | a-b \right |<\varepsilon$ for every $\varepsilon$ then $a=b$ .

Anonymous

Anonymous Wed 11 Sep 2019 13:59:27 No.10963950 Report

Quoted By: >>10963982 >>10964015

>>10963935
Those K's are indices, so they are natural numbers. x_1, x_2, ..., x_(K_a), and so on. Why divide by 3? Check what happens with that K.

Anonymous

Anonymous Wed 11 Sep 2019 14:22:50 No.10963982 Report

Quoted By: >>10963989 >>10964015

>>10963950
epsilon becomes bigger or equal to |x_n - a| and |x_n - b| ?

Anonymous

Anonymous Wed 11 Sep 2019 14:29:10 No.10963988 Report

Quoted By: >>10964015

>>10963935
If you do not draw something, you are probably not going to understand it.
The point of taking this value of epsilon is that if you take intervals of radius epsilon around a and b, then they are disjoint (anything smaller than |a-b|/2 would do).
But all terms of the sequence must eventually lie in both intervals simultaneously if it converges to both a and b, which is contradictory.

Anonymous

Anonymous Wed 11 Sep 2019 14:30:03 No.10963989 Report

Quoted By: >>10964015

>>10963982
$3\cdot \varepsilon = |a-b| = |a - x_n + x_n - b| \le |a- x_n| + |x_n - b| < \varepsilon + \varepsilon = 2\cdot \varepsilon$ .

Anonymous

View Same Google iqdb SauceNAO Capture+_2019-09-11-10-35-44.png, 121KiB, 1439x2281

Anonymous Wed 11 Sep 2019 14:39:08 No.10963997 Report

Quoted By: >>10964002 >>10964500 >>10964505

Does anyone know where I can find solutions for this book?

Anonymous

Anonymous Wed 11 Sep 2019 14:42:59 No.10964002 Report

Quoted By:

>>10963997
There may be no solutions manual out there. You can always try searching for solutions to specific problems.

Anonymous

Anonymous Wed 11 Sep 2019 14:45:48 No.10964007 Report

Quoted By: >>10964015 >>10964017 >>10964165

>>10963876
Because for any epsilon, there is an N1 for which for n > N1, |a - xn| < epsilon/2 and an N2 for which for n > N2, |a - xn| < epsilon/2.
Then for n > max(N1, N2), |a - b| <= |a - xn| + |xn - b| < epsilon.
Since epsilon was arbitrary, |a - b| = 0.

Anonymous

Anonymous Wed 11 Sep 2019 14:47:50 No.10964015 Report

Quoted By:

>>10963900
>>10963950
>>10963988
>>10963989
You're making this much more complicated than it needs to be. Stop confusing the dude.
>>10963982
Just look at >>10964007 , this proof is literally 2 lines.

Anonymous

Anonymous Wed 11 Sep 2019 14:48:50 No.10964017 Report

Quoted By:

>>10964007
Fuck, the N2 inequality should say |b - xn| < epsilon/2 of course.

Anonymous

Anonymous Wed 11 Sep 2019 14:57:34 No.10964038 Report

Quoted By: >>10964162 >>10968523

>>10961422
So it is true, yukariposter is a woman. Fascinating. I recall about last year asking you if gym is worth it and you told me its good and you go there with your bf. Either way, man or a woman, gay or straight you seem to know your shit. Thanks for your detailed replies on all of these threads, we're grateful.

Anonymous

Anonymous Wed 11 Sep 2019 14:58:00 No.10964040 Report

Quoted By:

is it even possible to do math on temperatures above 20Cº?

Anonymous

Anonymous Wed 11 Sep 2019 15:06:48 No.10964050 Report

Quoted By: >>10965752 >>10966585 >>10966965

>>10963900
what's with some /mg/ posters...
He's talking about real numbers, not some arbitrary topological space. The well-ordering axiom does what the separation axioms do for topological spaces and more. Not everything has to be general.

Anonymous

Anonymous Wed 11 Sep 2019 15:24:38 No.10964083 Report

Quoted By:

>>10963876
lim x_n - lim x_n = lim (x_n-x_n)=0, by the linearity of the limit operator.

Anonymous

View Same Google iqdb SauceNAO 1555323610562.jpg, 84KiB, 1080x1081

Anonymous Wed 11 Sep 2019 15:58:51 No.10964144 Report

Quoted By:

>>10963791
help

Anonymous

View Same Google iqdb SauceNAO yukari_(not cameron_diaz).png, 16KiB, 102x155

Anonymous Wed 11 Sep 2019 16:05:50 No.10964162 Report

Quoted By: >>10964235

>>10964038
I'm not the "I/we're not a 'he'" poster, but I appreciate your gratitude.

Anonymous

Anonymous Wed 11 Sep 2019 16:07:52 No.10964165 Report

Quoted By:

>>10964007
thanks!

Anonymous

Anonymous Wed 11 Sep 2019 16:31:47 No.10964235 Report

Quoted By:

>>10964162
girl (male)

Anonymous

View Same Google iqdb SauceNAO 1552784531311.jpg, 119KiB, 1080x1342

Anonymous Wed 11 Sep 2019 16:41:38 No.10964257 Report

Quoted By: >>10964287

I need a good lower bound for $\log_2 (1-x)$ for small $x \in [0,1)$ .

Any ideas?

Anonymous

Anonymous Wed 11 Sep 2019 16:55:30 No.10964287 Report

Quoted By: >>10964293 >>10964302

>>10964257
$ lim_{x \to 1^-} log_2(1-x) = lim_{x \to 1^-} log_2(0^+) = -\infty $

Anonymous

Anonymous Wed 11 Sep 2019 16:57:06 No.10964293 Report

Quoted By: >>10964295 >>10964299 >>10964302

>>10964287
I'm not sure what anon even wanted since that function is decreasing so maximum value is attained for x=0.

Anonymous

Anonymous Wed 11 Sep 2019 16:57:40 No.10964295 Report

Quoted By:

>>10964293
I think he meant for x close to 0

Anonymous

Anonymous Wed 11 Sep 2019 16:59:28 No.10964299 Report

Quoted By:

>>10964293
anon needs a lower bound for the codomain of his function
It's codomain is clearly $(-\infty; 0]$

Anonymous

View Same Google iqdb SauceNAO 1408868065493.jpg, 140KiB, 1024x974

Anonymous Wed 11 Sep 2019 16:59:50 No.10964302 Report

Quoted By: >>10964307 >>10964308 >>10964332 >>10964375

>>10964287
>>10964293
umm, let me be more specific. I need a simple function $f(x)$ such that $log_2(1-x) \geq f(x) \; \forall x \in [0,1)$ (or say, $\forall x \in [0, \frac12]$ or something) and is particularly accurate around 0.

Anonymous

Anonymous Wed 11 Sep 2019 17:01:58 No.10964307 Report

Quoted By: >>10964319

>>10964302
f(x)=x

Anonymous

Anonymous Wed 11 Sep 2019 17:02:12 No.10964308 Report

Quoted By:

>>10964302
how simple are we talking?
$f(x) = log_2(1-x) - 1$
would do the job

Anonymous

Anonymous Wed 11 Sep 2019 17:02:24 No.10964309 Report

Quoted By: >>10964472

>>10960662
>2019
>still using expressions like "dependent variable"
rly ?

Anonymous

Anonymous Wed 11 Sep 2019 17:04:30 No.10964319 Report

Quoted By:

>>10964307
this is not even true, lmao

Anonymous

Anonymous Wed 11 Sep 2019 17:08:21 No.10964332 Report

Quoted By:

>>10964302
$-x-\frac{x^2}{c}$ will do the trick for any c > 0

Anonymous

Anonymous Wed 11 Sep 2019 17:21:02 No.10964375 Report

Quoted By:

>>10964302
why do you even ask for this? it seems so weird
what are you trying to solve

Anonymous

Anonymous Wed 11 Sep 2019 17:23:46 No.10964382 Report

Quoted By: >>10964391 >>10964400 >>10964435 >>10964452

what is the correct way of computing equations like
a^-3=8 ?

Anonymous

Anonymous Wed 11 Sep 2019 17:26:46 No.10964391 Report

Quoted By: >>10964422

>>10964382
don't kids do this in elementary school?
I'm not judging you anon, you've got plenty of time to learn

Anonymous

Anonymous Wed 11 Sep 2019 17:28:24 No.10964395 Report

Quoted By:

>>10963878
Thank you

Anonymous

Anonymous Wed 11 Sep 2019 17:29:27 No.10964400 Report

Quoted By:

>>10964382
take log with base a on both sides
if you have no idea what I'm talking about, feel free to ask

Anonymous

Anonymous Wed 11 Sep 2019 17:37:32 No.10964422 Report

Quoted By: >>10964426

>>10964391
okay maybe something easier for you because the previous one was too hard
1+a=3

Anonymous

Anonymous Wed 11 Sep 2019 17:38:21 No.10964426 Report

Quoted By:

>>10964422
a=2

Anonymous

Anonymous Wed 11 Sep 2019 17:41:53 No.10964435 Report

Quoted By:

>>10964382
plug it into wolframalpha

Anonymous

Anonymous Wed 11 Sep 2019 17:50:01 No.10964452 Report

Quoted By:

>>10964382
That implies $a^3=\frac{1}{8}$ , which has one solution over $\mathbf{R}$ , and three solutions over $\mathbf{C}$ . No logarithms required.

Anonymous

Anonymous Wed 11 Sep 2019 18:00:13 No.10964472 Report

Quoted By:

>>10964309
it's actually really common in experimental physics and just about any of the natural sciences, not everyone in the world is a mathematician

Anonymous

Anonymous Wed 11 Sep 2019 18:08:44 No.10964488 Report

Quoted By: >>10964522 >>10964626 >>10964754 >>10966541

Could someone offer some intuition regarding the second countability requirement for a topological space to be a manifold. The Hausdorff condition and the space being locally euclidean are much more easily motivated, non-Hausdorff spaces are a bit unnatural in a lot of ways, one of them being the possibility of a sequence in the space to have multiple limits and such. Also if the space is locally euclidean you can sort of "locally do analysis" in R^n which is nice since a lot of theory has been developed in analysis on R^n. But why the second countability? I cannot really offer a satisfying reason why would one add that requirement to the construction. Anyone got any ideas?

Anonymous

Anonymous Wed 11 Sep 2019 18:15:33 No.10964500 Report

Quoted By: >>10964505 >>10965155

>>10963997
>Shlomo Sternberg
literally the most jewish name in existence

Anonymous

Anonymous Wed 11 Sep 2019 18:17:55 No.10964505 Report

Quoted By: >>10965155

>>10963997
>>10964500
yeah.. pretty sure that book just gets memed because of the name..

Anonymous

Anonymous Wed 11 Sep 2019 18:27:58 No.10964522 Report

Quoted By: >>10964754

>>10964488
Consider S1 times an aleph one set with the discrete topology.
Absolutely great manifold, innit?

Anonymous

Anonymous Wed 11 Sep 2019 19:07:45 No.10964626 Report

Quoted By:

>>10964488
It ensures that your space is of "reasonable" size.
Iirc, you need second-countability to define partitions of unity for any open cover, which are very handy tools to do all sorts of constructions (typically gluing local data)

Anonymous

Anonymous Wed 11 Sep 2019 19:50:10 No.10964754 Report

Quoted By:

>>10964488
check out the prufer manifold
>>10964522
someone could say that's not too bad: just a lot of disconnected copies of S1. Also S1 x (countable set with discrete topology) is not much better, and satisfies 2nd countability.

Anonymous

View Same Google iqdb SauceNAO 1564813032186.png, 1MiB, 1092x1080

Anonymous Wed 11 Sep 2019 20:50:53 No.10964970 Report

Quoted By: >>10965562

I don't know why, but for some reason I find it extremely pleasant that there is an isomorphism $H_*^G( *, M) \cong H_*(G, M)$ for any $G$ -module $M$ . Is this sensation what people refer to when they speak of mathematical beauty?

Anonymous

Anonymous Wed 11 Sep 2019 20:54:32 No.10964975 Report

Quoted By:

Choosing thesis subjects is hard when you have no hard loyalties anywhere.

Anonymous

Anonymous Wed 11 Sep 2019 21:47:30 No.10965155 Report

Quoted By: >>10965488 >>10965584

>>10964500

>>10964505

Do you guys think I should continue reading it? If not, are there any better books for multivariable/vector calc?

Anonymous

Anonymous Wed 11 Sep 2019 23:37:38 No.10965488 Report

Quoted By:

>>10965155
Munkres Analysis on Manifolds is the best

Anonymous

Anonymous Wed 11 Sep 2019 23:44:09 No.10965515 Report

Quoted By: >>10965566

How do I find the number of odd ,4th order permutations in the symmetric group 6.

Anonymous

Anonymous Wed 11 Sep 2019 23:56:17 No.10965562 Report

Quoted By: >>10972589

>>10964970
>mathematical beauty
This is a meaningless notion.

Anonymous

Anonymous Wed 11 Sep 2019 23:57:19 No.10965566 Report

Quoted By: >>10965585

>>10965515
>How do I find the number of odd ,4th order permutations in the symmetric group 6.
What have you tried?

Anonymous

View Same Google iqdb SauceNAO 81SXgQ+oFyL.jpg, 313KiB, 1398x1985

Anonymous Thu 12 Sep 2019 00:02:13 No.10965584 Report

Quoted By:

>>10965155
>If not, are there any better books for multivariable/vector calc?

Anonymous

Anonymous Thu 12 Sep 2019 00:02:50 No.10965585 Report

Quoted By: >>10966188

>>10965566
I know that the only kind of permutations that satisfy this condition are permutations like (abcd) (that affect 4 elements and keep 2 of them fixed)
I don't know how to quantify the number of these however.

Anonymous

Anonymous Thu 12 Sep 2019 00:56:06 No.10965745 Report

Quoted By:

>>10963876
If a =/= b, |x - y| =/= 0. Let this distance be ?, and consider the intervals (x - ?/2, x + ?/2) and (y - ?/2, y + ?/2). these sets are disjoint. Now there exist N, M natural numbers such that for every n > max(N,M), xn is in both of these open intervals, which is impossible.

Generally, a sequence in a Hausdorff (or even T1) space will converge to a unique point if it converges at all.

Anonymous

Anonymous Thu 12 Sep 2019 01:00:54 No.10965751 Report

Quoted By:

>>10963935
>And why make them elements of the natural numbers?
Read the definition of sequence convergence

Anonymous

Anonymous Thu 12 Sep 2019 01:03:28 No.10965752 Report

Quoted By:

>>10964050
>The well-ordering axiom does what the separation axioms do for topological spaces and more
What do you mean?
>Not everything has to be general.
What's so general about what he provided?

Anonymous

View Same Google iqdb SauceNAO stbonifacecollege2.jpg, 32KiB, 600x372

Anonymous Thu 12 Sep 2019 02:54:54 No.10966026 Report

Quoted By: >>10967817

Ok /mg/, two questions.

1. I was allowed to take a lower form of multivariable calculus for my degree, but I know the prof is shit so I want to read a textbook alongside the course. I really want to make sure I get the theory more than anything. Any recommendations?
>The course is intended for students in mathematically rich disciplines. Parametric curves, arc length and curvature. Functions of several variables. Level curves. Partial derivatives, gradient, divergence and curl. Max/min problems. Double and triple integrals, line and surface integrals of functions and vector fields, and applications. Green's, Stokes, and divergence theorems.

2. Are there any fields of pure math left where an undergrad student could do any semi-meaningful research. It could be a nearly trivial result.

Anonymous

Anonymous Thu 12 Sep 2019 03:58:41 No.10966188 Report

Quoted By:

>>10965585
This is just combinatorics at this point. How many ways are there to seat 4 people at a circular table from among 6 people?

Anonymous

Anonymous Thu 12 Sep 2019 07:09:30 No.10966541 Report

Quoted By:

>>10964488
The way I see it, it fulfills the same function as compactness does to metric spaces in real analysis. It ensures that the space is not crazy big.

Anonymous

Anonymous Thu 12 Sep 2019 07:26:35 No.10966563 Report

Quoted By:

>>10962352
Kevin "this would be easy in ZFC" Buzzard

Anonymous

Anonymous Thu 12 Sep 2019 07:46:41 No.10966585 Report

Quoted By:

>>10964050
>The well-ordering axiom does what the separation axioms do for topological spaces and more
dude what the fuck are you talking about, the well-ordering principle has literally nothing to do with R being hausdorff

Anonymous

Anonymous Thu 12 Sep 2019 11:52:54 No.10966837 Report

Quoted By: >>10967170

What is one book that if I read I'd be able to mogg 99% of mathfags?

Anonymous

Anonymous Thu 12 Sep 2019 13:07:59 No.10966965 Report

Quoted By:

>>10964050
>The well-ordering axiom does what the separation axioms do for topological spaces and more.
What the fuck are you saying man?

Anonymous

View Same Google iqdb SauceNAO 1567533871677.png, 821KiB, 1920x1080

Anonymous Thu 12 Sep 2019 13:37:44 No.10966998 Report

Quoted By: >>10967183

>>10961640
If you failed high school I'm going to assume you failed algebra. Start with, "Algebra by I
M. Gelfand". "Basic Mathematics", requires a knowledge in a few high school level maths to read.

Anonymous

View Same Google iqdb SauceNAO 444.jpg, 88KiB, 1201x626

Anonymous Thu 12 Sep 2019 13:56:05 No.10967023 Report

Quoted By: >>10967026 >>10967033

These are both integrals of the same thing.
How is it justified that they follow different paths depending on whether you opened the brackets before integrating or not?

Anonymous

Anonymous Thu 12 Sep 2019 13:59:59 No.10967026 Report

Quoted By:

>>10967023
+c

Anonymous

Anonymous Thu 12 Sep 2019 14:02:59 No.10967033 Report

Quoted By:

>>10967023
They are both antiderivatives of h, but they assume different values at 0, hence they differ by a constant. One curve is a translate of the other by 1/6 in the y-direction

Anonymous

Anonymous Thu 12 Sep 2019 14:08:05 No.10967042 Report

Quoted By: >>10967047

>>10961072
>>10961422
Wait wait wait so the physics 2hu anon is also the not a "he" anon? Big if true
Are you a "she", or something else? Cis or trans?

Anonymous

Anonymous Thu 12 Sep 2019 14:11:58 No.10967047 Report

Quoted By:

>>10967042
He's a fat chinese gay man.

Anonymous

Anonymous Thu 12 Sep 2019 14:16:49 No.10967060 Report

Quoted By: >>10967072

When one tries to determine all the solutions in the positive integers of a certain Diophantine equation and you got the general formula for x and y, how do I determine the range so that that x and y becomes positive?

Anonymous

Anonymous Thu 12 Sep 2019 14:20:50 No.10967066 Report

Quoted By: >>10967067 >>10967083

whats the deal with commutative algebra?

Anonymous

Anonymous Thu 12 Sep 2019 14:22:11 No.10967067 Report

Quoted By:

>>10967066
Take a ring, assume it is commutative, and proceed.

Anonymous

Anonymous Thu 12 Sep 2019 14:23:01 No.10967072 Report

Quoted By:

>>10967060
Nvm, I did a mistake which made me doubt everything, I figured it all out. :)

Anonymous

Anonymous Thu 12 Sep 2019 14:27:19 No.10967079 Report

Quoted By: >>10967082 >>10967083 >>10967170 >>10968827

how do you think about rings, ideals, etc...
apparently thinking of integers is a bad idea

Anonymous

Anonymous Thu 12 Sep 2019 14:28:41 No.10967082 Report

Quoted By:

>>10967079
purely think about their associated properties and the hierarchy between them

Anonymous

Anonymous Thu 12 Sep 2019 14:29:14 No.10967083 Report

Quoted By: >>10967090

>>10967066
>>10967079
geometry

Anonymous

Anonymous Thu 12 Sep 2019 14:32:57 No.10967090 Report

Quoted By: >>10967137

>>10967083
what do you mean?

Anonymous

Anonymous Thu 12 Sep 2019 15:06:33 No.10967137 Report

Quoted By:

>>10967090
commutative algebra is dual to (affine) algebraic geometry. On the geometric side almost all concepts from CA have a simple intuitive description. However, the theorems that say that your geometric intuition is well-founded are generally easier to prove in terms of commutative algebra. Studying one without the other is fruitless imo.

Anonymous

Anonymous Thu 12 Sep 2019 15:25:05 No.10967170 Report

Quoted By:

>>10966837
Villani's brick on optimal transport.
>>10967079
Ye.
If someone says "commutative domain", think Z[x].

Anonymous

View Same Google iqdb SauceNAO geljew.png, 72KiB, 506x831

Anonymous Thu 12 Sep 2019 15:30:08 No.10967183 Report

Quoted By: >>10967198 >>10967321

>>10966998
I think due to highly positive Amazon reviews that book is fairly good, but I've tried it and I couldn't wrap my head around his method of counting and so on. Even tho it's elementary it feels like number theory for highschoolers to me it's hard as fuck

Anonymous

Anonymous Thu 12 Sep 2019 15:37:05 No.10967198 Report

Quoted By:

>>10967183
Just keep trying and take breaks anon, sure you can do it. You can skip it if you need to. That part is not really needed for the rest of the book.

Anonymous

Anonymous Thu 12 Sep 2019 16:51:33 No.10967321 Report

Quoted By:

>>10967183
fun problem

Marry, Fuck, Kill

View Same Google iqdb SauceNAO berns.jpg, 3KiB, 125x125

Marry, Fuck, Kill Thu 12 Sep 2019 18:22:35 No.10967560 Report

Quoted By: >>10967609 >>10967824 >>10968371

Marry, Fuck, Kill, operator topology edition.

Your options:

Norm, Strong, Weak

Anonymous

Anonymous Thu 12 Sep 2019 18:37:06 No.10967609 Report

Quoted By:

>>10967560
Marry norm, fuck ultrastrong, kill strong.

Anonymous

Anonymous Thu 12 Sep 2019 20:00:07 No.10967817 Report

Quoted By: >>10968122

>>10966026
>I really want to make sure I get the theory more than anything
With the exception of a few theorems like Stokes (which rely on the theory of differential forms to really explain properly, and aren't proved in calculus courses anyway), the "theory" behind multivariable calculus is almost trivial. It's all just extensions of tools you already developed in single-variable calc. There's nothing mechanically new in the course; what's new are the concepts, so it's better to focus your effort on taking the time to actually grasp the geometric intuition of what you're doing.

>Are there any fields of pure math left where an undergrad student could do any semi-meaningful research. It could be a nearly trivial result.
Almost all of them, honestly, as long as your standards for "semi-meaningful" aren't too high.
Unless you are prodigiously talented, you aren't going to be able to produce independent research as an undergrad, but the majority of profs have some small research projects sitting around that are accessible to moderately talented 3rd/4th year students. If you're very lucky you might get a paper out of one of those but it's more realistic to expect that you'll spend a semester proving one lemma in your professor's paper or collecting computational data. Still great to have research experience if you want to grad school, and pretty often you even get paid for it.

Anonymous

Anonymous Thu 12 Sep 2019 20:03:18 No.10967824 Report

Quoted By:

>>10967560
Marry weak, fuck norm, kill strong.

Anonymous

Anonymous Thu 12 Sep 2019 20:28:19 No.10967884 Report

Quoted By: >>10969071

Can someone explain to me what are benefits of representing numbers as continued fractions ?

Anonymous

Anonymous Thu 12 Sep 2019 22:25:04 No.10968122 Report

Quoted By:

>>10967817
Thanks, that's really helpful. By semi-meaningful, I just meant non-trivial or better, so yeah, lemmas are cool, I'm down for that. I heard that the one pure math prof is starting to do some new research so I think I'll go talk to him about that.

Anonymous

View Same Google iqdb SauceNAO 1552668356179.png, 29KiB, 293x349

Anonymous Thu 12 Sep 2019 22:33:37 No.10968141 Report

Quoted By:

I had a job interview today for a money changing Travel company.

Only realised earlier I was supposed to multiply all the conversions and not divide and I've fucked it all.

Anonymous

View Same Google iqdb SauceNAO 6C495BA9-C2FE-4D7C-A99E-E23C1D75 (...).png, 655KiB, 1125x2436

Anonymous Thu 12 Sep 2019 23:44:19 No.10968272 Report

Quoted By: >>10968308 >>10968321 >>10968446 >>10969071

Can anyone explain how EM is equal to $[EA|EB]$
This is from Artin’s first chapter on matrices.
E is supposed to be elementary matrix so if author is multiplying with M which is $(m)x(n+1)$ in dimension then E must be $(mxm)$ . But how is he making a block inside with A being mxn and B being nx1

Anonymous

Anonymous Fri 13 Sep 2019 00:06:05 No.10968306 Report

Quoted By: >>10968321

>>10960203
Saved and thanks, anon.

Anonymous

Anonymous Fri 13 Sep 2019 00:06:39 No.10968308 Report

Quoted By: >>10968367

>>10968272
can anyone verify B’s dimension should be mx1

Anonymous

Anonymous Fri 13 Sep 2019 00:16:44 No.10968321 Report

Quoted By:

>>10968306
Will do better than saving meme and laughing at it? Like answer this person’s question?
>>10968272

Anonymous

Anonymous Fri 13 Sep 2019 00:37:19 No.10968359 Report

Quoted By: >>10968446 >>10970975

How rough is linear algebra? I got an A in all my calculus classes so far and I need to take linear and differential equations in order to transfer to a university.

Anonymous

Anonymous Fri 13 Sep 2019 00:46:20 No.10968367 Report

Quoted By:

>>10968308
Verified.

Anonymous

View Same Google iqdb SauceNAO yukari_twists_okina's_k-groups.jpg, 967KiB, 1296x1032

Anonymous Fri 13 Sep 2019 00:52:22 No.10968371 Report

Quoted By: >>10968767

>>10967560
Marry weak, kill strong and fuck Mackey

Anonymous

View Same Google iqdb SauceNAO matrix.png, 33KiB, 895x779

Anonymous Fri 13 Sep 2019 01:29:08 No.10968446 Report

Quoted By:

>>10968359
p easy

>>10968272
B is just the vector of results, and you need a result for every equation. think of it like every row is something to the effect of:
3x+5y+8z=9
4x-2y+z=0
x+0y-z=2
is the pic attached, A is the matrix [(3,5,8);(4,2,1);(1,0,-1)] and (9,0,2) is B.

Anonymous

Anonymous Fri 13 Sep 2019 01:55:54 No.10968496 Report

Quoted By:

dont u think the dimension of B mentioned shout be mx1?
A is mxn. X should be nx1 so B must be mx1. Is it not a typo?

Anonymous

Anonymous Fri 13 Sep 2019 02:13:19 No.10968523 Report

Quoted By: >>10968645 >>10974392

>>10964038
yukari is a well known tranny and attention whore, most of (her?) comments are not useful and are generally just attention posts. Don't encourage her.

Anonymous

Anonymous Fri 13 Sep 2019 03:05:24 No.10968645 Report

Quoted By:

>>10968523
>her

Anonymous

View Same Google iqdb SauceNAO 1568286870161.png, 1MiB, 1140x4777

Anonymous Fri 13 Sep 2019 03:15:31 No.10968678 Report

Quoted By: >>10968686 >>10969250 >>10969271 >>10970083 >>10971555

>>10960172
day 1: i just realized my plan before of math history is unironically way harder than pic related, so i am switching to it. it's about time someone finally went through the entire thing. apart from documenting everyday i will also post here whenever i finish a book.

Anonymous

Anonymous Fri 13 Sep 2019 03:19:01 No.10968686 Report

Quoted By:

>>10968678
o yeah btw, in case you guys are wondering, i have the original website where the meme spam image was posted. the first book in the series i am working on going through is zorich's analysis because the original russian dude who proposed this curriculum gave it as recommended

Anonymous

Anonymous Fri 13 Sep 2019 04:07:53 No.10968767 Report

Quoted By: >>10968828

>>10968371
>fuck Mackey
who?

Anonymous

View Same Google iqdb SauceNAO 9781498717496.jpg, 26KiB, 411x648

Anonymous Fri 13 Sep 2019 04:10:46 No.10968768 Report

Quoted By:

Quickly: Need a topic in number theory suitable for an undergraduate honour's project (30-40 pages)

Anonymous

Anonymous Fri 13 Sep 2019 05:13:13 No.10968827 Report

Quoted By:

>>10967079
It depends on the king of ring your looking at. General rings are too broad to have an all-encompassing example for, in the same way that topological spaces are too broad to imagine a "generic" space. Commutative rings I pretty much always think of as quotients of polynomial rings over Z or a field.

Anonymous

View Same Google iqdb SauceNAO yukari_impressed.png, 97KiB, 314x215

Anonymous Fri 13 Sep 2019 05:14:58 No.10968828 Report

Quoted By: >>10970170

>>10968767
https://en.wikipedia.org/wiki/Mackey_topology

Anonymous

Anonymous Fri 13 Sep 2019 09:15:42 No.10969071 Report

Quoted By:

>>10967884
Making explicit the sequence of good/best rational approximations.

>>10968272
It's effectively by definition, really.

If A is a matrix (say 3 by 3) and B (say 3 by 10), then computing A·B (via the definition of the matrix product) amounts to taking all 10 columns of B as vectors, and applying A to each of them.

Anonymous

View Same Google iqdb SauceNAO Screen Shot 2019-09-13 at 11.48.46.png, 79KiB, 393x503

Anonymous Fri 13 Sep 2019 09:54:06 No.10969101 Report

Quoted By:

I'm interested in the fixed points of the exponential function.
We have $\exp(i \pi/2) = i$ and of course $\exp(i \pi/2 + d) = i \cdot \exp(d)$ , so they repeat.
Are there other interesting points than these?

Also, I tried looking at it via a plot (absolute value, though). Is there a way in which I can parametrize that curve? I.e.
$t\mapsto \gamma (t)$ such that $|\exp( \gamma(t) )| = |\gamma(t)|$ . That might be the same as $\exp( \gamma(t)*\cdot \gamma(t) ) = \gamma(t)*\cdot \gamma(t)$

And then maybe even without the absolute value.

Anonymous

View Same Google iqdb SauceNAO Screen Shot 2019-09-13 at 11.55.15.png, 108KiB, 623x572

Anonymous Fri 13 Sep 2019 09:55:46 No.10969103 Report

Quoted By: >>10969159

I'm interested in the fixed points of the exponential function.
We have
$\exp(i \pi/2) = i$
and of course
$\exp(i \pi/2 + d) = i \cdot \exp(d)$ ,
so they repeat.
Are there other interesting points than these?

Also, I tried looking at it via a plot (absolute value, though). Is there a way in which I can parametrize that curve? I.e.
$t\mapsto \gamma (t)$
such that
$|\exp( \gamma(t) )| = |\gamma(t)|$

That might be the same as
$\exp( \gamma(t)^*\cdot \gamma(t) ) = \gamma(t)*\cdot \gamma(t)$ .

And then maybe even without the absolute value.

Anonymous

Anonymous Fri 13 Sep 2019 09:57:17 No.10969106 Report

Quoted By:

I meant

$\exp( \gamma(t)^* + \gamma(t) ) = \gamma(t)^* \, \cdot\, \gamma(t)$

Anonymous

Anonymous Fri 13 Sep 2019 09:58:37 No.10969109 Report

Quoted By:

I meant

$\exp( \gamma(t)^* + \gamma(t) ) = \gamma(t)^* \, \cdot\, \gamma(t)$

and whether the pi/2 is in the exp or not is not too important to me

Anonymous

Anonymous Fri 13 Sep 2019 10:36:25 No.10969159 Report

Quoted By: >>10969161

>>10969103
0 is the only fixed point of exp

Anonymous

Anonymous Fri 13 Sep 2019 10:37:28 No.10969161 Report

Quoted By:

>>10969159
nvm

Anonymous

Anonymous Fri 13 Sep 2019 11:16:04 No.10969191 Report

Quoted By: >>10969203 >>10969208 >>10969233

Ok I'm bad at proof but I think I managed to make one that holds - please tell me if does or not:

to prove:
Establish the statement: Every integer of the form n^4 + 4 with n > 1, is composite.

My proof:
Since n^4 + 4 = (n^2)^2 + 2^2 , and (n^2)^2 and 2^2 is both always even, then (n^2)^2 + 2^2 is always even too. Since it is always even, you can always divide it by 2, and must thus be composite. (2 is an even prime but the formula can never be 2).

Anonymous

Anonymous Fri 13 Sep 2019 11:20:44 No.10969203 Report

Quoted By: >>10969207 >>10969208

>>10969191
3^4 is not even

Anonymous

Anonymous Fri 13 Sep 2019 11:23:47 No.10969207 Report

Quoted By: >>10969213

>>10969203
fuck. but 9 is it divisor, so it's not a prime? i guess i could go from there

Anonymous

Anonymous Fri 13 Sep 2019 11:24:50 No.10969208 Report

Quoted By: >>10969224

>>10969191
As anon >>10969203 said, there is a gap in your reasoning.
Maybe try using induction. The base step is easy to check:
If $n=2$ then $n^{4}+4=2^{4}+4=20$ which is composite. Now assume this holds for some $n>2$ and proceed from there.

Anonymous

Anonymous Fri 13 Sep 2019 11:25:39 No.10969213 Report

Quoted By: >>10969224

>>10969207
I don't know. My first guess would be induction, but it doesn't look completely straight forward

Anonymous

Anonymous Fri 13 Sep 2019 11:31:10 No.10969224 Report

Quoted By: >>10969227 >>10969229

>>10969208
>>10969213
Okay, what about:

Since (n^2)^2 and 4 always have a divisor (n^2 and 2) that is something else than 1 or itself, and the sum of two values that are divisible is also divisble by something else other than 1 and itself, n^4 + 4 is composite

Anonymous

Anonymous Fri 13 Sep 2019 11:33:20 No.10969227 Report

Quoted By:

>>10969224
fuck that is not even true. reeee

Anonymous

Anonymous Fri 13 Sep 2019 11:34:07 No.10969229 Report

Quoted By: >>10969231

>>10969224
You have to prove that they have a common divisor (other than 1). You're claiming that since a is composite and b is composite, then a+b is composite, which isn't necessarily true. Look for example at 10+9=19, both 10 and 9 are composite but 19 isn't.

Anonymous

Anonymous Fri 13 Sep 2019 11:35:40 No.10969231 Report

Quoted By:

>>10969229
yeah i just realized

Anonymous

Anonymous Fri 13 Sep 2019 11:37:48 No.10969233 Report

Quoted By: >>10969247

>>10969191
Try completing the square, i.e $n^{4}+4=(n^2+2)^{2}-...$

Anonymous

Anonymous Fri 13 Sep 2019 11:51:06 No.10969247 Report

Quoted By: >>10969251

>>10969233
-((4n)^(1/2))^2, but so what? I cant see what to do from here

Anonymous

Anonymous Fri 13 Sep 2019 11:51:56 No.10969250 Report

Quoted By: >>10969564

>>10968678
That would be an interesting experiment, maybe you should make a blog if you're really serious about it, instead of posting on 4chan, where the messages are eventually going to disappear.

Anonymous

Anonymous Fri 13 Sep 2019 11:51:59 No.10969251 Report

Quoted By: >>10969261

>>10969247
Notice what you get by completing the square is a difference of squares.

Anonymous

Anonymous Fri 13 Sep 2019 12:01:08 No.10969261 Report

Quoted By: >>10969265 >>10969267

>>10969251
oh, so a difference between two squares is always composite? why? because x^2+y^2 = (x+y)(x-y) (unless x-y = 1), but i dont see why they neccessarily are composite

Anonymous

Anonymous Fri 13 Sep 2019 12:02:14 No.10969265 Report

Quoted By:

>>10969261
x^2-y^2* ofc

Anonymous

Anonymous Fri 13 Sep 2019 12:03:03 No.10969267 Report

Quoted By: >>10969268 >>10969445

>>10969261
$x^{2}-y^{2}$ is always composite (assuming x,y are integers), because it is equal to a product of two integers.

Anonymous

Anonymous Fri 13 Sep 2019 12:03:40 No.10969268 Report

Quoted By: >>10969270

>>10969267
oh. yea, ofc. lol, thx :)

Anonymous

Anonymous Fri 13 Sep 2019 12:04:15 No.10969270 Report

Quoted By:

>>10969268
No problem anon, we're here to help and encourage.

Anonymous

Anonymous Fri 13 Sep 2019 12:04:53 No.10969271 Report

Quoted By:

>>10968678
dude, if you actually manage to go through one of these meme guides and you document it, you will be the absolute hero of /sci/ and /mg/, trust me

Anonymous

Anonymous Fri 13 Sep 2019 12:46:13 No.10969308 Report

Quoted By: >>10969807

Is Anki good for learning maths?

Anonymous

Anonymous Fri 13 Sep 2019 12:56:29 No.10969318 Report

Quoted By: >>10969334 >>10969499

I want to solve a very large, very sparse system of linear equations Ax=b, where A's entries are either 0 or 1. How can I exploit this fact to solve the system faster?

Anonymous

Anonymous Fri 13 Sep 2019 13:07:21 No.10969334 Report

Quoted By: >>10970834

>>10969318
>very large
What size are we talking here?

>How can I exploit this fact to solve the system faster?
The sparsity can be exploited by using an appropriate data format.
Together with a decent enough iterative solver, BiCgStab is a commonly used one, you should be able to approximate your solution.
The chance is also pretty good that it's condition number is rather small.

>A's entries are either 0 or 1
I do not think that it can be exploited that it has just 1 as non-zero entries. You might get to save a single floating point computation per iteration per matrix element, but the effort of optimizing is most likely not worth it.

Anonymous

Anonymous Fri 13 Sep 2019 14:36:24 No.10969445 Report

Quoted By: >>10969538

>>10969267
> because it is equal to a product of two integers
One of those integers might be 1. In fact, every odd number (prime or composite) can be written as the difference of consecutive squares. If x=2k+1, (k+1)^2-k^2=x. So you need to exclude this.

In this case, n^4+4
=(n^2+2)^2-(2n)^2
=(n^2-2n+2)(n^2+2n+2)
=((n-1)^2+1)((n+1)^2+1)
This is composite provided that neither factor is 1. The first factor is 1 iff n=1, the second iff n=-1. So both factors are >1 (and thus n^4+4 is composite) if n>1.

Anonymous

Anonymous Fri 13 Sep 2019 15:10:57 No.10969499 Report

Quoted By: >>10969571

>>10969318
Reduced row echelon matrix?
Read Artin frist chapter

Anonymous

Anonymous Fri 13 Sep 2019 15:33:23 No.10969538 Report

Quoted By:

>>10969445
You're right, but if applied to the problem at hand the method yields the correct result because it forces both factors to be different than 1.

Anonymous

Anonymous Fri 13 Sep 2019 15:36:38 No.10969543 Report

Quoted By: >>10969582 >>10969589 >>10969729

How important would you guys say is Sylow theory in field and Galois theory? I find it pretty tedious and I'm willing to skip it if it's not necessary to produce results in Galois theory. I'm doing calculations of Galois groups of fields right now and so far I didn't need any Sylow theorems, not even once. So can I skip it for now?

Anonymous

Anonymous Fri 13 Sep 2019 15:54:10 No.10969564 Report

Quoted By: >>10969568 >>10969688

>>10969250
oh i totally am. though i wont post it till i get passed some of the more babby bits cause i dont want to out myself as some plebian

Anonymous

Anonymous Fri 13 Sep 2019 15:57:58 No.10969568 Report

Quoted By: >>10969688

>>10969564
Wouldn't that take years? Like, 10 or more? I'm 4 years into properly learning math and I'm still waaay of.

Anonymous

Anonymous Fri 13 Sep 2019 16:01:40 No.10969571 Report

Quoted By:

>>10969499
>Reduced row echelon matrix?
Lol.
Using Gauß is retarded, learn numerical linear algebra.

Anonymous

Anonymous Fri 13 Sep 2019 16:11:40 No.10969582 Report

Quoted By:

>>10969543
i'm pretty sure you can skip it

Anonymous

Anonymous Fri 13 Sep 2019 16:16:09 No.10969589 Report

Quoted By:

>>10969543
Idk, Sylow theory is obviously relevant to the study of finite groups in general. If you are trying to list the subgroups of a finite group (to find intermediate extensions), then you might be interested in knowing the Sylow subgroups and how many there are. But obviously, this is only interesting if you are working with relatively large complicated groups

Anonymous

Anonymous Fri 13 Sep 2019 17:14:22 No.10969688 Report

Quoted By: >>10969743

>>10969564
I think making some kind of journal where you document everything math related you do, even the less important thing, could be beneficial to you so that you can see what progress you've made.
You don't have to go into the details, but make sure you write what you do each day, your thoughts, remarks, copy part of articles you find interesting etc. I'm thinking about doing something like that myself.

>>10969568
How old are you ? I wasn't interested in math in high school, but I started to look into it 2 years ago without ever taking a serious commitment to learn it. I really got into it a few weeks ago but it's kinda depressing to think that I've lost two years of learning (I'm 21 btw), but eh better late than never I guess.

Anonymous

Anonymous Fri 13 Sep 2019 17:29:50 No.10969724 Report

Quoted By:

>>10960933
Why is it always high-energy physics

Anonymous

Anonymous Fri 13 Sep 2019 17:30:54 No.10969729 Report

Quoted By:

>>10969543
Knowing the basic too Sylow theorems and their applications is essential to study finite fields.

Anonymous

Anonymous Fri 13 Sep 2019 17:34:41 No.10969743 Report

Quoted By: >>10969782

>>10969688
I'm 26, soon to be 27. I couldn't go to uni after highschool because we were broke and I had to find work. I did learn a solid bunch of math during that time, so as I started uni in 22 I didn't really have that much trouble with the uni work. I'm doing masters now, I'm primarily focused on commutative algebra and algebraic geometry.

It takes a lot of work, you really have to learn and relearn the material a lot of times. I went through 5 different books on algebra for example. Only after a couple of reruns I've started to really get comfortable with the ideas. And it's also frustrating, you are basically making mistakes all the time.
Anyway good luck anon, ganbatte

Anonymous

Anonymous Fri 13 Sep 2019 17:47:51 No.10969782 Report

Quoted By:

>>10969743
Inspiring story thanks, I hope you succeed in your endeavour mate.

Anonymous

Anonymous Fri 13 Sep 2019 17:50:12 No.10969791 Report

Quoted By: >>10969797

How do I start reading papers? Do I just pick a field I'm interested in and look for the classic papers? Is it normal to not understand most of the material at first, or does that mean I should read some prerequisite text?

Anonymous

Anonymous Fri 13 Sep 2019 17:51:46 No.10969797 Report

Quoted By: >>10969857

>>10969791
I think the proper time to start is when textbooks you're using start referencing specific papers.

Anonymous

Anonymous Fri 13 Sep 2019 17:55:54 No.10969807 Report

Quoted By:

>>10969308
Depends, for problem solving? No, unless you can't look up definitions and have trouble remembering them.
In general it's decent for learning a number of definitions or proof sketches, for example in preparation for an oral exam.
Specifically if u understand everything but have problems remembering details.

Anonymous

Anonymous Fri 13 Sep 2019 18:14:22 No.10969857 Report

Quoted By: >>10969885

>>10969797
>pick up literally any algeo textbook
>it references Serre's Faisceaux coherents

Anonymous

Anonymous Fri 13 Sep 2019 18:22:55 No.10969885 Report

Quoted By:

>>10969857
Literally any textbook tangentially related to measure theory or applications references Rudin too.

Anonymous

Anonymous Fri 13 Sep 2019 18:24:50 No.10969894 Report

Quoted By: >>10969964 >>10969969 >>10970186

Jesus christ, algebraic topology is a fucking mess, is it really useful? I have no idea why I'm learning all of this. Interested in mathematical physics and my profesor wants to get into field theory, but I can't see why is this useful at all.

Anonymous

Anonymous Fri 13 Sep 2019 18:46:19 No.10969964 Report

Quoted By: >>10969975

>>10969894
When Einstein theorised relativity in the 1910's, differential geometry was mostly seen as something amusing but without too much practical impact, because for all the problem we had so far, a classic, rigid 3D space was more than enough.
Then we realised we were wrong and today differential geometry is integral to our understanding of modern physics. Same could be said for functional analysis and QM.

Point is, you may never know when a mathematical tool is going to be used until someone has a stroke of genius and applies it. As for algebraic topology, topology in general seems to be a trendy topic (if the PhDs offered talking about it are any indication), and the algebraic approach is immensely powerful.

Anonymous

Anonymous Fri 13 Sep 2019 18:47:36 No.10969969 Report

Quoted By: >>10969975

>>10969894
what exactly are you learning ?

Anonymous

Anonymous Fri 13 Sep 2019 18:50:35 No.10969975 Report

Quoted By: >>10970008 >>10970618

>>10969964
Do you have particual exampkes of algtop used in physics?
>>10969969
Basic homology and homothopy. Starting Cohomology next week. I understand that the topological data I get with constructions are usuful for clarification theorems, which in itself are interesting, I just don't see why this data is important in field/gauge theories or whatever.

Anonymous

Anonymous Fri 13 Sep 2019 19:02:15 No.10970008 Report

Quoted By: >>10970097

>>10969975
https://www.findaphd.com/phds/project/topological-mesoscopic-superfluidity-of-3he/?p104533
https://www.findaphd.com/phds/project/applications-of-topology-to-soft-matter-physics/?p107820

Topology is also useful for the study of fluids, as it describes "global" properties of the fluid. V. Arnold wrote a book on it.

Anonymous

Anonymous Fri 13 Sep 2019 19:27:49 No.10970083 Report

Quoted By: >>10970833

>>10968678
>introduction to quantum mechanics (Kostrikin-Manin)

Anonymous

Anonymous Fri 13 Sep 2019 19:31:40 No.10970097 Report

Quoted By:

>>10970008
Thanks lad.

Anonymous

Anonymous Fri 13 Sep 2019 19:55:40 No.10970170 Report

Quoted By:

>>10968828
never done topology before.
currently doing LA.

Anonymous

Anonymous Fri 13 Sep 2019 20:00:43 No.10970185 Report

Quoted By:

Is there an infinite dimensional version of a manifold? How does that look like?

Anonymous

Anonymous Fri 13 Sep 2019 20:00:54 No.10970186 Report

Quoted By:

>>10969894
Topology problems are hard, in the sense that a naive approach would get you nowhere. You should think of algebraic topology as a collection of easy to compute gadgets that help you tell two spaces apart, among other things.

Anonymous

Anonymous Fri 13 Sep 2019 22:07:39 No.10970618 Report

Quoted By:

>>10969975
Eberhard Zeidler wrote 3 huge books about QTF, using algebraic topology as core for many theories.
Quantum Field Theory
I: Basics in Mathematics and Physics

Anonymous

Anonymous Fri 13 Sep 2019 22:43:58 No.10970737 Report

Quoted By: >>10970907

Has anyone had success using a theorem prover like Coq for writing notes and doing exercises when going through a maths text?

Anonymous

Anonymous Fri 13 Sep 2019 23:23:30 No.10970833 Report

Quoted By:

>>10970083
it's the linear algebra book that's in the pic. the creator of the list is a massive mathematical physics fag so the books he recommended usually try connecting rigorous mathematics to physics from time to time. this one in particular had sections dedicated to intro qm stuff. im going to read that one after zorich

Anonymous

Anonymous Fri 13 Sep 2019 23:24:03 No.10970834 Report

Quoted By: >>10971666

>>10969334
>What size are we talking here?
On the order of a few billion rows/columns.

Anonymous

Anonymous Fri 13 Sep 2019 23:57:37 No.10970907 Report

Quoted By: >>10972293

>>10970737
use agda

Anonymous

Anonymous Sat 14 Sep 2019 00:04:33 No.10970916 Report

Quoted By: >>10970938

How do you study /mg/? Just paper and pen?

Anonymous

Anonymous Sat 14 Sep 2019 00:16:17 No.10970938 Report

Quoted By:

>>10970916
>Just paper and pen?
LaTeX

Anonymous

Anonymous Sat 14 Sep 2019 00:21:11 No.10970944 Report

Quoted By: >>10973542 >>10974782

I'm taking topology and real analysis at uni this fall what should I expect

Anonymous

View Same Google iqdb SauceNAO Atiyah Completion.png, 173KiB, 782x551

Anonymous Sat 14 Sep 2019 00:33:15 No.10970973 Report

Quoted By: >>10971986 >>10972165 >>10972579

I am reading Intro to commutative algebra by Atiyah.
In pic related, G is an abelian topological group.
Could someone explain me what is the topology on the completion G^ of G ?

Anonymous

Anonymous Sat 14 Sep 2019 00:34:26 No.10970975 Report

Quoted By:

>>10968359
>linear algebra
Possibly some of the easiest math i had to learn at Gymnasium.

Anonymous

Anonymous Sat 14 Sep 2019 02:19:18 No.10971233 Report

Quoted By:

How the fuck do I solve mixing problems, I feel retarded

Anonymous

View Same Google iqdb SauceNAO Capture.png, 10KiB, 322x93

Anonymous Sat 14 Sep 2019 04:02:43 No.10971425 Report

Quoted By: >>10971445

Is there a way to do this with algebra and not using the quadratic formula or factoring? You can get 13/5 but how do you do it to get the -1?

Anonymous

View Same Google iqdb SauceNAO 1567261222995.jpg, 124KiB, 496x1070

Anonymous Sat 14 Sep 2019 04:03:56 No.10971428 Report

Quoted By: >>10971441

>found a breakthrough matrix preconditioning algorithm
>lets me solve giant finite element simulations on my six year old laptop
>not going to tell anyone about it
>going to use it to become iron man instead
And nobody can stop me.

Anonymous

Anonymous Sat 14 Sep 2019 04:11:21 No.10971441 Report

Quoted By:

>>10971428
Iron Man isn't the suit, honey. He's the brains, the money, the personality, the man.

Anonymous

Anonymous Sat 14 Sep 2019 04:12:43 No.10971445 Report

Quoted By: >>10971452

>>10971425
(5t-4)^2 = 81
=> sqrt((5t-4)^2) = sqrt(81)
=> |5t-4| = 9
=> 5t-4 = 9 or -(5t-4) = 9
=> 5t = 13 or -5t = 5
=> t = 13/5 or t = -1

Anonymous

Anonymous Sat 14 Sep 2019 04:16:58 No.10971452 Report

Quoted By: >>10971474

>>10971445
Why did you do abs val instead of +-sqrt?

Anonymous

Anonymous Sat 14 Sep 2019 04:36:05 No.10971474 Report

Quoted By:

>>10971452
>Why did you do abs val instead of +-sqrt?
sqrt(a^2) = |a|

Anonymous

Anonymous Sat 14 Sep 2019 04:41:11 No.10971485 Report

Quoted By: >>10971497 >>10971729

Math noob here taking a comp sci course.

Explain this please (n is subscript) for the function S

Use a program to evaluate and tabulate both
Sn(1)
and
e?Sn(1)
for n = 7,8,9, . . . ,16.

What does subscript mean and what is this asking me to do? I thought the parentheses meant the value being passed in like f(x). But it's saying to solve this for s(1) with a subscript. I just don't get it. Where is the subscript being used in the function?

Anonymous

View Same Google iqdb SauceNAO poly.png, 7KiB, 507x77

Anonymous Sat 14 Sep 2019 04:45:08 No.10971497 Report

Quoted By: >>10971729

>>10971485
edit i think it might be saying to extend the infinite series they gave us to have up to 16 additions to it.

Anonymous

Anonymous Sat 14 Sep 2019 05:12:57 No.10971535 Report

Quoted By: >>10971732

>>10961675
>>10961695

> reads the wikipedia page once
> repeats the slander by the media

Why did you fucking do this? The guy dedicated his life to math, wrote tons of books, but because he asks questions about a controversial topic, the media makes sure that's the only thing you know about him.

"aids denier" is a label intended you to think he is a bad guy. It is not a criticism.

Please fuck off and stop quoting wikipedia pages.

Anonymous

Anonymous Sat 14 Sep 2019 05:19:11 No.10971544 Report

Quoted By:

>>10962352

> believing math is essentially a formal system.

Computer formalized proofs are less convincing because no person can understand them. It's an excruciating amount of detail that you just have to trust both the computer, and the translation process. How do you know it was typed in correctly, doesn't this double the possibility of error?

Just give it up. Math is a social process. Proofs are mostly about the insights behind them, not the formalism.

Anonymous

Anonymous Sat 14 Sep 2019 05:26:18 No.10971555 Report

Quoted By:

>>10968678
this is the biggest meme. Galois theory in high school is absurd unless you attend a Massachusetts prep schools and your parents are professors.

if you did linear algebra in high school, you are well on your way to being a mathematician.

Anonymous

Anonymous Sat 14 Sep 2019 06:35:27 No.10971666 Report

Quoted By:

>>10970834
Okay, but much more important is the NNZ, if they are in the range of a few billion too you should be able to just use the already existing LAPACK BiCGStab for sparse matrices.

Roughly guessing one matrix vector multiplication takes a minute to an hour or so (if it really is just a *few* billion) so I would assume it will take maybe a couple of days to a week to get a somewhat decent residual.

If you want more you have to look into how you can parallelize the problem and get your hands on some decent hardware.

Anonymous

Anonymous Sat 14 Sep 2019 07:03:53 No.10971729 Report

Quoted By:

>>10971485
>>10971497
They are saying to write down a table of the values S7(1), S8(1), S9(1), ... S16(1). And then those numbers subtracted from e.
What is S9(1)? It's the sum from n = 0 to 9. What's S14(1)? It's the sum, but now from n = 0 all the way to 14.
So right there you do have the correct expression for S7(x).
Note that these are all just polynomials. Also, when you see how close to e these get, you'll see a bit better why we care about them.

Anonymous

Anonymous Sat 14 Sep 2019 07:04:55 No.10971732 Report

Quoted By: >>10971956

>>10971535
Oh look, Lang's back.
Don't you have another undergraduate level introductory text to slave over? The adults are trying to discuss real mathematics here.

Anonymous

View Same Google iqdb SauceNAO sakuyachan.jpg, 70KiB, 960x388

Anonymous Sat 14 Sep 2019 07:06:08 No.10971734 Report

Quoted By: >>10971821 >>10972884

>if you did linear algebra in high school, you are well on your way to being a mathematician.
can you imagine someone posting this unironically
lmao

Anonymous

Anonymous Sat 14 Sep 2019 08:32:00 No.10971821 Report

Quoted By: >>10972905

>>10971734
I don't get it. What is Linear Algebra even?

Anonymous

Anonymous Sat 14 Sep 2019 10:39:42 No.10971951 Report

Quoted By: >>10971959 >>10973203

ok /mg/, i've posted somewhere else but here it's again.
I wanted to learn about abstract algebra since first year of uni, tried many times and dropped because i couldn't understand some proofs, and shit is so deep i can barely get what it is all about. I can't see the implications of what i'm learning.

I've been trying to learn this stuff for the Galois theory and it's implications on solving polynomials by radicals.
>why?
Don't know, just for the sake of knowing stuff.

any advice for this?

Anonymous

Anonymous Sat 14 Sep 2019 10:50:58 No.10971956 Report

Quoted By: >>10973364

>>10971732
Why the hate on people who write undergraduate textbooks ? It is an important job and somebody has to do it.

Anonymous

Anonymous Sat 14 Sep 2019 10:52:15 No.10971959 Report

Quoted By: >>10971965

>>10971951
JUST DO IT.

Read a book and do the exercises?

Anonymous

Anonymous Sat 14 Sep 2019 10:54:51 No.10971965 Report

Quoted By:

>>10971959
any recomendations for a brainlet?
I've tried starting reading Herstein book but man, wth

Anonymous

View Same Google iqdb SauceNAO 997B3689-A68F-40B4-BB74-D618F5DA (...).jpg, 104KiB, 731x306

Anonymous Sat 14 Sep 2019 10:59:26 No.10971971 Report

Quoted By: >>10971988

Im a brainlet, how do I solve this? My answer keeps coming out wildly different from the book.

Anonymous

Anonymous Sat 14 Sep 2019 11:15:36 No.10971982 Report

Quoted By:

>>10961000
Feel the need to understand.
Do you remember law of cosines by heart?

Anonymous

Anonymous Sat 14 Sep 2019 11:18:36 No.10971986 Report

Quoted By:

>>10970973
Sorry I wish I could help. I am topologylet right now.

Anonymous

Anonymous Sat 14 Sep 2019 11:21:54 No.10971988 Report

Quoted By: >>10972000

>>10971971
You have to use ODE.
First differential is gram per litre.
Second is litre per min.
Just try to form an identity and solve. I have forgotten ODE.

Anonymous

Anonymous Sat 14 Sep 2019 11:38:07 No.10972000 Report

Quoted By: >>10972286

>>10971988
I have no idea how to set up the problem. I get to dA/dt = 30 - A/200+t but then i solve the standard form and i my number is way off.

Anonymous

View Same Google iqdb SauceNAO 666.jpg, 2KiB, 74x44

Anonymous Sat 14 Sep 2019 12:53:28 No.10972096 Report

Quoted By: >>10972100 >>10972164 >>10972221 >>10972225 >>10972233 >>10972237

How do you deal with this shit, when there's nothing to work with in the first place?

Anonymous

Anonymous Sat 14 Sep 2019 12:55:23 No.10972100 Report

Quoted By:

>>10972096
farts

Anonymous

View Same Google iqdb SauceNAO HMM.png, 105KiB, 529x742

Anonymous Sat 14 Sep 2019 13:26:10 No.10972144 Report

Quoted By: >>10972174 >>10972295 >>10972323 >>10972373 >>10972430 >>10973402 >>10974182

Is it possible for someone with a 2.5 GPA in an unrelated subject to get into a top Math PhD program (say Princeton or Harvard) by writing a really impressive paper and submitting it to a professor there?

Anonymous

Anonymous Sat 14 Sep 2019 13:48:59 No.10972164 Report

Quoted By: >>10972240

>>10972096
Fourier transform

Anonymous

Anonymous Sat 14 Sep 2019 13:51:42 No.10972165 Report

Quoted By:

>>10970973
bump

Anonymous

Anonymous Sat 14 Sep 2019 13:58:13 No.10972174 Report

Quoted By:

>>10972144
>submitting it to a professor there
Make it three or four good papers, submitted to journals, plus not being old as shit.

Anonymous

Anonymous Sat 14 Sep 2019 14:18:10 No.10972203 Report

Quoted By:

I really like Lax's Multivariable Calc, but I'm not sure whether it's an actually good textbook or just my autism acting up about how he explains linear functionals, matrices and the rest through the long route, so I'd like a second opinion before I start recommending it to people.
Has anyone here read it? What did you think about it? Do you think it's a solid introductory text?

Anonymous

Anonymous Sat 14 Sep 2019 14:30:48 No.10972221 Report

Quoted By:

>>10972096
Mathematica tells me

$\int x^2 \sin(k x) \mathrm{d } x= -\frac{1}{8k^2} \left(-\frac{\cos (2 k x)}{8 k^2}-\frac{x \sin (2 k x)}{4 k}+\frac{x^2}{4}\right)$

Suggests to me you use those rules about powers of trigonometric functions and their frequency, i.e.
cos^2(x) => cos(2x) + ...
and those things

Anonymous

Anonymous Sat 14 Sep 2019 14:32:47 No.10972225 Report

Quoted By: >>10972237 >>10972240

>>10972096
Mathematica tells me

$\int x \sin(2kx) dx = -\frac{\cos (2 k x)}{8 k^2}-\frac{x \sin (2 k x)}{4 k}+\frac{x^2}{4}$

Suggests to me you use those rules about powers of trigonometric functions and their frequency, i.e.
$cos^2(x)$ to $cos(2x) + ...$
and those things

Anonymous

Anonymous Sat 14 Sep 2019 14:33:59 No.10972226 Report

Quoted By:

? x sin(kx)^2 dx
on the left hand side I mean

Anonymous

Anonymous Sat 14 Sep 2019 14:39:49 No.10972233 Report

Quoted By:

>>10972096

Notice the bounds are symmetric about the y axis, so your going to want to appeal to symmetry. $\int_{-2}^{2} x\sin^2(x) \,\mathrm{d}x = 0$ since $f(x)=x$ is an odd function and $\sin^2(x)$ is even, so the entire integrand is odd.

Anonymous

Anonymous Sat 14 Sep 2019 14:41:26 No.10972237 Report

Quoted By: >>10972240

>>10972225
>>10972096
Express the square as double argument and integrate by parts.

Anonymous

Anonymous Sat 14 Sep 2019 14:43:45 No.10972240 Report

Quoted By:

>>10972164
>>10972225
>>10972237
Y'all are being calculation monkeys. Just think about what the graph of the integrand looks like. The value of the integral is zero.

Anonymous

Anonymous Sat 14 Sep 2019 15:16:58 No.10972286 Report

Quoted By:

>>10972000
> I have no idea how to set up the problem. I get to dA/dt = 30 - A/200+t
I get that, where A is the total amount of chemical in grams.
Solving gives A=(15t^2+6000t+C)/(t+200). A=1600 at t=0 => C=300000 => A=(15t^2+6000t+300000)/(t+200) which equals 35700/13=2746g at t=60. The volume is 3(t+200) = 780L at t=60, giving a concentration of 35700/10140 = 595/169=3.521g/L.

Anonymous

Anonymous Sat 14 Sep 2019 15:20:43 No.10972293 Report

Quoted By: >>10972369

>>10970907
What's the difference?

Anonymous

Anonymous Sat 14 Sep 2019 15:21:28 No.10972295 Report

Quoted By: >>10972323

>>10972144
delusional

Anonymous

Anonymous Sat 14 Sep 2019 15:44:04 No.10972323 Report

Quoted By: >>10972380

>>10972295
>>10972144
Isn't that Ed Witten's story? He was some nobody studying history then somehow got into Math/Physics and ended up with a Field's Medal.

Anonymous

Anonymous Sat 14 Sep 2019 16:14:35 No.10972369 Report

Quoted By:

>>10972293
style points and mixfix notation

Anonymous

Anonymous Sat 14 Sep 2019 16:18:05 No.10972373 Report

Quoted By:

>>10972144
Possible? If you're being pedantic then yes. Otherwise, no.

Anonymous

Anonymous Sat 14 Sep 2019 16:21:37 No.10972380 Report

Quoted By:

>>10972323
>some nobody
No, he was a jew with the phenotype and connections, completely different.

Anonymous

Anonymous Sat 14 Sep 2019 16:50:19 No.10972430 Report

Quoted By:

>>10972144
You wouldn't be asking this question if you actually saw the admissions process. No dude, you have no chance whatsoever. 0%.

Anonymous

View Same Google iqdb SauceNAO attent.jpg, 236KiB, 901x600

Anonymous Sat 14 Sep 2019 17:52:02 No.10972576 Report

Quoted By: >>10972815

We have that

$\mathrm { det } ( \exp(A) ) = \exp( \mathrm { tr } (A) )$

for matrices A where

$\exp(A) = \lim_{n\to \infty} \sum_{k=0}^n \tfrac {1}{k} A^k$

Can we say something nice already about

$\mathrm { det } \left( \sum_{k=0}^n \tfrac {1}{k} A^k \right)$

?

Anonymous

Anonymous Sat 14 Sep 2019 17:53:42 No.10972579 Report

Quoted By:

>>10970973
i'm not sure but you'd probably want that that ? is a continuous group homomorphism. so my bet is that you just take the finest topology such that ? is continuous

Anonymous

Anonymous Sat 14 Sep 2019 17:59:30 No.10972589 Report

Quoted By:

>>10965562
spotted the heretic

Anonymous

Anonymous Sat 14 Sep 2019 19:19:11 No.10972815 Report

Quoted By: >>10972879 >>10972910

>>10972576
i highly doubt it. consider the very simplest case, when A is a 1x1 matrix A=[a]. Can you say anything nice about $\sum_{k=0}^n a^k/k!$ , where a is an arbitrary real number?

Anonymous

Anonymous Sat 14 Sep 2019 19:41:27 No.10972879 Report

Quoted By: >>10972910

>>10972815
Good point, thx.

Also, sad.

Anonymous

Anonymous Sat 14 Sep 2019 19:43:35 No.10972884 Report

Quoted By: >>10973354

>>10971734
the insecurity on this board is incredible. guess what, that age you took XYZ won't make you a successful person. most high achievers who get 4.0s, triple major, graduate early, etc, proceed to work an unremarkable office job for the rest of their career.

Anonymous

Anonymous Sat 14 Sep 2019 19:49:45 No.10972905 Report

Quoted By: >>10973203

>>10971821
differential equations and linear algebra are the last math classes undergraduate engineers are required to take. its typically a sophomore level class for non-math majors.

if you mastered calculus and linear algebra in high school, you are ready to jump into analysis and abstract algebra as a freshmen, which as I said, is a great start to being a mathematician.

larpers and insecure fags on this board like to pretend they are hyper geniuses who invented analysis from first principles.

Anonymous

View Same Google iqdb SauceNAO darcat.jpg, 5KiB, 250x250

Anonymous Sat 14 Sep 2019 19:50:19 No.10972910 Report

Quoted By: >>10972914 >>10974007

>>10972815
>>10972879
Btw. I got to that question by wondering what conditions on A we must impose to guarantee that that finite sum is invertible.
That question is sort of natural, I think, because exp(A) is always invertible while it's not so clear when the sum is. If A is a diagonal n times n matrix, then

$\sum_{k=0}^n \tfrac{1}{k} A^k = 1_n + P(A)$
where
$P(A) := \sum_{k=1}^n \tfrac{1}{k} A^k$

so this is just asking for a complex value $a$ where $P(a) = 1$ .

Anonymous

Anonymous Sat 14 Sep 2019 19:51:23 No.10972914 Report

Quoted By:

>>10972910
-1 I mean

Anonymous

Anonymous Sat 14 Sep 2019 21:26:13 No.10973203 Report

Quoted By: >>10973605

>>10972905
some sources (books or vids or whatever) reccomendations anon? i'm the anon in >>10971951

Anonymous

Anonymous Sat 14 Sep 2019 22:21:11 No.10973354 Report

Quoted By: >>10973605

>>10972884
yes, and so do most imperfect students. in fact, a far far far higher proportion of them.
doing anything worthwhile takes a bit of luck and a bit of persistence. but one can maximize their chances by practicing a modicum of foresight.

Anonymous

Anonymous Sat 14 Sep 2019 22:22:29 No.10973364 Report

Quoted By:

>>10971956
>write worse version of *insert existing classic here*
>wow i just spent my time so wisely!
lmao

Anonymous

Anonymous Sat 14 Sep 2019 22:39:00 No.10973402 Report

Quoted By:

>>10972144
If you are black women or jewish women, transwomen.

Anonymous

Anonymous Sat 14 Sep 2019 23:41:57 No.10973542 Report

Quoted By: >>10974007 >>10974651

>>10970944
Thanks for all the replies guys

Anonymous

Anonymous Sun 15 Sep 2019 00:03:11 No.10973605 Report

Quoted By: >>10974365

>>10973354
I actually suspect this is even truer for these early academic performers. they are good at following rules and staying on track, not doing new or risky things.

>>10973203
sure anon. there is a free and open source text book called Abstract Algebra by Tom Judson. it works up from basic groups to galois theory and is well written.

Anonymous

View Same Google iqdb SauceNAO 702A7F4A-A815-42B4-945E-220408A6 (...).jpg, 2MiB, 4032x3024

Anonymous Sun 15 Sep 2019 00:19:13 No.10973647 Report

Quoted By: >>10973686 >>10973779

Why am I reducing -10 and 4 by 2, and -260 by 4? Why not -260/2 ?

Answer was provided, I just don’t understand why we should reduce by some arbitrary multiple. Shit, why not -260/5 ?

Anonymous

Anonymous Sun 15 Sep 2019 00:32:00 No.10973686 Report

Quoted By:

>>10973647
are you dense?

Anonymous

Anonymous Sun 15 Sep 2019 01:06:04 No.10973779 Report

Quoted By: >>10973788

>>10973647
I'm not sure I understand what you're asking here :

$ x = \frac{-10 \pm \sqrt{-260}}{2} = \frac{(-5 \cdot 2) \pm 2i\sqrt{65}}{2 \cdot 2} = \frac{-5 \pm i\sqrt{65}}{2} $

Anonymous

Anonymous Sun 15 Sep 2019 01:12:40 No.10973788 Report

Quoted By:

>>10973779
Maybe I should have added that :

$\sqrt{260}=\sqrt{4 \cdot 65} = \sqrt{4}\cdot\sqrt{65}=2\sqrt{65}$

Anonymous

Anonymous Sun 15 Sep 2019 03:24:51 No.10974007 Report

Quoted By: >>10974960

>>10973542
Stop asking dogshit questions if you want replies.
>>10972910
Working over the product strikes me as easier than with the sum, but I know absolute jack shit about infinite products.

Anonymous

Anonymous Sun 15 Sep 2019 05:01:48 No.10974182 Report

Quoted By:

>>10972144
Who in their right mind wants to get a Math PhD?

Anonymous

Anonymous Sun 15 Sep 2019 07:15:01 No.10974365 Report

Quoted By:

>>10973605
thanks anon, i appreciate it

Anonymous

Anonymous Sun 15 Sep 2019 07:37:53 No.10974392 Report

Quoted By:

>>10968523
butthurt much?

Anonymous

Anonymous Sun 15 Sep 2019 09:52:04 No.10974651 Report

Quoted By:

>>10973542
>Thanks for all the replies guys
What did you expect as an answer?

If you want to know what either of theses topics is, read the Wikipedia article, if you want to have book recommendations ask for book recommendations.
But LITERALLY no one here knows what you should expect.

Anonymous

Anonymous Sun 15 Sep 2019 11:17:35 No.10974782 Report

Quoted By:

>>10970944
Maybe you should check out the Infinitely Large Napkin, it's a free PDF book written by an Harvard student that aims to give an overview of many higher math topics :

http://web.evanchen.cc/napkin.html

Anonymous

Anonymous Sun 15 Sep 2019 11:51:55 No.10974856 Report

Quoted By: >>10974925

I'm starting my first year in a couple of weeks. What are some practices I should adopt right now in order to maximise my chances of getting into a good grad school?

Anonymous

View Same Google iqdb SauceNAO Frier1998.jpg, 29KiB, 578x421

Anonymous Sun 15 Sep 2019 12:25:12 No.10974925 Report

Quoted By:

>>10974856
Hang out with the smart guys who'll still be there in 1 year.
Don't get friends with 5 people, 4 of which will drop the major, leaving you at square one.
Talk with people smarter than you - there's gonna be some higher year people who can and like to talk.

Dedicate 2 hours on reading stuff you don't understand and that's not needed on Friday afternoons. Find out what the actual research in the fields are, not the uni curricula that you'll learn in the next few years. Two hours per week isn't that bad and getting to know what's out there helps even if you don't get it, really.

Start a notebook, or wiki, or blog if that's your thing.

Ask stupid questions when nobody dares to.

Go to events when you're invited.

Show women that you actually like women, don't be a nice guy.

Anonymous

Anonymous Sun 15 Sep 2019 12:36:55 No.10974949 Report

Quoted By: >>10974960 >>10974965

is the sequence (Xn)n>=1 = (n)n>=1 bounded from below? I mean, it will never become negative?

Anonymous

Anonymous Sun 15 Sep 2019 12:40:02 No.10974960 Report

Quoted By: >>10974973

>>10974949
Not being max-lazy in asking your question would help. It's hard to decipher.

>>10974007
Thanks, I came to the same conclusion.
(Sidenote: The finite product is of course also a sum, but det(X^n)=det(X)^n helps a lot)

Anonymous

View Same Google iqdb SauceNAO drftgyhu.png, 188KiB, 560x399

Anonymous Sun 15 Sep 2019 12:42:14 No.10974965 Report

Quoted By: >>10974973

>>10974949
>(Xn)n>=1 = (n)n>=1

Anonymous

View Same Google iqdb SauceNAO 70395806_1890159224420111_706297 (...).jpg, 521KiB, 3024x4032

Anonymous Sun 15 Sep 2019 12:46:25 No.10974973 Report

Quoted By: >>10974976

>>10974960
>>10974965

Anonymous

Anonymous Sun 15 Sep 2019 12:49:34 No.10974976 Report

Quoted By: >>10974979 >>10974984

>>10974973
It seems you're actually asking what the expression $(n)_n$ means.
Otherwise I don't see how you could think it would become negative.

Anonymous

Anonymous Sun 15 Sep 2019 12:50:22 No.10974979 Report

Quoted By:

>>10974976
le 1+2+3+...=-1/12 face xD kappa lmao

Anonymous

Anonymous Sun 15 Sep 2019 12:52:54 No.10974984 Report

Quoted By: >>10974987 >>10974989

>>10974976
But I see similar examples where the sequence is not bounded, even when it doesn't become negative. Like n^2 is supposed to be unbounded

Anonymous

Anonymous Sun 15 Sep 2019 12:54:45 No.10974987 Report

Quoted By:

>>10974984
Yeah, it's unbounded because it can get arbitrary big. But not negative.

Anonymous

Anonymous Sun 15 Sep 2019 12:56:22 No.10974989 Report

Quoted By: >>10974995

>>10974984
Yeah, it's unbounded because it can get arbitrary big. But not negative.

n^2 is bounded from below but not from above.

Start by writing down the formal definitions of each and work with them.
And when you read this, I mean write down the formal definition, not just go back and read them. I know you cunt.

Anonymous

Anonymous Sun 15 Sep 2019 13:02:11 No.10974995 Report

Quoted By:

>>10974989
I do read the formal definitions, that's almost all I do, but it doesn't help. How is it unbounded when it can't become negative? How is it not bounded below? How is (n) different from (n^2) when they're both always n>= 1 either way?

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches