🧵 /mg/ maths general
Anonymous at Sun, 5 May 2024 08:59:52 UTC No. 16160352
[math]/\mathfrak{mg}/[/math]
the King of mathematics edition
talk maths, formerly >>16135585
Anonymous at Sun, 5 May 2024 10:02:18 UTC No. 16160436
>>16160352
[math]\mathfrak{first}[/math] for Emil Post
Anonymous at Sun, 5 May 2024 10:35:43 UTC No. 16160468
>>16160030
Well, I think we're talking past each other a little bit. I'm also certain that the undergrad measure theory in my university is not taught to the same level of rigour as a proper graduate course. That's not what I was saying.
I attached the table of contents of our lecture notes, iirc we went through chapters 1-5 and 8 in the measure theory course. This was 8 weeks, 8 contact hours per week.
Comparing this to axler's book, we went through the equivalent of his chapters 2,3,5, and 7. There was also a course on functional analysis immediately following it which went through the equivalent of his chapters 6, 8, and 10.
For the graduate probability courses: it's interesting. We have some masters courses just like yours, but in it we rushed through the measure theory in, say, 10 contact hours, to get to the probability, with the understanding it's been covered before.
These three separate semester-long courses then cover roughly the same topics as yours, with (as far as I can tell) some extra also.
At least, I recognize most of the topics in his overview as being treated in two of our courses (one on measure theoretic probability and one on stochastic (markov) processes). Then we also covered the stochastic calculus of semimartingales in a third semester.
One very interesting aside is that there are essentially no examples or applications in these courses. I always thought that was a shame, and it's something I think american universities do better, because the applied courses don't actually require the theoretical ones as prerequisites, making it feel pointless to some.
Relatedly, since you've some experience with teaching (in america, I assume, too?): I noticed it's a lot more common to have year-long courses, when that basically doesn't occur here. Do you think there is any particular reason behind it? Here, it's done to relieve the instructors somewhat, so they don't have the workload of teaching and grading for 6 months continuously.
Anonymous at Sun, 5 May 2024 13:38:06 UTC No. 16160647
One of the worst things mathematicians ever did was ceasing to be mindful of the fact that they were approximating when they were approximating, merely because the margin of error became infinitely small (infinitesimal). Something is only exact when no part of it or bit of it is wrong or inaccurate.
Anonymous at Sun, 5 May 2024 14:04:05 UTC No. 16160673
>>16160468
The UC system is actually a good bit closer to a "European" model in that they do 4 10 week sessions in a year instead of 2 6 month semesters (as is more common in the US). As far as I'm aware Todd's classes on Probability Theory were intended to be fit into 3 consecutive 10 week blocks. I'm much more used to the "east coast" way of doing things in the US where we have 2 14-16 week semesters (length depends on location) and then 2 shorter sessions (a 10 week summer and 6 week winter) for optional and accelerated classes.
It's funny that you bring up the year-long courses as an odd occurrence. I actually really like when they are able to do this because it allows for students to have a seamless development of a complicated topic (e.g., measure theoretic probability and stochastic processes) without a lot of turnover or breaks in between.
When I've taught measure theoretic probability at US universities, if most of the students finished their measure theory course in the previous spring it makes it much easier to jump into properly probability oriented material in the fall semester. It all just kind of hinges on how your institution intends the "flow" of material to function (and whether anyone can actually follow that intended plan).
I like the TOC for that course by the way. It does seem like a "hollowed out" version of a graduate measure course so I'm sure it was a good one. The more abstract and challenging details can be filled in later.
One thing that is kind of surprising to me is how late you guys did normed spaces. At my university normed spaces pretty much immediately follow from integrability and the convergence theorems (because that's really all L^p is, the set of equivalence classes of p-integrable functions). We used L^p spaces as a gateway to signed and product measures. Lp is especially important for Radon-Nikodym as the p norm lets you easily define normalized Rad-Nik induced measures.
Sorry for being cantankerous my Kraut friend.
Anonymous at Sun, 5 May 2024 14:33:57 UTC No. 16160720
I don't know much about algebraic topology. Is there a generalization of covering spaces to higher homotopy groups? I mean the following: The universal covering is defined to be simply connected. Does it make sense to talk about an n-connected covering where pi_n is trivial? Where can I read about this?
Anonymous at Sun, 5 May 2024 14:56:52 UTC No. 16160745
I have to take
> 1 semester of diffential geometry
Or
> half a semester complex analysis
> AND half a semester diff equations
Thoughts? My favourite classes were topology and probability theory
Anonymous at Sun, 5 May 2024 15:17:10 UTC No. 16160768
>>16160352
I have 1 day to study for AP Stats. I know nothing about stats at all. I just want to pass with a 3/5. Is it possible?
Anonymous at Sun, 5 May 2024 17:46:19 UTC No. 16160923
>>16160745
Is the differential equations class just memorizing solutions or is there any theory?
Anonymous at Sun, 5 May 2024 18:06:50 UTC No. 16160957
>>16160352
Who is he?
>>16160790
Can I complete this in one lifetime? I am 22 btw
Anonymous at Sun, 5 May 2024 18:10:34 UTC No. 16160961
>>16160790
Someone edit this with pictures that aren't blurry
Anonymous at Sun, 5 May 2024 18:22:18 UTC No. 16160981
>>16160957
>Who is he?
Joshua King
>Joshua King came to Cambridge from Hawkshead Grammar School. It was soon evident that the school had produced someone of importance. He became Senior Wrangler, and his reputation in Cambridge was immense. It was believed that nothing less than a second Newton had appeared. They expected his work as a mathematician to make an epoch in the science. At an early age he became president of Queens’; later, he was Lucasian Professor. He published nothing; in fact, he did no mathematical work. But as long as he kept his health, he was an active and prominent figure in Cambridge, and he maintained his enormous reputation. When he died, it was felt that the memory of such an extraordinary man should not be permitted to die out, and his papers should be published. So his papers were examined, and nothing whatever worth publishing was found.
Anonymous at Sun, 5 May 2024 18:57:00 UTC No. 16161032
We consider set of binary sequences [math]\gamma \in \{0,1\}^{\mathbb N}[/math].
Let [math]A_n \subset \{0,1\}^{\mathbb N}[/math] be the set of sequences which among their first 2n entries have the same number of 0's and 1's.
E.g. [math]A_3[/math] holds, among others, all sequences starting with
0,1,0,1,1,0
but not those starting with e.g.
1,1,0,1,1,0
1. What's [math]\dfrac{|A_n|}{2^{2n}}[/math] as a function of n, i.e. how many sequences have that type?
2. Likewise, taking the union below n, what's [math]{|\bigcup_{k\le n}A_k|}/{2^{2n}}[/math]
3. Taking the union of such set together, in the countable limit, what's the ratio [math]|\bigcup_{n\in{\mathbb n}} A_n|[/math] over [math]|\{0,1\}^{\mathbb N}|[/math]?
(My motivation is that I want to find a countable collection of decidable/detachable subsets of sequences, such that the countable union isn't decidable anymore, and one where the canonical measure on them isn't trivial (0 or 1). I assume the value in 3 is strictly between 0 and 1, although I'm not sure.)
Anonymous at Sun, 5 May 2024 19:16:32 UTC No. 16161075
>>16161032
As you have written it the [math]A_n[/math] all have uncountable infinite cardinalities.
There are [math]{2n \choose n}[/math] possiblities for the first [math]2n[/math] entries and then [math]2^{\aleph_0}[/math] possibilites for the remaining entries.
Anonymous at Sun, 5 May 2024 19:25:57 UTC No. 16161102
>>16161075
Yeah in the finite cases I mean to just take the sequences of length 2n and compare them with all possibilities of that length, 2^(2n).
1 is probably easy (binomial (2n,n) you say?).
The finite union case 2 is maybe more annoying to compute, as there will be overlaps I guess, but the value for 2 is not so interesting for me anyway.
The meat is with 3. While all sequences will be 2^\alpeh, I wonder about the fraction of sequences that have a balanced initial segment of length 2m for _some_ m. I don't know if this is measure zero or it's compliment, or if there's a real between 0 and 1 for that ratio.
Anonymous at Sun, 5 May 2024 20:10:50 UTC No. 16161203
>>16160923
Pretty theory heavy I think. It's a class for math majors in their last year of undergrad.
Anonymous at Sun, 5 May 2024 22:10:06 UTC No. 16161383
I'm studying for a test tomorrow and there is a question that is supposed to require a method that we haven't studied yet (generating functions).
I've tried it solving the stuff we've covered already which is the inclusion exclusion principle but it seems quite hard.
Find the number of integer solutions for the equation x1+x2+x3+x4=20 with x1, x2 even, x3, x4 odd, and x4 <= 3.
So far I have:
total of solutions with no restrictions:
N = CR(4,20) = C(23,20) = 1771
Next step for the I. E. P. would be to calculate number of integer solutions such that x1 is odd.
The furthest I've gotten is that the number of solutions with that restriction is the same as the total number of solutions for 2*x1+1+x2+x3+x4=21 but I don't know how to find it.
The final answer for the whole problem is 100.
Anonymous at Sun, 5 May 2024 22:19:50 UTC No. 16161405
>>16161383
Just introduce new variables
x1 = 2 y1
x2 = 2 y2
x3 = 1 + 2 y3
x4 = 1 + 2 y4
Then you get rid of the odd/even restrictions.
Anonymous at Sun, 5 May 2024 23:45:15 UTC No. 16161515
>>16161405
Thanks, that worked nicely.
Anonymous at Mon, 6 May 2024 03:53:20 UTC No. 16161696
>>16161203
Is it before or after Lebesgue integrals and Sobolev spaces? My assumption is that it's before because you're saying senior undergrads are taking it but you never know I guess.
Anonymous at Mon, 6 May 2024 04:10:07 UTC No. 16161709
Lol you people don't even know basic geometry
Anonymous at Mon, 6 May 2024 07:42:02 UTC No. 16161865
>>16160981
Such humiliation on a Wikipedia page
Anonymous at Mon, 6 May 2024 07:51:10 UTC No. 16161869
https://www.msn.com/en-us/news/us/t
Hey guys, TND tourist here. Did these ladies actually do it? It's old news but I guess its making the rounds again.
Anonymous at Mon, 6 May 2024 08:07:03 UTC No. 16161874
>>16161032
for 3: consider a sequence of infinitely many coin-flips with p=1/2 of heads, ad translate it into a binary sequence. What is the probability that your sequence is never in A_n for any n? It is probability zero. Therefore the measure of that union is 1.
The situation changes if you change the probability p. In your setting that would correspond to distorting the measure on your space, could be incompatible with what you’re asking (not sure)
https://en.wikipedia.org/wiki/Rando
https://en.wikipedia.org/wiki/Kolmo
Anonymous at Mon, 6 May 2024 08:31:07 UTC No. 16161892
>>16161869
They did give a proof for the theorem but it's not a "problem that stumped the math world for centuries".
🗑️ Anonymous at Mon, 6 May 2024 09:53:45 UTC No. 16161976
>>16161869
It seems to be at least not identical to other known proofs. There is, however, a very very similar proof which I very very much think must be where they got the idea from. Pic related. The difference is that the old proof takes the original triangle and constructs more triangles inside of it, and the new proof takes the original triangle and constructs more triangles outside of it. If they did get the idea from this older proof, I think it is more honest to say so. Also the thing people are claiming about trigonometry appears to be nonsense.
Anonymous at Mon, 6 May 2024 10:01:44 UTC No. 16161989
It seems to be at least not identical to other known proofs. There is, however, a visually similar known proof. Pic related. The main difference is that the old proof takes the original triangle and constructs more triangles inside of it, and the new proof takes the original triangle and constructs more triangles outside of it. If they got the idea from this older proof, they probably should say so. As for the trigonometry thing, it seems to be not quite true, but stuff like that normal in science reporting.
Anonymous at Mon, 6 May 2024 13:52:00 UTC No. 16162263
What is a manifold?
I stopped studying math in high school.
Anonymous at Mon, 6 May 2024 14:00:51 UTC No. 16162270
>>16162263
a second countable Hausdorff space that is locally like n-dimensional Euclidean space
Anonymous at Mon, 6 May 2024 14:07:53 UTC No. 16162282
Thoughts on Elements de Mathematique by Bourbaki?
Anonymous at Mon, 6 May 2024 16:40:37 UTC No. 16162455
>>16162282
about as useful as principia mathematica
Anonymous at Mon, 6 May 2024 16:43:26 UTC No. 16162458
>>16162455
Which is to say?
Anonymous at Mon, 6 May 2024 16:55:40 UTC No. 16162470
>>16162458
pointless aim, with substandard propaedeutic value
Anonymous at Mon, 6 May 2024 17:01:10 UTC No. 16162475
>>16162470
What are the best mathematics textbooks for all respective fields, then?
Anonymous at Mon, 6 May 2024 17:05:04 UTC No. 16162479
>>16162475
there is no best, only whatever works for you
Anonymous at Mon, 6 May 2024 17:19:04 UTC No. 16162495
>>16161696
Before
Anonymous at Mon, 6 May 2024 18:02:24 UTC No. 16162563
Do humans exist for the purpose of solving and finding new mathematics? (Pure)
Or does math exist for the purpose of helping humans in the practical world? (Applied)
Anonymous at Mon, 6 May 2024 18:10:24 UTC No. 16162590
>>16162563
neither
Anonymous at Mon, 6 May 2024 20:03:49 UTC No. 16162847
>>16162590
Then in your opinion, what is the purpose of math, and the purpose of humans?
Anonymous at Mon, 6 May 2024 20:34:28 UTC No. 16162882
>>16162847
Just say man instead of reddit human
Anonymous at Mon, 6 May 2024 22:14:36 UTC No. 16163013
>>16162882
>>16162847
>>16162563
both underaged. sad
Anonymous at Mon, 6 May 2024 22:53:49 UTC No. 16163084
>>16163013
Wrong
Anonymous at Mon, 6 May 2024 22:59:55 UTC No. 16163099
>>16162495
Then you probably should be fine in terms of difficulty for the ODE/PDE course. I personally really like differential equations but a lot of people find them tedious, especially at an undergrad level.
Anonymous at Mon, 6 May 2024 23:04:15 UTC No. 16163113
>>16162563
Man was made in God’s perfect image. Mathematics is Man’s quest to find the language to describe that image.
Anonymous at Mon, 6 May 2024 23:20:22 UTC No. 16163136
What skills do pure mathematicians have that physicists/engineers and the like don't? How much would the latter two benefit from having those skills?
Anonymous at Mon, 6 May 2024 23:44:02 UTC No. 16163168
>>16161383
>>16161405
>>16161515
The test went very well. I still don't have the result, I'm not 100% sure on all the answers but I didn't completely blank on any of them.
Now no more math tests for half a semester.
Anonymous at Tue, 7 May 2024 00:10:43 UTC No. 16163209
>>16163113
Source on mathematics ever leading to any sort of natural language development? I'm no linguist, but this is news to me.
Anonymous at Tue, 7 May 2024 02:50:05 UTC No. 16163408
Since libgen sucks now can someone with access download these for me?
https://www.tandfonline.com/doi/ful
https://www.tandfonline.com/doi/ful
https://www.tandfonline.com/doi/ful
https://www.tandfonline.com/doi/ful
https://www.tandfonline.com/doi/ful
Anonymous at Tue, 7 May 2024 06:29:54 UTC No. 16163634
Query on the notation of summations:
What's the consensus if I have, say, 2 conditions on the range of a summation? Example:
[math]\sum_{\substack{x\in A,\\ 2\vert x,x\notin B}}x[/math]
In this example, it's the "summation of all [math]x[/math] in [math]A[/math] such that [math]x[/math] is divisible by 2 and is not in [math]B[/math]".
Is it considered "standard" to allocate the first line of the subscript of [math]\sum[/math] to the range and the 2nd line for the conditions on the range? That is, [math]\sum_{\substack{range\\condit
Using the example given above, is it then considered incorrect to write it as
[math]\sum_{\substack{x\in A, 2\vert x,\\x\notin B}}x[/math]? In this case, the condition of it being divisible by both 2 and not in [math]B[/math] is split into two separate lines.
Sorry for this weirdly specific question.
Anonymous at Tue, 7 May 2024 06:30:56 UTC No. 16163635
Just to clarify on >>16163634, the superscript of the summation is not used. It's all subscript, and the subscript has 2 lines.
Anonymous at Tue, 7 May 2024 07:41:52 UTC No. 16163668
If there isn't enough space to the side of an equation, is it alright to put the "because", i.e. [math]\because[/math] between a line of equation and the next? Like so
= bla bla bla
= bla bla bla
= bla bla bla
([math]\because[/math].....)
= bla bla bla
= bla bla bla
Anonymous at Tue, 7 May 2024 12:19:46 UTC No. 16163865
>>16163634
You should put it directly below the sigma. Apparently you can use \displaystyle for that
Anonymous at Tue, 7 May 2024 12:21:09 UTC No. 16163866
>>16163865
I already do that, the only reason it appears as though to the side is because of the formatting on /sci/. It's directly below the sigma in my LaTeX software.
Anonymous at Tue, 7 May 2024 16:37:51 UTC No. 16164154
Any good books to introduce me to graph theory?
Anonymous at Tue, 7 May 2024 23:02:11 UTC No. 16164888
>>16163866
Then yeah, use as many lines as you want, since they won't be confused with a superscript that way.
Anonymous at Tue, 7 May 2024 23:53:31 UTC No. 16164948
>>16163168
Damn, I got the answer sheet and it actually went very bad lol. Fuck me.
Anonymous at Wed, 8 May 2024 00:27:08 UTC No. 16164987
>>16161383
>Find the number of integer solutions for the equation x1+x2+x3+x4=20 with x1, x2 even, x3, x4 odd, and x4 <= 3.
>generating functions
Implied assumption is x_i >= 0 (since that gives the answer 100)
f1=f2=1/(1-x^2) = 1+x^2+x^4+...
f3=x/(1-x^2) = x+x^3+x^4+...
f4=x+x^3
Answer is the coefficient of x^20 in f1*f2*f3*f4. Use partial fractions.
f1*f2*f3*f4
= x^2*(1+x^2)/(1-x^2)^3
= 1/8 * (1/(x+1) - 3/(x+1)^2 + 2/(x+1)^3 - 1/(x-1) - 3/(x-1)^2 - 2/(x-1)^3)
power series coefficient is 20th derivative of this evaluated at zero divided by 20!. 20th derivative is
1/8 * (20! / (x+1)^21 - 3*21!/(x+1)^22 + (2*22!/2) * /(x+1)^23 - 20!/(x-1)^21 - 3*21!/(x-1)^22 - (2*22!/2)/(x-1)^23)
Evaluate at zero and divide by 20! gives
1/8 * (1-3*21+2*21*22/2+1-3*21+2*21*22/2)
Anonymous at Wed, 8 May 2024 06:33:57 UTC No. 16165355
For those of you that do math at a grad level, how do you get over constantly feeling like a retard? It's gratifying when you finally figure out some proof that you've been spending days on but it's brutal constantly feeling like it's never good enough.
Anonymous at Wed, 8 May 2024 06:38:40 UTC No. 16165359
>>16165355
Feeling like a retard is part of the process. If you *don't* feel like a retard you aren't pushing yourself hard enough.
Anonymous at Wed, 8 May 2024 16:09:50 UTC No. 16165997
kurwa zmieniłem tę jebaną odpowiedź i nie będę miał 100 kurwaaaaa
Anonymous at Wed, 8 May 2024 16:17:37 UTC No. 16166008
>>16163209
Do you know what hypotenuse means
Anonymous at Wed, 8 May 2024 16:42:41 UTC No. 16166033
>>16165359
Thank you for the encouragement. I guess I am a retard, I'll just slowly become a retard that's moderately okay at measure and functional analysis.
Anonymous at Wed, 8 May 2024 16:44:02 UTC No. 16166037
Are there any good YouTube lectures for Measure Theory?
Anonymous at Wed, 8 May 2024 16:47:47 UTC No. 16166039
>>16166033
As a fellow retard, I'll add that it can be worth it to skip a proof or two, at least for a while.
Sure, it feels bad, but in the time you save you can learn plenty of different things that you _can_ figure out.
I've found that, usually, when I come back to something later, I have lots of different ideas about the topic than I had initially.
Anonymous at Wed, 8 May 2024 17:52:33 UTC No. 16166122
>>16163209
it is thought that Dynkin Diagrams would be of use in communicating with Aliens>
>>16163634
a notation that is common in some circles [math]\sum \{ij : 0 \leq i <j\leq 3\}[/math], which would evaluate to something like 11. an oddball notation is Einstein notation, check that shit out. but most people just play it by ear with superscripts and subscripts that make sense to them
Anonymous at Wed, 8 May 2024 17:57:53 UTC No. 16166129
>>16165355
It's the same process as weight lifting. At first it's really heavy and you can barely do a rep but if you keep at it eventually you can do multiple reps and wonder why you ever had problems. When you make it through your first upper division course you will also gain a lot of confidence (say like intro algebra top or algebraic geometry, measure theory, whatever).
Anonymous at Wed, 8 May 2024 17:58:14 UTC No. 16166130
>>16163634
>>16166122
also check out Dijkstra notation. its strictly better but not worth trhe trouble of switching over
Anonymous at Wed, 8 May 2024 18:22:26 UTC No. 16166153
>>16166144
>On average 20%
There is no way to answer this for sure without knowning the exact probability distribution. If it's possible that 100% of the water of a bucket will be lost then even 999 buckets could be low if you're unlucky.
Anonymous at Wed, 8 May 2024 18:22:56 UTC No. 16166154
>>16166144
You lose 20% of the water you bring, which means you're left with 80%.
You want 160 litres of water, so 160 should be 80% of the number of litres, and thus the number of buckets, that you gather.
Hence [math]160=0.8b[/math]
Anonymous at Wed, 8 May 2024 18:31:38 UTC No. 16166161
>>16166154
Thank you.
Anonymous at Wed, 8 May 2024 18:35:57 UTC No. 16166169
Best textbook to learn General relativity for mathematicians?
Anonymous at Wed, 8 May 2024 19:08:59 UTC No. 16166200
>>16166144
what game?
Anonymous at Wed, 8 May 2024 21:56:27 UTC No. 16166483
>>16166169
>Best textbook to learn General relativity for mathematicians?
Anonymous at Wed, 8 May 2024 21:59:20 UTC No. 16166487
>>16160030
Hello, I'm not the anons you were replying to but thanks for the course recommendation. If one were to follow this probability course, is there any accompanying text that would be recommended along with it, like a set of lecture notes or something for reference and maybe exercises, or a separate exercise set?
Anonymous at Wed, 8 May 2024 22:45:44 UTC No. 16166536
>>16160352
What to study for algebraic geometry
Anonymous at Wed, 8 May 2024 23:08:59 UTC No. 16166556
>>16166536
commutative algebra, basic differential geometry.
Anonymous at Wed, 8 May 2024 23:23:01 UTC No. 16166569
>>16166487
They use B.K. Driver's Probability Tools with Examples. Super rigorous and very "analysis forward" presentation of probability theory.
I like it quite a lot as a "secondary" measure theoretic probability text after you've already gotten a good feel for things but it might not be the easiest as a first read introduction to the topic. There's a ton of exercises and the standard homework assignment list in the beginning of the book if I'm remembering correctly and it should be free through UC San Diego's website.
Anonymous at Wed, 8 May 2024 23:42:23 UTC No. 16166583
>>16165355
Nobody I know spends more than a couple hours a day fiddling with a problem that you're making no progress on
There are many other things you can (and need to) do which you're actually capable of that you should always be able to give yourself a daily reminder that your brain isn't complete cottage cheese
Anonymous at Thu, 9 May 2024 01:17:20 UTC No. 16166657
>>16166129
My post was because I just finished measure. I got a B+ (which was above average for my class) but I feel like I honestly didn't earn that grade even though in some sense I objectively did. I definitely learned a ton in that course but I'm not sure I'm much more confident in my proofs than I was prior because I'm just kind of a retard sometimes.
It doesn't help that I'm not actually a math PhD and am instead doing a "math minor" for my EE PhD. It's kind of funny though. In some sense we have an advantage in EE because we have so much exposure to such advanced math so early, and as a result dealing with PDEs and complex analysis isn't that scary. We definitely don't focus on proofs though, and as a result I have a pretty underdeveloped skill set in that regard despite being in some sense more apt at the "computation" side of math than my math grad peers.
Anonymous at Thu, 9 May 2024 02:38:47 UTC No. 16166712
What to study for algebraic topology
Anonymous at Thu, 9 May 2024 04:11:37 UTC No. 16166820
Gaitsgory solved geometric langlands
Anonymous at Thu, 9 May 2024 05:43:24 UTC No. 16166883
>>16160352
Condensed Proof of Riemann Hypothesis
Anonymous at Thu, 9 May 2024 06:42:33 UTC No. 16166927
Damn, y'all some high IQ niggas up in here.
Well, I'll leave you to it.
Anonymous at Thu, 9 May 2024 15:33:21 UTC No. 16167472
>>16160352
test
Anonymous at Thu, 9 May 2024 15:36:13 UTC No. 16167474
>>16160647
It is a simple logical fact that
[eqn] \forall \epsilon > 0 \quad | a - b| < \epsilon \iff a = b [/eqn]
>But le heckin REALS
It's also true that
[eqn] \forall n \in \mathbb N \quad | a - b| < 1/n \iff a = b [/eqn]
Anonymous at Thu, 9 May 2024 15:37:17 UTC No. 16167476
>>16164154
Jungnickel for algorithmic graph theory.
Anonymous at Thu, 9 May 2024 15:40:59 UTC No. 16167483
>>16162263
Something that looks like Euclidian space when you zoom into a small point. For example, you can draw longitudes and latitudes on a sphere, but if you consider a small portion of it , they will look like a grid i.e., the 2d Euclidean place. It's basically a fancy word for smooth shapes.
Anonymous at Thu, 9 May 2024 18:08:35 UTC No. 16167696
>>16166712
jump right into hatcher if you're solid on point-set.
Anonymous at Thu, 9 May 2024 18:15:40 UTC No. 16167704
is the Khan academy statistics course any good?
i'm starting a research gig soon and I literally can't remember how to do anything.
🗑️ Anonymous at Thu, 9 May 2024 19:09:33 UTC No. 16167783
>>16166712
tom Dieck
>>16166712
skip shartcher
Anonymous at Thu, 9 May 2024 19:39:22 UTC No. 16167833
>>16166712
tom Dieck, skip shartcher >>16167696
Anonymous at Thu, 9 May 2024 20:20:37 UTC No. 16167907
>>16167704
What's your level of math background and how serious does your working knowledge of statistics need to be? You might just be better off slowly working through a PDF of one of the standard undergrad books.
Sheldon Ross's Introduction to Probability and Statistics for Scientists and Engineers is free online and pretty good.
Anonymous at Thu, 9 May 2024 23:22:45 UTC No. 16168143
Can anyone give a comparison between Janich, Vector analysis, and Munkres, Analysis on manifolds?
Anonymous at Fri, 10 May 2024 00:27:51 UTC No. 16168218
Guys, I'm proud of myself.
I was trying to cook up a formula for a matrix with given eigenvectors and eigenvalues similar to how lagrange interpolation is done and I basically rediscovered the hodge star operation.
My whole motivation was to represent complex numbers as real 2x2 matrices (I'm trying to do quaternions too).
[math]1 \sim \begin{bmatrix}1 & 0\\ 0 & 1 \end{bmatrix},\ i \sim \begin{bmatrix}sinh(t) & cosh(t)\alpha \\ -cosh(t)/\alpha & -sinh(t) \end{bmatrix}.[/math]
Anonymous at Fri, 10 May 2024 03:56:30 UTC No. 16168486
>>16168143
Jänich = 4chan
Munkres = Reddit
Anonymous at Fri, 10 May 2024 09:59:17 UTC No. 16168764
>>16168486
Munkres, then.
Anonymous at Fri, 10 May 2024 10:31:51 UTC No. 16168795
>>16168764
Wrong.
Anonymous at Fri, 10 May 2024 13:42:59 UTC No. 16168969
>>16168930
IUTT truly is the ultimate expression of algebra. It so carefully walks the line between brilliance and pure schizo-babble that not even the most battle-hardened number theorists know what's real and what's just from not taking their meds.
Anonymous at Fri, 10 May 2024 17:15:17 UTC No. 16169280
>>16169230
He won. Rest in peace king.
Anonymous at Fri, 10 May 2024 17:29:29 UTC No. 16169296
>>16169230
>makes 30billion
>dies from chain smoking
Anonymous at Fri, 10 May 2024 17:33:33 UTC No. 16169305
>>16169230
I bet it was the VAXX
Anonymous at Fri, 10 May 2024 17:50:24 UTC No. 16169327
>>16169230
His interview from Numberphile:
https://www.youtube.com/watch?v=QNz
Anonymous at Fri, 10 May 2024 18:01:33 UTC No. 16169335
>>16166556
>>16166536
>algebric geometry
>differential geometry
Anonymous at Fri, 10 May 2024 18:09:13 UTC No. 16169341
>>16169335
Yeah? It's not necessary but having that knowledge beforehand helps with topics like smoothness and tangents. And there's a plenty of quality literature like Griffiths-Harris that assumes familiarity with differential geometry.
Anonymous at Fri, 10 May 2024 19:55:53 UTC No. 16169517
>Complex analysis
>Prof claims the following without reference or proof
>Almost all roots of polynomials with complex coefficients are complex
.
How does this work? R and C have the same measure
Anonymous at Fri, 10 May 2024 20:01:33 UTC No. 16169528
>>16169517
R has measure 0 in C.
Anonymous at Fri, 10 May 2024 20:15:19 UTC No. 16169548
>>16169528
How come?
Anonymous at Fri, 10 May 2024 20:15:32 UTC No. 16169549
I've been taking a online remedial mathematics course and I'm currently on long division. I feel like I need to start over because I rushed through the course and the course itself is quite lackluster. I've been passing the sections with flying colors but they only teach me how to follow one procedure and not how to gain number sense. The same exact problem plagues Khan academy so it isn't that good either.
If I'm asked to show how to solve a basic arithmetic problem in multiple different ways I would flounder. Currently I haven't gained the ability to do mental arithmetic quickly which would hinder me later down the road if I proceed to more advanced math topics.
Is there a book that can help me alleviate this issue?
Anonymous at Fri, 10 May 2024 20:20:04 UTC No. 16169558
>>16169549
Openstax, these books in this order, they are all free to download from the Openstax website:
Prealgebra 2e,
Elementary algebra 2e,
Intermediate algebra 2e,
College algebra 2e
Anonymous at Fri, 10 May 2024 20:23:30 UTC No. 16169562
>>16169548
What is the measure of R in R^2?
Anonymous at Fri, 10 May 2024 20:37:31 UTC No. 16169589
>>16169549
Euclids elements
Anonymous at Sat, 11 May 2024 07:38:01 UTC No. 16170411
>>16169549
This book would do it.
Anonymous at Sat, 11 May 2024 09:02:31 UTC No. 16170530
What do i need to know to make sure i score at least 30 on aleks math placement? Ive been out of school for years.
Anonymous at Sat, 11 May 2024 09:42:58 UTC No. 16170546
>>16166712
Bredon's Topology and Geometry is vastly superior to both of the books that were recommended to you. Unlike tom Dieck, it focuses on geometry and not categorical troon shit, and unlike Hatcher its proofs are precise and rigorous.
Cult of Passion at Sat, 11 May 2024 09:54:01 UTC No. 16170549
>>16169296
Or chain smoking made him 30 billion.
https://youtu.be/95g9fgH1Qmc
t.Doctor of M.D. and Pure Mathematics
I dont post in this thread because youre students trying to learn, not because I cant rek the place.
Anonymous at Sat, 11 May 2024 20:22:50 UTC No. 16171254
>>16170546
>categorical troon shit
obsessed
Anonymous at Sat, 11 May 2024 20:25:03 UTC No. 16171256
>>16170411
>human calculator
>obese
aparently this guy cant even do basic arithmetic
Anonymous at Sat, 11 May 2024 22:09:26 UTC No. 16171399
>>16160352
Any functioning ways around chegg paywall?
Is it even worth trying to bypass?
Anonymous at Sat, 11 May 2024 22:15:59 UTC No. 16171409
im averaging 5 pages a day of shilov's linear algebra. it seems to be filtering me hard. Is this normal? Any other books you guys can recommend?
🗑️ Anonymous at Sat, 11 May 2024 23:55:14 UTC No. 16171495
>>16171409
5 pages is fine.
Anonymous at Sat, 11 May 2024 23:59:50 UTC No. 16171502
>>16171409
5 pages is fine, but I don't like Shilov personally because he introduces determinants in the first chapter. I feel determinants don't really make much sense until you study analysis on manifolds. Personally, I prefer Halmos or Axler, but both need to be supplemented by a book that covers matrix algebra for a complete treatment.
Anonymous at Sun, 12 May 2024 00:00:29 UTC No. 16171503
>>16170411
pure sthetics
Anonymous at Sun, 12 May 2024 00:05:16 UTC No. 16171504
>>16171256
the shoemaker's son always goes barefoot
>>16171409
I only read Serge Lang in this subject, is Shilov a recommended read?
Anonymous at Sun, 12 May 2024 00:10:19 UTC No. 16171511
Do you guys use several different books to study one subject? I have Axler and Hoffman's linear algebra and I wonder if I should read them both or just focus on one of them.
Anonymous at Sun, 12 May 2024 00:53:45 UTC No. 16171547
>>16171511
I have like 8 books on Probability Theory because they all cover different topics in the second half and with different emphasis.
Anonymous at Sun, 12 May 2024 01:28:37 UTC No. 16171572
>>16171547
Probability is so stupid, something will either happen or it just won't. there's just no point worrying about it at all, much less dedicating several hours of study to it.
Anonymous at Sun, 12 May 2024 01:32:08 UTC No. 16171574
>>16171572
Lol, this is a funny joke
Anonymous at Sun, 12 May 2024 01:33:34 UTC No. 16171576
>>16171572
Incredible. This man might just be what we need to solve math once and for all.
Anonymous at Sun, 12 May 2024 02:11:27 UTC No. 16171603
>>16171511
Considering how unconventional Axler is, it does make sense to complement it with some other book, but not really Hoffman & Kunze; something more applied instead. With something like Analysis, it's better to just use one book because how homogenous the treatments of the subject are.
Anonymous at Sun, 12 May 2024 02:36:05 UTC No. 16171640
>>16170546
Why do troonies like category shit so much?
Anonymous at Sun, 12 May 2024 02:56:00 UTC No. 16171659
>>16171572
Brainlet
Anonymous at Sun, 12 May 2024 02:57:25 UTC No. 16171663
>>16171572
You should go buy thousands of lottery tickets. You either win or you dont so its 50/50
Anonymous at Sun, 12 May 2024 03:20:16 UTC No. 16171683
>>16171254
Kys, Zero.
Anonymous at Sun, 12 May 2024 03:25:19 UTC No. 16171691
>>16171640
Because it has a critical mass of like minded people to become a safe space. Or maybe just because it makes you buttmad.
Anonymous at Sun, 12 May 2024 03:41:10 UTC No. 16171714
>>16171663
You missed my point. Whether I buy 1 lottery ticket or 1000 it’s all completely pointless because the probability to win is extremely small, what’s the point in knowing whether that extremely small probability is 0.000000001% or 0.000000002%? So why worry?
Anonymous at Sun, 12 May 2024 03:43:56 UTC No. 16171717
>>16171714
Just think about it. You either win or you don't. That's 50/50.
Anonymous at Sun, 12 May 2024 03:45:17 UTC No. 16171721
>>16171714
Do you actually want an answer as to why one would study probability theory or do you just want me to call you a retard? I don't mind either (or both).
Anonymous at Sun, 12 May 2024 03:59:13 UTC No. 16171737
>>16171717
It’s not 50/50, but it’s a probability so small that you know you will never win, what’s the point in calculating it? What’s the point in knowing that if I buy two more tickets that probability will increase by 0.00000001%? There’s no fucking point, you know you’re not gonna win so why are you worrying so much about it?
>>16171721
I’ll tell you why people study probability theory and other stupid crap: because the entire academic world is based upon that. Do you think every physicist is researching the unknown phenomena from quantum mechanics or general relativity? No, most of them are studying an extremely obscure field just to have a job and funds. Do you think most mathematicians are trying to prove the millennium problems? No, instead they waste their time researching the “deep” intricacies of probability theory. The entire academic world is built upon this, people aren’t doing useful research, they aren’t moving their fields forward, they’re just trying to find an obscure subject so they can release dozens of papers on it every year and call themselves experts on that in the hopes that they will be hired by some good uni and raise their prestige. It’s pathetic.
Anonymous at Sun, 12 May 2024 04:02:03 UTC No. 16171740
>>16171737
First day on /sci/?
Anonymous at Sun, 12 May 2024 04:05:17 UTC No. 16171743
>>16171737
My brother in Christ, you are genuinely retarded beyond saving. Probability theory, Stochastic Processes and statistics are perhaps the most practical of all possible math disciplines for any applied science/engineering field. Probability theory literally forms the basis by which we analytically model experimental uncertainties. That's about as useful as it gets.
Anonymous at Sun, 12 May 2024 04:10:54 UTC No. 16171751
>>16171743
That’s not what I’m talking about. The basics of probability theory are useful, but do you honestly believe engineers and physicists are reading papers on probability theory? No, there’s no useful research being done in it, there’s just people using it to get funds and prestige, there’s no point in learning anything about it beyond undergraduate stuff. And for the layman there’s not even a point in learning it at all. What does it matter for the average person whether or not the probability of winning the lottery will be 0.000001% higher if they buy two tickets? What does it matter for the engineer whether or not an extremely obscure theorem has been discovered in probability theory?
Anonymous at Sun, 12 May 2024 06:04:33 UTC No. 16171906
>>16171751
> The basics of probability theory are useful, but do you honestly believe engineers and physicists are reading papers on probability theory? No, there’s no useful research being done in it, there’s just people using it to get funds and prestige, there’s no point in learning anything about it beyond undergraduate stuff.
I'm an engineer who focuses primarily on non-linear state estimation and non-linear signal detection theory. Both of these topics are applied in the sense that the fundamentals of the probability distributions relate to radar/sonar, but they are both heavily reliant on some fairly in depth topics in probability theory. In particular large deviations theory is very relevant to signal detection and allows for the primary mechanism of analysis of error rate curves for correlated sample sequences (as you can't use the standard CLT constructions with correlated samples in the sum). Renewal theory and ergodic processes are also central to state estimation for a target moving in the presence of process and measurement noise.
These are graduate level probability theory topics that have a lot of relevance to my engineering field.
Anonymous at Sun, 12 May 2024 06:22:56 UTC No. 16171918
>>16171737
Correct, and also why we will never reach the stars. Getting grants to research more useless shit rather than researching shit that matters,
Anonymous at Sun, 12 May 2024 07:05:47 UTC No. 16171949
>>16171511
Reading two books in parallel seems like a waste of time, but having several books is very useful
If an explanation isn't clicking for you it's good to be able to go read a different one rather than bashing your head into it
Plus different books will have different advanced/side topics, even if the core content is the same
Anonymous at Sun, 12 May 2024 12:57:06 UTC No. 16172217
>>16160790
retarded memeslop
Anonymous at Sun, 12 May 2024 14:04:40 UTC No. 16172320
Good morning, happy mother’s day, God bless you, Jesus loves you.
Anonymous at Sun, 12 May 2024 20:50:36 UTC No. 16172830
>>16167474
That's just an arbitrary statement one must, for themselves, accept as fact. If you cannot explain it rationally, perhaps it cannot be explained rationally. However, to accept what one has heard *merely* because one has heard it is irrational. Irrational application of mind is conducive to wrong viewpoints and thinking "true" that which is "untrue".
Anonymous at Sun, 12 May 2024 21:11:47 UTC No. 16172857
Here's a fun recreational maths problem I came up with.
In picrel is an equilateral triangle whose vertices are at (-1,0), (1,0) and (0,sqrt(3)). Point is picked from inside and then shortest paths are drawn from that point to reach of the sides. Viviani's theorem says the sum of those lengths is eaqual to the height of the triangle.
Find coordinates for the point such that the orange line is twice as long as the green line, and the blue line is twice as long as the orange line.
Anonymous at Sun, 12 May 2024 21:24:32 UTC No. 16172871
>>16172857
>In picrel is an equilateral triangle whose vertices are at (-1,0), (1,0) and (0,sqrt(3)).
those aren't the vertices of an equilateral triangle
Anonymous at Sun, 12 May 2024 21:36:43 UTC No. 16172889
>>16172871
You sure
🗑️ Anonymous at Sun, 12 May 2024 22:10:08 UTC No. 16172924
I am playing around with automated theorem provers and apparently given the following axioms (in first order logic):
all X (r(X) <-> ((exists N ((f(N)) = X)))).
all Y all Z (r2(Y) <-> exists Z ((Z=c1) -> r(c3))).
The following statement is true:
r2(c2).
Can anyone explain why is that so?
Here is the proof given by Prover9:
1 (all X (r(X) <-> (exists N f(N) = X))) # label(non_clause). [assumption].
2 (all Y all Z (r2(Y) <-> (exists Z (Z = c1 -> r(c3))))) # label(non_clause). [assumption].
3 r2(c2) # label(non_clause) # label(goal). [goal].
5 r(x) | f(y) != x. [clausify(1)].
8 r2(x) | c1 = y. [clausify(2)].
9 r2(x) | -r(c3). [clausify(2)].
10 -r2(c2). [deny(3)].
13 c1 = x. [resolve(10,a,8,a)].
14 -r(c3). [ur(9,a,10,a)].
19 r(x). [para(13(a,2),5(b,1)),unit_del(b,13
20 $F. [resolve(19,a,14,a)].
Anonymous at Sun, 12 May 2024 23:10:26 UTC No. 16172993
>>16172857
green line has length sqrt(3)/7
orange line has length 2sqrt(3)/7
find the line describing the left side of the triangle
parallel line whose distance is sqrt(3)/7
point on that line with y=2sqrt(3)/7
Anonymous at Sun, 12 May 2024 23:45:18 UTC No. 16173023
>>16160352
What if like the white light experiment we are observing reality as a mix and not what it is?
Anonymous at Sun, 12 May 2024 23:57:10 UTC No. 16173038
Wildberger is a genius.
Anonymous at Mon, 13 May 2024 00:21:35 UTC No. 16173071
>>16173023
This is the maths thread. If you want to "observe reality" you can go do it somewhere else.
Anonymous at Mon, 13 May 2024 01:14:37 UTC No. 16173126
>>16171714
You lose money in the long run. The more tickets you buy the more certain that becomes. Knowing the probability lets you determine what is worth spending your money on.
Anonymous at Mon, 13 May 2024 05:25:02 UTC No. 16173368
>>16172830
Hope you get well soon, anon
Anonymous at Mon, 13 May 2024 06:17:44 UTC No. 16173436
>>16172857
-1 + (5/4) / 7 + (3/2) / 7
2/7 * sqrt(3)
tried doing it in my head alone w/o writing anything down
Anonymous at Mon, 13 May 2024 12:13:39 UTC No. 16173764
>>16173368
I am well. I may seem upset but I'm not. I'm just viscerally aware of the theme of being correct.
Anonymous at Mon, 13 May 2024 12:44:40 UTC No. 16173806
>>16173071
Lol. Mathematics is an abstract observation of nature.
Anonymous at Mon, 13 May 2024 13:38:16 UTC No. 16173889
>>16173806
Maths has nothing to do with nature, physics is the study of nature through mathematical methods.
Anonymous at Mon, 13 May 2024 14:33:14 UTC No. 16173947
>>16173071
That view is retarded and everything wrong with modern maths.
Anonymous at Mon, 13 May 2024 14:56:59 UTC No. 16173978
>>16171254
ywnbaw mate
Anonymous at Mon, 13 May 2024 19:57:52 UTC No. 16174401
How to get into algebraic geometry
Which books, resources to study
I know algebra till ring theory, analysis ,topology, complex analysis
Anonymous at Tue, 14 May 2024 02:13:26 UTC No. 16174866
>>16174401
Haven't studied the subject but heard very very good things about Vakil's "The Rising Sea"
Anonymous at Tue, 14 May 2024 08:13:21 UTC No. 16175195
Asking for opinion; any student of algebra knows of the following result:
"In a finite ring [math]R[/math] with identity, every element is a unit or a zero divisor"
This result is not only well-known, but it is also very easily provable even by undergraduates. So my question is, if I were to use this in an article, do I even need to cite? Is there even a reference to go back to? Like any reader with an algebra background can prove this himself literally within 2 minutes. Is it okay if I just state in the article "the following well-known result....." and just don't bother with any citation?
Anonymous at Tue, 14 May 2024 09:21:48 UTC No. 16175233
>>16174401
wildberger's rational trigonometry series.
Anonymous at Tue, 14 May 2024 09:34:15 UTC No. 16175243
>>16175195
Do you use citations when you write 2+2=4?
Anonymous at Wed, 15 May 2024 02:19:29 UTC No. 16176509
Is there a 2x2 matrix A such that all the following hold:
(1) all entries of A are rational
(2) neither +1 nor -1 is an eigenvalue of A
(3) some positive integer power of A is the identity matrix
Anonymous at Wed, 15 May 2024 04:18:32 UTC No. 16176631
>>16176509
Sorry that question is dumb
I think this one is less obvious though: Is there a 2x2 matrix A such that all the following hold?
(1) all entries of A are rational
(2) +1 is not an eigenvalue of [math] A^4 [/math]
(3) some positive integer power of A is the identity matrix
Anonymous at Wed, 15 May 2024 05:22:01 UTC No. 16176689
>>16176509
>>16176631
I mean, are they actually obvious? A 2x2 matrix A that is diagonalizable has a QDQ^T form, so A^n = QD^nQ^T. For 2x2 matrices it's pretty easy to write all the values out, and you see that either the eigenvalues are either +/- each other or it comes out that A is a diagonal matrix, and both don't work for A^n = I unless you got 1 and -1s. This means A would have to be non-diagonalizable. For a 2x2 matrix there's the requirement that (a-d)^2 + 4bc = 0, so you can check that A^2 is also non-diagonalizable, and so on. At no point will you ever hit a diagonal matrix, which the identity matrix, I, is. Maybe something can be said about Jordan–Chevalley decomposition, idk much lin alg.
Anonymous at Wed, 15 May 2024 06:16:01 UTC No. 16176730
I like to come up with maths problems by myself and then try to solve them. Here's what I came up with recently.
>pick three uniformly random points from a square, connect them with lines to make a triangle
>repeat two more times so you have three triangles now inside the square
>pick one more random point inside the square
>the problem is as follows, what is the probability that the final point lies inside of all of the three triangles simultaneously
Anonymous at Wed, 15 May 2024 06:31:59 UTC No. 16176740
>>16176631
Consider the companion matrix of [math]\Phi_6(x) = x^2 - x + 1[/math]: [math]\pmatrix{0 & 1 \\ -1 & 1}[/math].
This matrix has integer coefficients and has two complex eigenvalues, the two primitive sixth roots of unity.
This is the most complex behavior you'll get out of 2x2 matrices, since the largest integer with [math]\phi(n) = 2[/math] is 6.
Anonymous at Wed, 15 May 2024 06:38:37 UTC No. 16176744
>>16169562
C isn't R^2
🗑️ Anonymous at Wed, 15 May 2024 07:19:29 UTC No. 16176778
>>16176730
Edit: the answer is probably 1331/2985984 by using google
Anonymous at Wed, 15 May 2024 07:57:35 UTC No. 16176798
>>16176744
Lebesgue measure does not use the arithmetic properties of C, so it sees C and R^2 the same.
Anonymous at Wed, 15 May 2024 10:28:32 UTC No. 16176888
>>16176879
For every number beta below 1 you show that you can find a bigger element in S. This implies [math]\sup{S} \geq 1[/math].
The observation at the start of the solution showed that every element in S is smaller than 1 so [math]\sup{S} \leq 1[/math].
Together this implies [math] \sup{S} = 1[/math] since [math] \leq[/math] is a total order.
Anonymous at Wed, 15 May 2024 11:42:10 UTC No. 16176941
>>16176888
wow makes thanks a lot. Do you recommend any books as such for this? I don't think I would've been able to figure it out on my own to be honest. Syllabus is in picrel
Anonymous at Wed, 15 May 2024 12:06:41 UTC No. 16176959
>>16176879
God, analysis is gay
Anonymous at Wed, 15 May 2024 18:03:23 UTC No. 16177235
Is there a name for the sequences of subsets, i.e. for
[math]{\mathbb N}\to{\mathcal P}X[/math]
?
Possibly ruling out that the values can be empty.
Basically nets, but on N.
Anonymous at Wed, 15 May 2024 19:29:33 UTC No. 16177326
>>16177235
subset sequence
Anonymous at Wed, 15 May 2024 21:32:30 UTC No. 16177511
>>16177507
The orthodox construction for 7.8
Anonymous at Wed, 15 May 2024 22:32:24 UTC No. 16177575
This is elementary number stuff, am I to believe that all these people that do cuckulus here dint even understand the most base number theory
Anonymous at Wed, 15 May 2024 22:48:53 UTC No. 16177596
>>16165355
>For those of you that do math at a grad level, how do you get over constantly feeling like a retard?
You don't. And it never goes away. If you don't feel like that, you're doing something wrong.
Anonymous at Wed, 15 May 2024 23:57:48 UTC No. 16177685
/sci/ is ignorant of geometry?
Anonymous at Thu, 16 May 2024 02:42:00 UTC No. 16177838
Springer has Greub's Multilinear Algebra on sale for only $17 ATM. Is it worth going through a multilinear algebra book to get a more comprehensive background in tensors or should going through something like Lee's smooth manifolds book be enough?
Anonymous at Thu, 16 May 2024 04:02:34 UTC No. 16177885
>>16177838
Math?
Anonymous at Thu, 16 May 2024 09:00:53 UTC No. 16178112
>>16177685
down with Euclid, death to triangles
Anonymous at Thu, 16 May 2024 10:50:30 UTC No. 16178202
I'm 24, self studying calculus and interested in going to university for math next year to get a degree for an engineering career but I live in a poor part of a shithole country (South Africa) with only a smartphone and it seems like the syllabus at the five universities I can reach expects desktop computer skills and programming knowledge but doesn't teach them and there aren't any colleges to help.
A cheap used windows laptop with okay specifications for running basic matlab, zoom, outlook and antivirus stuff would cost me about 7 months of disposable income (I only have 3 months' worth saved up and can't get a better job or more hours or lower rent+food costs).
What can I do to make this problem easier?
Anonymous at Thu, 16 May 2024 11:09:25 UTC No. 16178211
>>16178202
What does your problem have to do with mathematics?
Anonymous at Thu, 16 May 2024 11:20:40 UTC No. 16178228
>>16177885
>>16178211
you will never be a mod
Anonymous at Thu, 16 May 2024 11:25:38 UTC No. 16178239
>>16178202
Buy a used old latitude or thinkpad or elitebook. And install mint
Anonymous at Thu, 16 May 2024 12:35:31 UTC No. 16178320
>>16177885
Yes, I'm not sure if you are aware, but multilinear algebra and smooth manifolds are both topics within mathematics.
Anonymous at Thu, 16 May 2024 13:15:58 UTC No. 16178360
>>16178320
Your brain is a smooth manifold
Anonymous at Thu, 16 May 2024 13:24:54 UTC No. 16178365
>>16171640
they don’t anymore, those ones are 41% already. zoomer troons love Rustlang instead
Anonymous at Thu, 16 May 2024 13:32:31 UTC No. 16178371
>>16178360
Sometimes yeah. I wouldn't be asking for advice from people with more math experience than me if I wasn't a bit smooth brained. If you don't know the answer to the question that's fine, but it's definitely math related.
Anonymous at Thu, 16 May 2024 13:32:49 UTC No. 16178372
Euclid mogs cuckulus
Anonymous at Thu, 16 May 2024 14:11:25 UTC No. 16178406
Anonymous at Thu, 16 May 2024 14:45:08 UTC No. 16178445
>>16177838
How come springer sells those books for so cheap? There's some quite popular books listed for 17$, and I doubt that price is generating significant margins for them.
Anonymous at Thu, 16 May 2024 21:37:26 UTC No. 16178953
p-adic bros? How do I show that the set {1, 1/2, 1/3, 1/4, ...} is dense in the subset { x in Q_p : |x|_p >= 1}? The book only gives me the hint that the same statement holds for the inverses. But that is trivial and doesn't help me at all.
Anonymous at Thu, 16 May 2024 22:23:31 UTC No. 16179012
>>16178445
Probably just to move paperbacks they've printed a while ago that haven't sold. Printing paperbacks isn't exactly expensive, and if it's already been sitting on the shelf for a while there's not a ton of opportunity cost for selling it just barely above break even.
Anonymous at Thu, 16 May 2024 22:34:23 UTC No. 16179020
>>16178445
Maybe that's a softcover book, they are usually cheap
Anonymous at Thu, 16 May 2024 23:55:22 UTC No. 16179082
>>16179012
It's not expensive to print hardcovers either especially faux sewn hardcover they sell.
Anonymous at Thu, 16 May 2024 23:58:12 UTC No. 16179085
>>16179082
Well yeah, it's not expensive (hence why you'll see hardcovers for like $30 sometimes) but it's certainly cheaper than the $3-4 the soft covers cost them to print.
Anonymous at Fri, 17 May 2024 00:14:39 UTC No. 16179107
finite set theory is beautiful and amazing and incredible and i love it so much and it's just wonderful.
Anonymous at Fri, 17 May 2024 01:36:55 UTC No. 16179197
>>16179107
I prefer combinatorics
Anonymous at Fri, 17 May 2024 04:33:03 UTC No. 16179357
>>16178202
I don't live in a poor shit hole country, but in mine universities loan laptops out to poor people for use in university studies
I'd put together a CV of sorts showing what you've been self studying, what you plan to study, basically a document saying im not going to steal this and disappear
Enrolling would probably help, if you only have 3 months saved not sure how you plan on funding university but good luck
if they dont offer this no idea
If they require a pc they may have on campus?
Anonymous at Fri, 17 May 2024 04:38:55 UTC No. 16179366
>>16178372
Archadmides buckbroke Euclid and Cavalieri pointed the line to integral calculus
Cope and seethe
Anonymous at Fri, 17 May 2024 05:26:27 UTC No. 16179389
>>16179085
No, I mean they almost cost the same to make.
Anonymous at Fri, 17 May 2024 06:56:41 UTC No. 16179471
>>16178202
1. apply to nsfas nigga, lie if you have to
2. every university has a computer lab you can do your work in if you don't have a laptop
3. they don't expect you to know shit about programming coming in and you will almost certainly have an introduction to programming course
4. you can get a good quality refurbished thinkpad for about 5k
Anonymous at Fri, 17 May 2024 07:53:11 UTC No. 16179516
1. algebra or analysis?
2. d4 or e4?
Anonymous at Fri, 17 May 2024 08:06:22 UTC No. 16179532
>>16179516
1. I'm an algebra pilled analysis maxxer
2. f4
Anonymous at Fri, 17 May 2024 10:07:56 UTC No. 16179616
>>16179197
finite set theory is part of combinatorics so it's okay
Anonymous at Fri, 17 May 2024 14:38:54 UTC No. 16179956
so much disinformation peddled in mathematics teaching. like the "proof" that the square root of 2 is irrational. All it does is prove that it isn't a rational number. it doesn't define irrational numbers, it doesn't prove that the square root of two is a number, and it doesn't prove that it's an irrational number. At the heart of this is just relegation of the meaning of number to meta-mathematics, where it's dealt with extremely unseriously, using terms which aren't so precisely defined.
Anonymous at Fri, 17 May 2024 15:31:31 UTC No. 16180010
>>16179532
>f4
Retard
Anonymous at Fri, 17 May 2024 16:53:36 UTC No. 16180112
>>16179956
>All it does is prove that it isn't a rational number.
which is what it claims to prove.
Cult of Passion at Fri, 17 May 2024 17:17:06 UTC No. 16180141
The very thing it was required to show
Anonymous at Fri, 17 May 2024 17:23:24 UTC No. 16180151
>>16180010
Ha! It's supposed to look retarded. This adds to the humiliation of the defeated opponent.
Anonymous at Fri, 17 May 2024 17:25:16 UTC No. 16180152
>>16179532
>not f3
If you play any opening other than 1. f3 2. Kf2 I spit upon you
Anonymous at Fri, 17 May 2024 17:48:02 UTC No. 16180174
>>16179956
1: no rational number is the square root of two
2: there is a non-negative square root for every non-negative real (closure of sqrt)
2: is trivial and left to the reader.
Anonymous at Fri, 17 May 2024 19:40:14 UTC No. 16180374
>>16171714
>1 ticket
>1000 tickets
>0.000000001%
>0.000000002%
Midwit that can't even conjecture statistics on a hypothetical. Astounding. Assuming they were randomized and unique, the odds would be 1000x better which would absolutely make a difference and you would see it repeated over so many trials.
Anonymous at Fri, 17 May 2024 21:21:50 UTC No. 16180533
My understanding of math is that of an 8th grade. That's no joke. I completely dismissed maths when I was in high school and then went to the humanities. I started a Master's in NLP though and I'd like to get back to math and have some understanding of it, particularly for research papers.
Any ideas of where to start? I'm comfortable with programming by the way (Python, R, TypeScript) so I thought that perhaps learning some things with programming could be fun (with numpy for instance?) but I don't really know how to achieve that and if there are any resources online for tards like me (didn't find any). Otherwise if you have textbook recommendations I'd appreciate it.
Anonymous at Fri, 17 May 2024 21:39:03 UTC No. 16180564
>>16180533
AOPS Prealgebra.
Anonymous at Fri, 17 May 2024 21:42:11 UTC No. 16180570
>>16177838
>>16178445
Print-on-demand garbage. Get an old library copy from abebooks if you have to. Have some taste.
Or even better, use your library. And actually do problems. Stop becoming a book collector, and actually do math.
Anonymous at Fri, 17 May 2024 22:01:10 UTC No. 16180603
>>16180570
Well actually Springer publishes the best or edge of the science books
Anonymous at Fri, 17 May 2024 22:16:39 UTC No. 16180616
>>16180570
I don't think so? The last thing I got from Springer that was on sale was GTM 264 and my copy of came with a piece of paper showing a print date about a year before I ordered it.
I'm sure a lot of their stuff is print to order, but my guess is that some of the sales are for things that were printed for some bulk order that didn't go through or something or "regular stock" that didn't sell quickly or something.
Anonymous at Fri, 17 May 2024 23:19:51 UTC No. 16180670
How do I pirate math books? In the past I used to google book title + pdf and often find it, but google search has become unusable
Im interested in the workbooks of Chris McMullen
XF at Sat, 18 May 2024 00:23:08 UTC No. 16180750
>>16180533
so just get a high school maths book and go through it again? There are tons of free resources online also
Anonymous at Sat, 18 May 2024 04:44:46 UTC No. 16180995
>>16180936
That's a neat illustration and really intuitively demonstrates what's happening with that geometric series. Good work!
Anonymous at Sat, 18 May 2024 06:06:05 UTC No. 16181099
>>16180603
>>16180616
Retards like you is the reason why publishers got away with their awful print quality.
Anonymous at Sat, 18 May 2024 08:11:20 UTC No. 16181171
>>16181099
Springer has great print quality.
Anonymous at Sat, 18 May 2024 08:17:01 UTC No. 16181175
>>16181171
Well when you read kindergarten books many things look like poor quality ;d
Anonymous at Sat, 18 May 2024 09:12:30 UTC No. 16181212
>>16180936
I was way too distracted by the cool picture to realize that the only mathematical statement shown here is 2^2 = 4.
Anonymous at Sat, 18 May 2024 10:56:39 UTC No. 16181270
>Gauss grew to dominate his children and eventually had conflicts with his sons, because he did not want any of them to enter mathematics or science for "fear of lowering the family name", as he believed none of them would surpass his own achievements.
Based af
Anonymous at Sat, 18 May 2024 11:43:09 UTC No. 16181307
>>16181270
>BASED AF
Anonymous at Sat, 18 May 2024 11:45:07 UTC No. 16181310
>>16181307
For the gen alphas like you: Gauss had the skibidi rizz.
Anonymous at Sat, 18 May 2024 12:44:41 UTC No. 16181357
>>16181099
Where does my post say anything about print quality? I know a lot of Springer stuff is print to order, I'm just saying the book I got on sale recently wasn't.
Anonymous at Sat, 18 May 2024 12:51:22 UTC No. 16181370
>>16181270
based. when Gauss was a kid, JS Bach’s kids and grandkids already busy fucking up the Bach family name. I wouldn’t want my retard mongrel Hapa kids associated with my legacy either
Anonymous at Sat, 18 May 2024 17:06:14 UTC No. 16181716
>>16181171
Used to, old Springer prints are beautiful. What you get from them nowadays are shoddy print-on-demands.
Anonymous at Sat, 18 May 2024 17:39:02 UTC No. 16181765
>>16181270
HAHAHAHA omfg, such an asshole thing but you see his point a little. Like if MJ or Lebron forbade his kids from playing
Anonymous at Sat, 18 May 2024 19:15:10 UTC No. 16181852
I'm reading Knuth's Concrete Mathematics, and there is something very basic I cannot understand. How does I get to the U_n = 2^n solution which I should get withou being a genius as he states? Lmao. I'm actually retarded, my bad
For context, this is a proof by induction from the Hanoi tower recurrence.
Anonymous at Sat, 18 May 2024 19:33:34 UTC No. 16181864
>>16181852
[math]U_n[/math] is just [math]U_{n-1}[/math] times 2.
Since [math]U_0[/math] is [math]1 = 2^0[/math], [math]U_1[/math] will be [math]2 = 2^1[/math], [math]U_2[/math] will be [math]4 = 2^2[/math], [math]U_3[/math] will be [math]8 = 2^3[/math]...
the pattern sticks out pretty quickly, and since you're just doubling each time there's not much room for it to throw a curveball at you like a lot of the "obvious" patterns (i.e. traps) will
Anonymous at Sat, 18 May 2024 19:42:14 UTC No. 16181873
>>16181864
Thanks! That helped. One thing that I think is hard on studying math is that I have to rely a lot on baby steps. So I had to rewrite what you said in a way I couls understand. This gets better with practice, r-right...?
Anonymous at Sat, 18 May 2024 19:43:42 UTC No. 16181874
>>16181873
forgot to sned my train of thought
Anonymous at Sat, 18 May 2024 20:45:54 UTC No. 16181967
>>16181874
>>16181873
i can't read your handwriting but reading math does get easier with practice because you notice patterns and so most of what you read will be 'standard' and something you have already worked with before.
Anonymous at Sat, 18 May 2024 21:00:24 UTC No. 16181985
I hate complex analysis.
Anonymous at Sat, 18 May 2024 21:16:03 UTC No. 16182003
>>16178953
Taking inverses is a continuous function and thus maps dense subsets of any set S into dense subsets of the image of S.
Anonymous at Sat, 18 May 2024 21:34:24 UTC No. 16182022
>>16181967
NTA but I can read script. It says:
>I was supposed to know that U_n=2^n which means that
>T_n=(2^n)-1, but I can't figure out the reasoning. Let's try
>below:
>
>U_1=2U_0=2
>U_2=2U_1=4 Doing it in the most retardedly
>U_3=2U_2=8 visible way DOES HELP....
>
>Now I can see that U_n=2^n and U_n=T_n+1 -> T_n=(2^n)-1
Anonymous at Sun, 19 May 2024 12:26:02 UTC No. 16182687
I really like puzzle games. Levels have multiple solutions and it's calming to try random things or to intuitively solve it.
I loved arithmetic and geometry, then I got to algebra and it's just memorisation and punishment if you diverge from applying the agreed upon optimal method, there is even more punishment if you brute force and exhaust a certain part by guessing. Then I got to calculus and that felt just the same but more difficult.
It wasn't until I took logic that math was fun again.
So I started wondering, is there a more free and puzzle like way to study and get good at algebra and calculus or is that just how they are? Needing to know a bunch of methods that you know where to plug in like the most boring jigsaw puzzle ever? I mean Newton didn't have that.
Anonymous at Sun, 19 May 2024 12:46:41 UTC No. 16182709
>>16182003
Thank you.
Anonymous at Sun, 19 May 2024 17:23:35 UTC No. 16182986
Groups capture symmetries of an object. What do rings and fields represent?
Anonymous at Sun, 19 May 2024 17:57:28 UTC No. 16183032
>>16182986
Very loosely speaking, a ring represents a symmetry of abelian groups.
To put it more formally:
A symmetric group represents all automorphisms of a set, and all groups can be represented as subgroups of a symmetric group.
An endomorphism ring represents all endomorphisms of an abelian group, and all rings (at least, those with a multiplicative identity) can be represented as subrings of the endomorphism ring of the underlying group.
and then a field is just a very particular type of ring, which doesn't really give way to a good representation on its own along these lines
Anonymous at Sun, 19 May 2024 20:02:12 UTC No. 16183241
WELSH BEST
https://en.m.wikipedia.org/wiki/Lis
Anonymous at Sun, 19 May 2024 23:14:14 UTC No. 16183475
>>16160352
Does anyone here have any book recommendations for category theory? I've got a BA in mathematics and we never touched up on it in any meaningful way.
Anonymous at Mon, 20 May 2024 00:31:21 UTC No. 16183610
>>16183475
"A First Course in Category Theory" in Springer's UTX series has good reviews and is pretty cheap. No idea if it's any good because I don't know anything about category theory (engineer who only cares about analysis and a bit of geometry).
Anonymous at Mon, 20 May 2024 02:11:40 UTC No. 16183718
Assume that a positive integer solution for [math]a_1, a_2, …, a_m, b, n[/math] exists for the equation [math]a_1^n + a_2^n + … a_m^n = b[/math], where [math]m ≥ 2[/math]. Let [math]T(n)[/math] be the minimum possible [math]m[/math] for each value of [math]n[/math]. [math]T(1) = 2[/math] is trivial. [math]T(2) = 2[/math] is Pythagoras' theorem. Fermat's last theorem states that [math]T(n) ≥ 3[/math] for all [math]n ≥ 3.[/math] Euler's (disproved) sum of powers conjecture claimed that [math]T(n) = n[/math] for all [math]n ≥ 3[/math].
My question is, has any further progress been made on this? In particular, has Euler's conjecture been proven (or disproven) to be an upper bound of [math]T(n)[/math] for all [math]n ≥ 3[/math]? As in, can for each [math]n[/math], can you construct such an equation, and prove it holds for all [math]n[/math]?
Anonymous at Mon, 20 May 2024 03:12:29 UTC No. 16183777
>>16182986
Fields (and more generally ternary rings) represent projective planes.
Anonymous at Mon, 20 May 2024 03:16:14 UTC No. 16183784
>>16162475
I'll say that Linear Algebra by Gilbert Strang sucks. Khan academy has far superior instruction.
Anonymous at Mon, 20 May 2024 03:26:50 UTC No. 16183794
>>16160745
Complex analysis is pretty and so is the theory of differential equations. Can't speak for differential geometry as I never took a course in that.
Anonymous at Mon, 20 May 2024 03:37:40 UTC No. 16183811
>>16183718
I don't know what you are asking.
I think you are talking about Waring's problem?
https://en.wikipedia.org/wiki/Warin
The way you stated your problem makes it seem like T(n)=1 for all n since letting b=(a1)^n gives a solution.
Looking for answers is way harder if you can't even ask questions properly.
Anonymous at Mon, 20 May 2024 03:51:01 UTC No. 16183821
>>16183718
>>16183811
Fuck, I always mess up somewhere. The equation should be [math]a_1^n + a_2^n + … + a_m^n = b^n[/math]
Anonymous at Mon, 20 May 2024 04:00:32 UTC No. 16183826
Algebra question: Are there actually mathematicians or any literature out there that does not require zero divisors in a ring to be non-zero? I've been taught my whole life that 0 is never a zero divisor, but then I read someone tell me otherwise.
Anonymous at Mon, 20 May 2024 04:22:26 UTC No. 16183844
>>16183839
>down arrow is whited out
Did you just downvote? kek
Anonymous at Mon, 20 May 2024 07:08:28 UTC No. 16184055
>>16160745
Complex analysis is more important, but differential geometry is very interesting.
Anonymous at Mon, 20 May 2024 10:57:42 UTC No. 16184283
Is there any easy way to visualise a map from [0,1) to the 2-sphere?
Anonymous at Mon, 20 May 2024 11:01:26 UTC No. 16184288
>>16184283
It's just a curve drawn on a ball.
Anonymous at Mon, 20 May 2024 15:40:06 UTC No. 16184638
>>16183839
they should make an Asian Pride In Math
>>16184288
not necessarily, but as long as its continuous then yeah
Anonymous at Mon, 20 May 2024 17:10:05 UTC No. 16184735
>>16160352
How does one get better at reading and understanding math symbology and notation?
Anonymous at Mon, 20 May 2024 17:57:19 UTC No. 16184781
Answering my own question from a couple threads ago (>>16122260)
https://warosu.org/sci/thread/16113
I went with the suggestion to start with group theory (>>16122265), and I purchased two books:
"Visual Group Theory" by Nathan Carter, and
"A Book of Abstract Algebra - Second Edition" by Charles C. Pinter
Here's a comparison of how they both define what a group is:
Visual Group Theory's definition
https://files.catbox.moe/ne0fml.jpg
https://files.catbox.moe/9jgvnc.jpg
https://files.catbox.moe/gdr8op.jpg
https://files.catbox.moe/yj2ywv.jpg
https://files.catbox.moe/zd57k4.jpg
https://files.catbox.moe/aqvtne.jpg
A Book of Abstract Algebra's definition
https://files.catbox.moe/n5twme.jpg
https://files.catbox.moe/r9nl0z.jpg
https://files.catbox.moe/c94vk3.jpg
https://files.catbox.moe/vhi8oo.jpg
https://files.catbox.moe/e9xevu.jpg
https://files.catbox.moe/gqeafo.jpg
"Visual Group Theory" is excellent if you're just getting into abstract algebra-- it's especially great if you love pictures and diagrams. I was able to pick everything up intuitively and easily. "A Book of Abstract Algebra" makes for a good supplement. They compliment each other very nicely and it will help you flesh out more the "mathy" side of things. I would highly recommend getting both rather than one or the other.
The exercises in "Visual Group Theory" are a little easier than the ones in the other book, but I've found it to be particularly beneficial to do the exercises from the first book, then do the exercises from the second book (after I read content from both textbooks) and that has been working great so far.
>inb4 The books are expensive, just find a PDF and use that
Ordering the physical copies is easier for me to annotate, bookmark, and work without distractions. The physical copies are worth the price imo.
Cheers, hope this helps someone
Anonymous at Mon, 20 May 2024 18:27:28 UTC No. 16184825
>>16184735
If you can, read old math textbooks. They always have a plethora of knowledge right in the front cover (see picrel, it's a scan from my copy of "Handbook of Mathematical Tables and Formulas" from 1947). Flip through the pages, read the content, and be curious. Don't make an attempt to learn it all at once either, that's a recipe for burnout. If something doesn't make sense, this thread, the math stack exchange (https://math.stackexchange.com), and ChatGPT are your friends. This should at the very least bolster your ability to look at an equation and get a rough idea for what's happening.
Now comes the dreaded part of the answer: practice. Do math problems, apply it to the world around you, have fun with it. People always think that "practicing math" is sitting down, grinding out 400 problems, and moving on to the next thing. It's not. Just find a math book which is at your level, read the content, and see what you can do with it. Can you calculate how long it takes for you to get to work if you speed? How about if you don't speed? Is it beneficial for you to speed in the mornings? Stuff like that. Obviously, sitting down and doing some of the exercises in the book will be extremely helpful to you, don't stress it. If you're not enjoying it, then take a break. You won't learn if you're frustrated or angry.
As a final word of advice, set a goal. You can't understand all of math's symbols and notations at once. Find a field or part of math that excites you and start there. Start small, work at it day by day, and you'll be cruising in no time flat.
Cheers. Feel free to reply if you have any more questions.
Anonymous at Mon, 20 May 2024 18:34:12 UTC No. 16184834
>>16184825
I didn't expect a thoughtful and detailed answer. Thank you. I'll look for that book.
Another question: I'm interested in getting back into mathematics, but it's been so long since I was in school, I'm not sure *where* I should start as a foundation.
Anonymous at Mon, 20 May 2024 18:36:28 UTC No. 16184840
How do i do Guassian elimination?
Where should i start
Anonymous at Mon, 20 May 2024 18:37:16 UTC No. 16184843
>>16184840
With the first row of your augmented matrix. That's generally where you start.
Anonymous at Mon, 20 May 2024 18:40:50 UTC No. 16184852
>>16184843
I don't really understand the swapping
Anonymous at Mon, 20 May 2024 19:24:32 UTC No. 16184930
>>16184834
Of course, happy to help.
>I'll look for that book
Don't. Look for more than just that one book in particular. Just look for old math textbooks in general and look for stuff that piques your interest.
>where to start in math
It's always tough to give a straight answer to this without knowing where you left off, but I can give some general guidance. The easy answer is to "Pick up where you left off", but this naturally brings a lot of caveats with it, the biggest being that your current knowledge of math is patchy and you only remember certain things-- the best analogy is that rather than a clear cut path across a pond, some people's knowledge is more akin to a set of stepping stones (I hope that makes sense, if it doesn't, my apologies).
Assuming you know how to do basic arithmetic and that you're capable of solving simple algebraic equations, I would say the best place for you to get the ball rolling is with algebra (I, then II). If you know it well, then reviewing it will be easy, and won't take you long. You could probably knock this out in 2-3 weeks if you're serious, maybe a month if you're learning it casually (assuming decent proficiency).
After this, you can dive into Geometry and Trigonometry, which takes that algebra and applies it to shapes. This sets you up for calculus, which you can dive into afterwards. Calculus, or rather, the study of change, is usually split up into three major sections, I, II, and III. I and II are usually taught together and are the (in my opinion) the most difficult of the three. Calculus III is vector analysis/multivariable calculus. This path is obviously just a suggestion and you can modify this at your own discretion. I would highly recommend getting all the way up to at least Calculus III, because only a small percentage of people can do it, and it's insanely useful for modeling the world around us and how it changes.
Hope that gives you an idea, at least.
Anonymous at Mon, 20 May 2024 19:41:27 UTC No. 16184959
>>16184721
Using mod arithmetic as a proof, ur solution and (58823529412, 235294117648) are the only ones. At some point in the math you can narrow it down to only 4 possible ways to get that property, so you try all of them.
Notice for both pairs (a,b). b is ~ equal to 4a. For each path you take, you get one solution each.
If you try b ~= 6a, for both paths you take, you cycle about three numbers that are not powers of 10 (one of them is 29, 14, and 31, I didn't write down what the other cycle was), so you never get a solution.
Fun coding problem. Since ur multiplying big numbers it would be dumb if anyone who wants to try it to do it by hand. Just code it up
Anonymous at Mon, 20 May 2024 19:46:59 UTC No. 16184966
>>16184930
>Hope that gives you an idea, at least.
Yes, it does. I, again, appreciate your help. Is there a way to get in contact with you outside the board?
Anonymous at Mon, 20 May 2024 19:50:54 UTC No. 16184971
>>16184869
Dude, youre getting filtered so early.
>row operations
>ROW!!!!!
>Line 2 + 3/2 Line 1 becomes the new Line 2
>Line 3 + Line 1 becomes the new Line 3
Have you even tried youtubing a vid on this? There's def a shit ton where people actually do problems for you.
Anonymous at Mon, 20 May 2024 20:07:03 UTC No. 16184998
>>16183826
I've seen people use both conventions. I instinctively think of 0 as counting, but if you check Lang he excludes it.
As far as I can tell excluding zero is kind of a pointless convention. I'm not sure what it accomplishes other than soothing somebody's autism
Anonymous at Mon, 20 May 2024 20:15:31 UTC No. 16185004
>>16184966
No, sorry. I'd like to stay anonymous. I appreciate the sentiment, though.
Anonymous at Mon, 20 May 2024 21:08:18 UTC No. 16185078
>>16160352
test
Anonymous at Mon, 20 May 2024 21:55:24 UTC No. 16185136
>>16184998
I see, thanks. One final question: do you know which of the two is the more widely accepted definition of zero divisor? Non-zero or includes zero?
Anonymous at Mon, 20 May 2024 23:40:32 UTC No. 16185299
Idk if this is the right thread but does anyone know a method for drawing a wireframe sphere with latitude and longitude lines, so that the lines are evenly spaced, using a compass and a ruler?
Anonymous at Tue, 21 May 2024 01:46:17 UTC No. 16185433
>>16185299
good one but it would require an 3d space and an limited partice number to make that question a good bait.
Anonymous at Tue, 21 May 2024 04:53:26 UTC No. 16185606
>>16184721
Oh wait im dumb, i missed stuff in >>16184959
there's a lot more. I missed a lot
>https://www.researchgate.net/publi
Anonymous at Tue, 21 May 2024 09:52:40 UTC No. 16185952
>>16184825
>If you can, read old math textbooks. They always have a plethora of knowledge right in the front cover
almost all math books have an index for symbols. You'd know that had you read them
Anonymous at Tue, 21 May 2024 09:57:58 UTC No. 16185958
>>16184834
https://sheafification.com/the-fast
Anonymous at Tue, 21 May 2024 10:02:06 UTC No. 16185965
>>16184834
Read Lang's Basic Mathematics. Don't waste too much time on precalc, just refresh on the very basics and then get into proof-based math
Anonymous at Tue, 21 May 2024 10:21:37 UTC No. 16185985
>>16185965
Lang is a meme.
Anonymous at Tue, 21 May 2024 14:15:32 UTC No. 16186217
What's the best foundation of maths. And what do you think of bourbaki's elements.
Anonymous at Tue, 21 May 2024 15:47:37 UTC No. 16186286
I have to be the dumbest nigger possible to not be able to solve this jewish bullshit, the fuck am I doing wrong.
>-7u-10=-4(u-5)
>Distribute first
-7u-10=-4u-20
>Combine like terms
>Add 4u to the left hand side of the equation
-7u+4u=20
>Combine like terms
>-3u=-20
>Move -3 to the right side of the equation
>u=-20+3
>Simplify
>u=-17
>Correct answer -10?
Fuck, this shit boils my temper.
Anonymous at Tue, 21 May 2024 15:56:08 UTC No. 16186302
>>16186286
What is (-4)(-5)? You were close.
Anonymous at Tue, 21 May 2024 15:58:15 UTC No. 16186305
>>16186302
I get 20 with calculator.
Anonymous at Tue, 21 May 2024 15:58:18 UTC No. 16186306
>>16186286
>the fuck am I doing wrong.
Stop being a racist first
Anonymous at Tue, 21 May 2024 16:00:31 UTC No. 16186312
>>16185952
Here's the worked answer, if it helps.
Anonymous at Tue, 21 May 2024 16:06:20 UTC No. 16186325
>>16186312
Thank you anon, I really appreciate you taking the time to work that out for me,
>I think what is confusing me is the second step
-3u-10=20
>for some reason my brain wants to minus ten as ten is a positive number however if ten is being subtracted I suppose it would be added to move over?
>Some of these I seem to get right and others not some much, I assume some of these that make a little bit harder on purpose to really test you wether this is one that is intentionally hard or not it is confusing to me how I can get the correct answer on some yet not others.
Anonymous at Tue, 21 May 2024 16:46:20 UTC No. 16186374
>>16185965
>proof-based math
Like what?
Anonymous at Tue, 21 May 2024 16:46:56 UTC No. 16186375
>>16185965
>Lang's Basic Mathematics
Seems like I'd be better off following the basic courses through Khan Academy, no?
Anonymous at Tue, 21 May 2024 16:48:40 UTC No. 16186376
>>16186312
What kind of paper is that?
Barkon at Tue, 21 May 2024 16:58:34 UTC No. 16186384
>>16186376
Fag paper. Made specially for you to read and write on.
Anonymous at Tue, 21 May 2024 16:59:03 UTC No. 16186385
>>16186325
>Thank you anon, I really appreciate you taking the time to work that out for me,
Of course, happy to help!
>>16186376
Engineering paper. Blank on the front, graph paper on the back.
Anonymous at Tue, 21 May 2024 17:02:37 UTC No. 16186389
>>16186385
based
>>16186384
faggot
Anonymous at Tue, 21 May 2024 18:09:33 UTC No. 16186480
>>16184781
I already have the one on the right, thanks for the tip for getting the other as well
Anonymous at Tue, 21 May 2024 19:03:20 UTC No. 16186586
>>16186305
Okay, so the right side of the equation in >>16186286 is what?
-7u -10 = -4u + 20 or -20?
Anonymous at Tue, 21 May 2024 19:47:15 UTC No. 16186623
>>16160923
Differential equations is a mix of both, leaning towards theory, especially in the beginning (see picrel, bottom line). As you progress through the class, the theory practically becomes second nature and you'll establish for yourself a framework by which you can manipulate a differential equation, similar to how one would manipulate an algebraic expression.
In a nutshell, differential equations is just like algebra in a sense, except you're solving for equations and you're using calculus to do so.
Near the end of the class you'll learn about the Laplace transform, which transforms a differential equation into an algebraic one. With the Laplace transform comes a number of transforms, which are helpful to memorize.
It may seem like a grind at first but it really starts to feel like a math after you learn about power reductions and method of undetermined coefficents.
Anonymous at Tue, 21 May 2024 20:11:04 UTC No. 16186646
>>16186325
it is not a difficult problem by any stretch. anyone who didn't fail algebra 1 should be able to solve it quickly
now that's not the case because of various other reasons, but this is a very simple problem in the grand scheme of algebra 1
Anonymous at Wed, 22 May 2024 02:19:21 UTC No. 16187204
>>16160790
calculus, linear algebra, a programming language and ai is all you need
Anonymous at Wed, 22 May 2024 02:40:47 UTC No. 16187239
>>16187204
>calculus
what are some real use cases for this?
Anonymous at Wed, 22 May 2024 02:46:51 UTC No. 16187244
>>16187239
Many, but solving differential equations is the biggest one.
Anonymous at Wed, 22 May 2024 02:53:41 UTC No. 16187253
>>16187244
>>16187239
For example,
y'(x)=y(x), y(0)=1
y(0)=0, y'(0)=1, y''(x)= -y(x)
Are the simplest differential equations, their solution gives us exp(x) with x=1 giving e, and sin(x) with smallest positive root being pi.
Recurrence equations are just finite differential equations. This is all the theoretical knowledge a mathematician needs to understand why pi and e appears everywhere, their problem can simply be rephrased as a counting problem.
Applied mathematics will give many more and diverse problems than the study of mathematics could ever.
Anonymous at Wed, 22 May 2024 06:08:32 UTC No. 16187403
new >>16187402