Anonymous at Wed, 25 Sep 2024 16:18:46 UTC No. 16397598

>maths
kys

Anonymous at Wed, 25 Sep 2024 17:12:51 UTC No. 16397639

>>16397584
Layering (cascading) AES in CBC and ECB modes eliminates all attacks and makes it almost perfectly secure. That is all. Just do one pass in CBC 256bit, then another pass in ECB 128bit.

Anonymous at Wed, 25 Sep 2024 17:24:58 UTC No. 16397650

>>16397639
Furthermore, if you are worried about RNG backdoors, you can take random bits from your OS facilities and do this to them in streaming fashion to make perfectly secure keys or whatever else you need. You can also use this method with compatible asymmetric functions. Get on board with cascading cipher modes in AES wherever you need it to be truly secure.

Anonymous at Wed, 25 Sep 2024 19:10:23 UTC No. 16397777

>>16397639
Stop being a retard and use an AEAD mode.

Anonymous at Wed, 25 Sep 2024 20:35:24 UTC No. 16397905

>>16397777
>Use GCM
Alright if I'm communicating with a recipient or sender. Not helpful if I'm keeping a secret on disk or in source control. Also, WTF am I supposed to do about replay attacks?
>Use a message counter
Good God. No. Fuck you to death.

Anonymous at Wed, 25 Sep 2024 20:35:56 UTC No. 16397906

Anonymous at Wed, 25 Sep 2024 20:45:17 UTC No. 16397918

>>16397905
Well yes, you keep a message counter in the associated data (fuck yourself my dude). Disk encryption: use XTS mode.

Anonymous at Thu, 26 Sep 2024 01:20:21 UTC No. 16398302

Do you guys like hopf algebras

Anonymous at Thu, 26 Sep 2024 01:26:14 UTC No. 16398311

>>16398302
No theyre kinda lame and oversymmetric

you should be able to do this at Thu, 26 Sep 2024 03:08:38 UTC No. 16398383

[math]f:[a,b] \to \mathbb{R}[/math] is a continuous function. If [eqn]\lim_{h \to 0}\frac{f(x+h)+f(x-h)-2f(x)}{h^2}=0[/eqn] holds for all [math]x \in [a,b][/math], prove that [math]f[/math] is linear on its domain.
I was thinking assuming strict convexity/concavity on small intervals and arriving at a contradiction may help since the expression really just checks convexity in small intervals around [math]a[/math], and had f been twice differentiable, would just be the second derivative written in a different way. Haven't written things down yet. Any other ideas anons?

Anonymous at Thu, 26 Sep 2024 03:09:51 UTC No. 16398387

/mu/ here with w combinations question

Im examining the total number of possibilities two hands can play a bar of 4/4, 8th notes, so each hand can play on one of 8 beats. Each beat can be occupied by one of 7 notes. How many combinations exist?

For example I can play the 1st of 7 notes on the first 1 of 8 beats in the left hand, for each note and beat in the right hand, and I want to know how many total combos exist

Gpt is saying it's in the millions which can't be right

Anonymous at Thu, 26 Sep 2024 03:23:02 UTC No. 16398394

>>16398387
(7 notes * 8 beats) ^ 2 hands = 3136
If you added another note I would be
(7 notes * 8 beats * 2 note per bar)^2 hands = 12544

Anonymous at Thu, 26 Sep 2024 03:28:40 UTC No. 16398395

>>16398387
If rests are allowed, 2^48 = ~281 trillion
If not, 7^16 = ~ 33 trillion

Anonymous at Thu, 26 Sep 2024 03:43:11 UTC No. 16398406

>>16398395

Garrote at Thu, 26 Sep 2024 04:00:22 UTC No. 16398415

>>16398383
Uhh, if the limit exists (since it equals 0), then it is twice differentiable? So integrate twice.

Anonymous at Thu, 26 Sep 2024 11:03:29 UTC No. 16398669

>>16398302
yes, but only because I like group schemes

Anonymous at Thu, 26 Sep 2024 12:19:09 UTC No. 16398713

>>16397598
Why are vomiting cats so funny?

🗑️ Anonymous at Thu, 26 Sep 2024 12:25:49 UTC No. 16398720

>>16397584
https://amp.theguardian.com/world/2022/nov/29/interview-pope-francis-fury-russia


Yes, in all likelihood, it is the white pig that is cruel. Subhuman white pedo Christians should disappear from this world along with the retarded Pope.

White people made the atomic bombs, dropped them on Japan, and genocided the Japanese, an Asian people

fuck White cockroach

All whites are descended from Nazis.

https://www.dailymail.co.uk/news/article-10797707/amp/Russian-brags-using-FSB-torture-method-slicing-open-Ukrainians-fingers-toes-penis.html

Anonymous at Thu, 26 Sep 2024 14:35:31 UTC No. 16398827

>>16398720
not science or math

Anonymous at Thu, 26 Sep 2024 17:33:00 UTC No. 16398996

>>16397584
I typed RSA equation in CASIO calculator, and that little mother fucker broke private key from public one.

Anonymous at Thu, 26 Sep 2024 21:03:22 UTC No. 16399182

Is 5.0101101110111101111101111110111111101111111101... rational or irrational number?

Anonymous at Thu, 26 Sep 2024 21:39:00 UTC No. 16399209

>>16397584
>they made the card itself carry an encrypted message
Kek.

Anonymous at Thu, 26 Sep 2024 22:51:37 UTC No. 16399299

>>16399182
It's either irrational or [math] \frac { 50101101110111101111101111110111111101111111096 } { 9999999999999999999999999999999999999999999999 } [/math]

Anonymous at Fri, 27 Sep 2024 07:20:42 UTC No. 16399653

>>16399182
Are you asking how to show that it is irrational?

Anonymous at Fri, 27 Sep 2024 13:47:20 UTC No. 16399936

What is your stance on Asians being good at math because they leverage techniques like anime girls, while the white man continues to bumble around with flesh humans?
https://www.youtube.com/watch?v=mEBRdWlCXYM

Anonymous at Fri, 27 Sep 2024 13:53:35 UTC No. 16399943

I've been wasting a lot of time staring at this
https://rreusser.github.io/smooth-life/
A continuous verson of Conway's life

Anonymous at Fri, 27 Sep 2024 19:17:51 UTC No. 16400260

>>16399653
no, I just needed the answer like yes or no

Anonymous at Fri, 27 Sep 2024 20:25:32 UTC No. 16400318

>>16400260
Are you stupid? The answer is obvious.

Anonymous at Fri, 27 Sep 2024 23:13:37 UTC No. 16400397

What’s a set in R that’s not a Borel set

Anonymous at Fri, 27 Sep 2024 23:41:36 UTC No. 16400412

>>16400397
The Vitali set

Anonymous at Sat, 28 Sep 2024 08:06:48 UTC No. 16400768

>not using blowfish
Why are you on /sci/ even?

Also what do you guys think of (crystals)-kyber?

Anonymous at Sat, 28 Sep 2024 13:04:15 UTC No. 16400893

>>16398387
>Both hands must play notes, and those notes must be different
(7*6)^8
>Both hands must play notes, and those notes can be the same
(7*7)^8
>Both hands can not play notes, but any notes played must be different
(7*6+7+7+1)^8
>Both hands can not play notes, and notes played can be the same
(7*7+7+7+1)^8

Shit gets more complicated if for example the left hand playing the 1st note and the right hand playing the 2nd is treated the same as the inverse.

Anonymous at Sat, 28 Sep 2024 19:43:27 UTC No. 16401427

Suppose I have an even integer x that is defined as:
[math] x = 2k for some integer k [/math]
If I substitute 2k for x in the following expression:
[math] 3x^{2} + 5x - 1 [/math]
I'll get an expression of the form:
[math] 2j - 1 for some integer j [/math]
Is there a way I can rewrite the derived expression to obtain
[math] 2j + 1 [/math]
I know that both expressions yield an odd integer, but the latter is the only acceptable definition of an odd integer according to my instructor. How can I rewrite the former expression to obtain one of the form of the latter? Please no bully. I'm not good at maths.

Anonymous at Sat, 28 Sep 2024 20:02:36 UTC No. 16401442

Look at these prime numbers I discovered

Anonymous at Sat, 28 Sep 2024 22:40:08 UTC No. 16401611

>>16401442
'mirin

Anonymous at Sun, 29 Sep 2024 05:18:34 UTC No. 16401921

>>16399182
I'm shit at math so I don't know, but if this is the fractional part you're describing then it's not rational, looks more like a transcendental.

Anonymous at Sun, 29 Sep 2024 05:54:44 UTC No. 16401942

>>16401921
Good god has this board gone retarded? If the decimal expansion is not periodic then the number is not rational.

Anonymous at Sun, 29 Sep 2024 06:19:22 UTC No. 16401949

>>16401442
These are just the primes I needed. How do I cite a 4chan post?

Anonymous at Sun, 29 Sep 2024 09:11:14 UTC No. 16402010

Nobody on this board knows basic algebraic topology. Sad.

Anonymous at Sun, 29 Sep 2024 09:12:15 UTC No. 16402011

>>16399943
>continuous
>computer simulation
Choose one and only one.

Anonymous at Sun, 29 Sep 2024 09:39:58 UTC No. 16402046

>>16402010
I know some basics of AT. What's your question?

Anonymous at Sun, 29 Sep 2024 11:35:55 UTC No. 16402089

He doesn't know how to compute with arbitrary precision lmao >>16402011

Anonymous at Sun, 29 Sep 2024 15:00:50 UTC No. 16402313

Is there something like an introduction to algebraic geometry for physicists? I'm really interested in the topic but I don't have the time to go through highly technical books. Maybe some text explaining the intuition, the most beautiful results and applications?

Anonymous at Sun, 29 Sep 2024 15:43:16 UTC No. 16402379

>>16402313
how much ring theory do you know

Anonymous at Sun, 29 Sep 2024 15:50:56 UTC No. 16402390

>>16401427
rewrite j as j + 1 - 1

Anonymous at Sun, 29 Sep 2024 16:02:06 UTC No. 16402406

>get into math because I heard it's a solitary hobby
>trying to teach myself real analysis
>Prove theorem
>not sure if my proof is valid or not
>realize there's no way for me to know without asking someone

Yeah math sucks dick

Anonymous at Sun, 29 Sep 2024 16:02:54 UTC No. 16402409

>>16402379
Not much. I've seen very basic concepts like spectrum and localization but I don't know anything about modules or homological algebra yet.

Anonymous at Sun, 29 Sep 2024 16:04:16 UTC No. 16402414

>>16402406
Post it then.

Anonymous at Sun, 29 Sep 2024 16:07:34 UTC No. 16402419

>>16402406
Ask yourself whether the proof would convince a skeptical reader. Are there any questions a reader might ask about the assumptions or the steps in your proof, and would you be able to answer these questions?

Anonymous at Sun, 29 Sep 2024 16:14:05 UTC No. 16402425

>>16402409
you could probably read an intro algebraic geometry textbook and follow along well enough

Anonymous at Sun, 29 Sep 2024 16:28:40 UTC No. 16402444

>>16402425
I tried this with two different books but stopped them again after reading half of them. I was missing the geometry or intuition part. The treatment of varieties usually stays abstract and algebraic, and the few things I've read about schemes seemed to be even more divorced from physics. But that's only my limited experience.

Anonymous at Sun, 29 Sep 2024 17:17:27 UTC No. 16402499

Would numerical analysts prefer a constructive framework in principle? Supposedly they develop things in ZFC, but wouldn't it be better for them if everything had numerical meaning for the start? Or is it still simply easier to prove things in ZFC?

Anonymous at Sun, 29 Sep 2024 22:49:00 UTC No. 16402963

Any way to use SIMD on the SHA2 mix functions?
I managed to parallelize the schedule function but the mix function looks like it can't be parallelized at all unless to do 4/8 unrelated checksums at the same time.

Anonymous at Mon, 30 Sep 2024 05:44:57 UTC No. 16403319

>>16402444
Huybrecht & Tomasiello for physics.

You don't need schemes unless going for specific niche topics that are somewhat unpopular within the community.

Anonymous at Mon, 30 Sep 2024 06:18:01 UTC No. 16403352

>>16403319
>Huybrecht & Tomasiello for physics.
I didn't find the book. Whats the title?

Anonymous at Mon, 30 Sep 2024 06:45:37 UTC No. 16403377

>>16403352
Huybrecht : Complex geometry an introduction
Tomasiello : Geometry of string compactifications

Anonymous at Mon, 30 Sep 2024 06:54:03 UTC No. 16403384

>>16402963
You could check out the OpenSSL source code or a repo like https://github.com/minio/sha256-simd

Anonymous at Mon, 30 Sep 2024 14:30:07 UTC No. 16403748

>>16402011
Continuous

Anonymous at Mon, 30 Sep 2024 20:05:38 UTC No. 16404189

any new research on the category of axioms?

Anonymous at Mon, 30 Sep 2024 23:33:06 UTC No. 16404411

>>16402409
Modules are easy, it's the same definition as vector space but the scalars are in a ring and not necessarily a field

Anonymous at Mon, 30 Sep 2024 23:34:07 UTC No. 16404413

>>16404189
what's that

Anonymous at Mon, 30 Sep 2024 23:36:55 UTC No. 16404415

>>16402409
Go read Atiyah-Macdonald

Anonymous at Tue, 1 Oct 2024 00:10:44 UTC No. 16404465

I didn't think I'd be able to take any classes this semester and registered late, I'm only taking gen eds; I essentially have a free semester. Next Math class I'll take is Calc 2. The professor I'm looking to take does things a little differently than the others--he's the head of the Math department I think. He incorporates proofs into the coursework and goes about teaching the curriculum in a semi-rigorous manner. I say "teach", but he leaves the studying to us and then goes over it via class discussion. This is what I've heard from my Maths senpai (who only knows from friends of his; he hasn't taken that professor), so I don't know how true this is, but I've heard that he's not a very good lecturer and that most people bitch over his class. I don't care much since I'm not a faggot, but is it worth taking his class, or should I take a simple introduction to Calc 2 instead? Regardless of the professor.

I plan on studying either Maths or Physics, but I'm a little 'tarded, so keep that in mind. I believe it would do me some good to take his class. It would not only challenge me and serve to increase my Mathematical maturity, but will function as an aptitude test of sorts to gauge what my abilities are, and whether I'm cut out for the field--I don't really give a fuck if I'm too retarded for it nor if my work is niggerlicious, this is just undergrad anyway.

My question then is, to prepare myself for the following semester--considering that I have no experience with proofs; I've only done computational Maths--should I read up on Set Theory and how to write proofs, should I just read through Stewart's to become familiarize myself with the concepts, or should I forgo reading Stewart's and read Apostol's Calculus with Halmos' Naive Set Theory and some text on proofs serving as preliminary reading? How long should I spend on each? I'll probably go through the entirety of Vol 1 to relearn Calc 1 concepts.

Anonymous at Tue, 1 Oct 2024 00:14:46 UTC No. 16404470

>>16404189
Yeah, I proved ZFC is inconsistent

Anonymous at Tue, 1 Oct 2024 00:24:58 UTC No. 16404485

>>16404465
Also, this probably sounds arrogant of me, but I'm considering taking either Discrete Maths or an Intro to Probability and Stats course alongside Calc 2 next semester to make up for lost time. This is contingent on how I fare through this initial self-study exposure of Calc 2 however, but it's something I plan on doing. I plan on taking courses during the Winter intersession, which cover the curriculum much faster than the Summer one--at mach fuck you--so It'd be best to have covered as much ground as possible in whichever route mentioned in my previous post I decide to go with; I won't have much of any time to dedicate to studying Maths during the intersession.

🗑️ Anonymous at Tue, 1 Oct 2024 04:48:07 UTC No. 16404741

I unironically spent the past 7 hours on this problem and the answer is still incorrect, am I too retarded for math? Fuck this shit

Anonymous at Tue, 1 Oct 2024 04:54:33 UTC No. 16404747

I unironically spent the last 4 hours working on this problem and it's still incorrect
Give it to me straight lads, am I a retard?

Anonymous at Tue, 1 Oct 2024 07:12:49 UTC No. 16404858

Let n be a sum of any five powers of two. Is 10n always a sum of any five powers of two?

Anonymous at Tue, 1 Oct 2024 09:55:08 UTC No. 16404929

>>16404747
You seem to solve [math]y''+y'-2y=0[/math] fine.
Since you get a term [math]e^{2x}[/math] in your homogeneous solution and in your right-hand side, guessing a particular solution of the form [math]A e^{2x}+Be^{-2x}[/math] won't work.
The next thing I usually try is then a solution of the form [math]Axe^{2x}+Be^{-2x}[/math], which works here as well.

Anonymous at Tue, 1 Oct 2024 10:50:00 UTC No. 16404978

>>16404858
No.
Proof: Consider the binary representation of n. If n is the sum of distinct powers of 2, it will have precisely 5 1s. If there are repeated powers of 2 in this expansion, it will have fewer. All we need is to find an example of n such that this is true of n but not of 10n.

A simple example: 47 is 101111 (so 32+8+4+2+1), but 470 is 111010110 (so its simplest possible representation is 256+128+64+16+4+2, which requires 6).
If for some reason you don't like considering 1 as a power of 2, then the same argument works for n=94

Anonymous at Tue, 1 Oct 2024 13:52:58 UTC No. 16405100

>>16404978
Plenty of numbers that are the sum of five powers of two have less than five ones in their binary representation, like ten (2+2+2+2+2)

Anonymous at Tue, 1 Oct 2024 13:58:00 UTC No. 16405105

>>16404413
Schizobabble

Anonymous at Tue, 1 Oct 2024 14:01:54 UTC No. 16405111

>>16405100
see
>If there are repeated powers of 2 in this expansion, it will have fewer
The point is not that there are exactly five. The point is that there are no more than five.

Anonymous at Tue, 1 Oct 2024 15:30:07 UTC No. 16405199

the words "collection" and "subcollection" are so retarded, just say set and subset. I don't care if you think it makes it less "ambiguous."

Anonymous at Tue, 1 Oct 2024 15:40:02 UTC No. 16405210

>>16405199
It's not for reasons of ambiguity (I don't even understand what you're trying to say by that) but to make the terminology less repetitive.

Anonymous at Tue, 1 Oct 2024 21:02:22 UTC No. 16405603

What do I need to read to analytically solve a clicker video game? If you want me to explain further, let me know.

Anonymous at Tue, 1 Oct 2024 21:17:00 UTC No. 16405624

>>16397906
isnt picrel better for a curriculum bros?

Anonymous at Tue, 1 Oct 2024 21:17:46 UTC No. 16405627

>>16405603
Regardless of what clicker game it is, isn't it almost optimal to make the maximum number of inputs that do stuff per frame?

Anonymous at Tue, 1 Oct 2024 21:20:51 UTC No. 16405631

>>16405624
Gelfand is bad, do openstax instead if you are unable to keep up with skipping directly to basic mathematics. Do real analysis and linear algebra before set theory, otherwise it's ok.

Anonymous at Tue, 1 Oct 2024 21:25:08 UTC No. 16405637

>>16405624
>Lang
stopped readiing

Anonymous at Tue, 1 Oct 2024 21:26:36 UTC No. 16405640

>>16405627
I want a way to analytically calculate the best strategy for some clicker game when the player's clicking speed is a variable that is included in the calculations. I don't know any game theory but I don't know if it's useful - since the whole thing is a single-player game, isn't it better to use concepts from discrete mathematics?

Anonymous at Tue, 1 Oct 2024 21:28:04 UTC No. 16405641

>>16405624
Stitz Zeager is the best precalc book, fyi

Anonymous at Tue, 1 Oct 2024 21:49:55 UTC No. 16405659

>>16405631
I skipped Gelfand and just did Precalc by Stewart + Basic Mathematics.
Rn I am doing Set Theory, Linear Algebra, Abstract Algebra, and finishing Calculus
>>16405641
>>16405637
What about the rest of the curriculum? I am already familiar with the basics

Anonymous at Tue, 1 Oct 2024 21:57:09 UTC No. 16405669

>>16405603
The only way to solve a (complicated) idle game is to basically brute force it, unless you have some really good heuristics that's probably going to be incredibly slow and is fairly unnecessary anyways. Just use a greedy algorithm along the lines of:
1: Evaluate all available upgrades/buildings using picrel
2: Wait until you can buy the upgrade/building, then buy it
3: GOTO 1

Anonymous at Tue, 1 Oct 2024 21:58:48 UTC No. 16405670

Anyone working with p-adics? I would like to see some sort of as elementary as possible explanation of its uses. I got the feeling that they are useful for diophantine stuff or cryptography, but I have no clue if that's true or bs.

Anonymous at Tue, 1 Oct 2024 22:22:58 UTC No. 16405690

[ math ]H^k(X \times_{spec(k)} Y; \pi_{1}^* \mathcal{F} \otimes_{spec(k) \times \mathcal{O}_X} \pi_{2}^* \mathcal{G}) \cong \oplus_{i + j = k} H^i(X, \mathcal{F}) \otimes_{spec(k)} H^j(Y, \mathcal{G}) [ /math ]

Anonymous at Tue, 1 Oct 2024 22:25:15 UTC No. 16405693

[math]H^k(X \times_{spec(k)} Y; \pi_{1}^* \mathcal{F} \otimes_{spec(k) \times \mathcal{O}_X} \pi_{2}^* \mathcal{G}) \cong \oplus_{i + j = k} H^i(X, \mathcal{F}) \otimes_{spec(k)} H^j(Y, \mathcal{G})[/math]

Anonymous at Tue, 1 Oct 2024 23:18:15 UTC No. 16405762

>>16404929
Did I simplify the hyperbolic function correctly? That was the part I was kainly stuck on

Anonymous at Wed, 2 Oct 2024 00:40:28 UTC No. 16405860

>>16405670
The primary use of p-adics from the number theory perspective are local-to-gloabl principles.

The idea that you can understanding something over Q, if you can understand it over Q_p for each p and R.

See this for the traditional example https://en.wikipedia.org/wiki/Hasse_principle

Anonymous at Wed, 2 Oct 2024 00:52:41 UTC No. 16405877

>>16405693
You mean
[math]
H^k(X \times_{spec(k)} Y; \pi_{1}^* \mathcal{F} \otimes_{\mathcal{O}_{X\times_{spec(k)} Y}} \pi_{2}^* \mathcal{G}) \cong \oplus_{i + j = k} H^i(X, \mathcal{F}) \otimes_{k} H^j(Y, \mathcal{G})
[/math]

Fibered product are over schemes, tensor products are over rings

Anonymous at Wed, 2 Oct 2024 01:50:29 UTC No. 16405930

If you have three blue disks of area 1, you aren't able to arrange them in a way where;
> the midpoint of any blue disk lies on the boundary of at least one other blue disk
> they can completely cover a red disk of area 1+e (arbitrarily small e).
You need a minimum of 4 blue disks.
In three dimensions, you need a minimum of 5 solid 2-balls.
As you generalise this to higher dimensions, do you always need D+2 covering balls?

Anonymous at Wed, 2 Oct 2024 01:56:43 UTC No. 16405942

>>16402406
You should have known better when you had to read a book some else wrote
>let another man mind-fuck him with his thought-dick
faggot

Anonymous at Wed, 2 Oct 2024 04:56:18 UTC No. 16406078

>>16405930
what am I missing here

Anonymous at Wed, 2 Oct 2024 09:15:12 UTC No. 16406229

>>16405942
>faggot
Why the homophobia?

Anonymous at Wed, 2 Oct 2024 13:14:54 UTC No. 16406376

>>16405860
Thanks!

Anonymous at Wed, 2 Oct 2024 14:49:07 UTC No. 16406457

>>16405762
[math]2\text{cosh}(2x)=e^{-2x}+e^{2x}[/math], yes

Anonymous at Thu, 3 Oct 2024 14:18:11 UTC No. 16407618

>>16398395
Nice

Anonymous at Thu, 3 Oct 2024 14:57:02 UTC No. 16407645

Is an analytic solution to a problem always a closed-form expression?

Anonymous at Thu, 3 Oct 2024 15:24:12 UTC No. 16407675

>>16407645
No because it may use non-elementary analytic functions.

🗑️ Anonymous at Thu, 3 Oct 2024 17:54:05 UTC No. 16407838

i started reading an old school analysis book and i'm having trouble with the statement:
for y > 0 the intersection of these intervals is empty
[math](0,y) \supset (0, \frac{y}{2}) \supset \dots \supset (0, \frac{y}{n}) \supset \dots[\math].
it should follow from the archimedean property somehow, can anyone help me?

Anonymous at Thu, 3 Oct 2024 17:55:06 UTC No. 16407839

i started reading an old school analysis book and i'm having trouble with the statement:
for y > 0 the intersection of these intervals is empty
[math](0,y) \supset (0, \frac{y}{2}) \supset \dots \supset (0, \frac{y}{n}) \supset \dots[/math].
it should follow from the archimedean property somehow, can anyone help me?

Anonymous at Thu, 3 Oct 2024 18:02:16 UTC No. 16407851

>>16407839
Suppose you have an x in the intersection then for all n you must have
0 < nx < y
Which is impossible by the archimedean property.

Anonymous at Thu, 3 Oct 2024 18:10:53 UTC No. 16407862

>>16407851
let me rephrase it: if we consider the interval (0, y/n) with an x in this interval and the condition nx < y, then the archimedean property tells us that the next nested interval (with n+1) exists and violates the condition and we can repeat this reasoning for ever, correct?

Anonymous at Thu, 3 Oct 2024 18:25:11 UTC No. 16407891

>>16407862
more like, if $x$ is in the intersection, then it must be that $x\in(0,y/n)$ for all $n$. but this implies that $0<x<y/n$ for all $n$.

Anonymous at Thu, 3 Oct 2024 18:46:53 UTC No. 16407924

>>16406229
why not?

Anonymous at Thu, 3 Oct 2024 19:15:07 UTC No. 16407952

>>16405637
>he doesn't know

Anonymous at Thu, 3 Oct 2024 19:17:13 UTC No. 16407960

>>16407952
I'm not a "he".

Anonymous at Thu, 3 Oct 2024 19:33:40 UTC No. 16407974

>>16407952
why would anyone do this

🗑️ Anonymous at Thu, 3 Oct 2024 20:56:04 UTC No. 16408069

Snap crackle pop lock drop

Anonymous at Fri, 4 Oct 2024 18:45:34 UTC No. 16409722

can anybody explain why the fuck number 24 and its relatives are so common in modular forms? any other batshit numbers like 691 and 11 (in ramanujans congruences for example) or 12, 12^3 in j invariant are explained by the appearance of 24, for example 691 comes from the bernoulli number 12 and 12 comes from 24. existence and construction of univalent automorphic forms on hecke modular subgroups and dedekind sums are also really weird. why does this all happen? where does this seemingly random ass number appear out of nowhere while studying objects with no obvious connection to this number.
(also i studied modular functions and dirichlet series by apostol and dont have a good understanding of the algebraic aspects of modular forms)

Anonymous at Fri, 4 Oct 2024 20:03:29 UTC No. 16409807

>>16409722
24 and its divisors are the only multiplicative groups with no exponent > 2 and whose dirichlet characters are are real.
see also
https://doi.org/10.2307/3621490
https://doi.org/10.4169/math.mag.85.5.366

Anonymous at Sat, 5 Oct 2024 01:56:24 UTC No. 16410138

>>16409807
Doesn’t the dicyclic group of order 24 have a degree 6 element

Anonymous at Sat, 5 Oct 2024 01:57:37 UTC No. 16410141

>>16410138
Oh I didn’t notice multiplicative

Anonymous at Sat, 5 Oct 2024 03:34:02 UTC No. 16410202

What's the problem here?

[eqn]
\begin{aligned}
\frac{x}{y} & = \frac{x}{y}\\
\frac{x}{y} + d(\frac{x}{y}) & = \frac{x + dx}{y + dy}\\
d(\frac{x}{y}) & = \frac{x + dx}{y + dy} - \frac{x}{y}\\
d(\frac{x}{y}) & = \frac{xy + y\,dx}{y^2 + y\,dy} - \frac{xy + x\,dy}{y^2 + y\,dy}\\
d(\frac{x}{y}) & = \frac{y\,dx - x\,dy}{y^2 + y\,dy}
\end{aligned}
[/eqn]

Anonymous at Sat, 5 Oct 2024 05:23:25 UTC No. 16410273

>>16410202
What does the second line even mean and why should it be true? I'm assuming d is meant to be something to do with derivatives and not just a variable? Neither side really makes sense as a derivative though.

Anonymous at Sat, 5 Oct 2024 05:40:35 UTC No. 16410283

>>16410202
This is utter nonsense.

Anonymous at Sat, 5 Oct 2024 05:43:28 UTC No. 16410284

>>16410202
You are retarded

df(x,y)=(∂f/∂x)dx+(∂f/∂y)dy

so d(x/y)=(1/y)dx+(-x/y^2)dy

Anonymous at Sat, 5 Oct 2024 06:43:34 UTC No. 16410311

>>16397598
If you would just learn to read you wouldn't have that reaction to math

Anonymous at Sat, 5 Oct 2024 10:25:18 UTC No. 16410396

>>16409807
arent these trivial? also how does these relate to the things i mentioned

Anonymous at Sat, 5 Oct 2024 10:34:08 UTC No. 16410402

>>16410396
IQ IS trivia. Fagademic

Anonymous at Sat, 5 Oct 2024 11:22:05 UTC No. 16410431

>>16410283
No it isn't. If you write one side as its own variable it works:

[eqn]
\begin{aligned}
z & = \frac{x}{y}\\
zy & = x\\
(z + dz)(y + dy) & = x + dx\\
zy + z\,dy + y\,dz + dz\,dy & = x + dx\\
z\,dy + y\,dz + dz\,dy & = dx\qquad \text{(\(dz\,dy\) is negligible)}\\
z\,dy + y\,dz & = dx\\
y\,dz & = dx - z\,dy\\
dz & = \frac{dx - z\,dy}{y}\\
dz & = \frac{dx - \frac{x}{y}\,dy}{y}\\
y\,dz &= \frac{ydx - x\,dy}{y}\\
dz &= \frac{ydx - x\,dy}{y^2}\\

\end{aligned}
[/eqn]

Anonymous at Sat, 5 Oct 2024 12:10:20 UTC No. 16410453

[eqn]
\begin{aligned}
d(\frac{x}{y}) & = \frac{y\,dx - x\,dy}{y^2 + y\,dy}\\
y^2\,d(\frac{x}{y}) + y\,dy\,d(\frac{x}{y}) & = y\,dx - x\,dy\qquad \text{(\(y\,dy\,d(\frac{x}{y})\) is negligible)}\\
y^2\,d(\frac{x}{y}) & = y\,dx - x\,dy\\
d(\frac{x}{y}) & = \frac{y\,dx - x\,dy}{y^2}\\
\end{aligned}
[/eqn]

Anonymous at Sat, 5 Oct 2024 13:28:15 UTC No. 16410519

Books for information theory?

Anonymous at Sat, 5 Oct 2024 13:31:41 UTC No. 16410523

>>16410519
BATTLESTATIONS

Kys now

Anonymous at Sat, 5 Oct 2024 13:34:23 UTC No. 16410525

>>16410523
bot post

Anonymous at Sat, 5 Oct 2024 13:39:42 UTC No. 16410534

>>16410525
60000 yearaz

Anonymous at Sat, 5 Oct 2024 15:55:43 UTC No. 16410678

>>16404747
You decomposed cosh.
The only hard part is handling the e^(-2x) term since it is in the kernel of your operator.
(D+2)(D-1)y = e^(-2x)
Let y = e^(-2x)*g.
(D+2)(D-1)e^(-2x)*g = e^(-2x)D(D-3)g = e^(-2x)
You get
D(D-3)g = 1
(D-3)g = x+c
This is first order and easy to solve

You should get y = hom + e^(2x)/4 + e^(-2x)*g

I used the property De^(ax) = e^(ax)(D+a)

Anonymous at Sat, 5 Oct 2024 16:06:42 UTC No. 16410692

>>16410202
No problem.
Do the geometric expansion and forget higher order dx and dy to get:
dx/y -xdy/y^2
which agrees with the usual way
d(x/y) = d(x)*(1/y) + x*d(1/y) = dx/y - x*dy/y^2

Anonymous at Sat, 5 Oct 2024 16:57:36 UTC No. 16410757

>>16397584
Science & Engineering grads design + build stuff as a hobby activity.
Is entering competitions all math dudes do?
Don't math chads ever aspire to create?

Anonymous at Sat, 5 Oct 2024 16:59:19 UTC No. 16410759

how do you study from math books? what's your method?

Anonymous at Sat, 5 Oct 2024 17:21:59 UTC No. 16410783

>>16410757
You poor, poor fool

Anonymous at Sat, 5 Oct 2024 17:37:01 UTC No. 16410806

How do I get a cryptography job with a masters in math? I know C/C++, Python, Lisp, etc. but I've never really "built anything". I keep being told not to "roll my own". What do?

Anonymous at Sat, 5 Oct 2024 17:38:17 UTC No. 16410808

>>16410783
I was serious. Doesn't it get shit boring?
Yous never make anything.

Anonymous at Sat, 5 Oct 2024 17:43:12 UTC No. 16410816

>>16410808
Mathematicians either solve mathematical problems or they create new theory.

>NOOOOOOO it's not tangible!
Software isn't tangible and neither are many major ideas that have real world applications.

But you're obviously a troll.

Anonymous at Sat, 5 Oct 2024 17:44:38 UTC No. 16410818

>>16410816
Zzzzzzzzzz.......

Anonymous at Sat, 5 Oct 2024 17:51:10 UTC No. 16410834

>>16410818
That's your best response? lmao

Anonymous at Sat, 5 Oct 2024 17:51:16 UTC No. 16410836

>>16410808
and that's exactly why it's not boring - in mathematics, you're not bound by things like "reality" or "practicality"
I can speak of objects that exist in 196882-dimensional space in a meaningful, coherent, and important manner. How many dimensions can you build in, engie-boy?

Anonymous at Sat, 5 Oct 2024 18:00:42 UTC No. 16410854

>>16410834
>>16410836
You never built a go-cart out out of a lawn mower as a teen, then stacked in a race and broke your arm?
You never made your own 20 Band LED Display Graphic Equalizer & 1000W car audio amp and did bog laps thru the nightlife spots with your drunk buddies?
You ever lived? (outside mommies basement)

Anonymous at Sat, 5 Oct 2024 18:01:51 UTC No. 16410857

>>16409722
no answers? does anybody here even know what a modular form is or is this place full of muh iq retards? the dirichlet character guy seems to be talking about random shit

Anonymous at Sat, 5 Oct 2024 18:10:02 UTC No. 16410868

this shit worth it? i dont get much sleep

Anonymous at Sat, 5 Oct 2024 18:19:58 UTC No. 16410879

>>16409722
he's not, though he did a piss-poor job at elaborating on it
Terry Gannon (not that Terry Gannon) speculated that 24's significance in higher-level mathematics is related that property, but that is, again, only speculation.

"More" concretely, it's one of those mathematical mysteries that has yet to be fully explained beyond "magic". Maybe that's an uncomfortable truth, or maybe that's an opportunity

Anonymous at Sat, 5 Oct 2024 18:22:37 UTC No. 16410882

>>16410879
meant to include >>16410857as a reply. fuck

Anonymous at Sat, 5 Oct 2024 19:04:36 UTC No. 16410925

>>16410857
>full of muh iq retards?
this and bots and schizos
>does anybody here even know what a modular form is
no

Anonymous at Sat, 5 Oct 2024 19:04:45 UTC No. 16410926

WHERE ARE THE FUCKING INITIAL VALUES FOR (b)

Anonymous at Sat, 5 Oct 2024 19:30:16 UTC No. 16410948

>>16407960
Tits + timestamps or you are a "he"

Anonymous at Sat, 5 Oct 2024 19:31:18 UTC No. 16410950

>>16410926
What book is this

Anonymous at Sat, 5 Oct 2024 20:00:01 UTC No. 16410971

>>16410926
You don't need any there.

Anonymous at Sat, 5 Oct 2024 20:26:47 UTC No. 16410999

>>16410926
Solve it in terms of [math] a_0 [/math].
That's why it's called a GENERAL solution. Do you ask for what is the function when solving differential equations?

Anonymous at Sat, 5 Oct 2024 21:58:06 UTC No. 16411167

I'm programming mathematical algorithms in Rust, I did variations of simplex and gradient descent. Years back I programmed RK4 multivariable diff eqs.
What maths do you suggest I program next? Which topics are feasible to do computationally? I'm thinking of going back through my abstract algebra book to do cryptograpny

Anonymous at Sat, 5 Oct 2024 22:42:51 UTC No. 16411294

>>16411167
Sounds as if you might enjoy a site like Project Euler, though the early questions are pretty simple and it doesn't focus on numerical methods like gradient descent.

Anonymous at Sat, 5 Oct 2024 22:59:00 UTC No. 16411339

>>16411294
I did some Project Euler for learning new languages, but I settled on codewars because you can copy paste the tests and add your own tests. I'm looking for bigger projects now that I handle well the basics of programming in general

Anonymous at Sun, 6 Oct 2024 08:33:36 UTC No. 16411966

>>16410999
it says *particular solution* on the question. i have no idea what that means

Anonymous at Sun, 6 Oct 2024 10:51:34 UTC No. 16412070

>>16411966
It means A and B should be actual numbers, not expressions involving variables.
>>16410926
Well, what possibilities are compatible with the solution having that form? If there's only one then it's that one. If not then probably you can just pick whatever's easiest.

Anonymous at Sun, 6 Oct 2024 10:55:27 UTC No. 16412077

>>16410806
>he fell for the masters in math meme
all you can do now is do a phd in cryptography or math for cryptography

Anonymous at Sun, 6 Oct 2024 15:14:33 UTC No. 16412321

>>16412077
Why? So even if I built a solid portfolio I'm forever stuck as an academic?

Anonymous at Sun, 6 Oct 2024 21:01:18 UTC No. 16412887

is this example right? I don't get which points are the nearby local minimizers. Are they in the room with us?

Anonymous at Sun, 6 Oct 2024 21:18:14 UTC No. 16412907

so dx was initially supposed to be an infinitesimal by Leibniz but was then changed in more rigorous definitions to mean a variable approaching zero, almost turning dx into a homonym for concepts of sorts, a limit or lack thereof would rule its concept but people speak about it like a homonym. It still often gets taught as an infinitesimal even when limits are being used in a calculus course, either because the teacher has a limited understanding of the subject or because they're attempting to give students some type of a more physical intuition through the concept of infinitesimals. It just makes calculus look so messy to me, especially its pedagogy at least.
This is stressful when I'm trying to learn math because there's always an underlying sense that something is wrong, that the material is totally ignoring the background. An author says "Think of this dx here as something infinitely small" and then a person says "there are no infinitesimals in calculus anymore, they were removed through using more rigorous methods". But Keisler showed a rigorous method to use them so now both conceptual understandings of dx can be thought of as rigorous.
This is as bad as my introductory philosophy class teaching Plato's theory of forms through the concepts of an ideal apple which all apples emanate from, and then jumping all the way to renaissance philosophers.
I'm aware of language being ambiguous and math being a language but am I wrong to have found it bad to have these symbols skimmed over or used in different way without placing detail on it?

Anonymous at Mon, 7 Oct 2024 00:08:50 UTC No. 16413140

Why is this true? Is this a name for this result?

Anonymous at Mon, 7 Oct 2024 00:11:28 UTC No. 16413143

>>16413140
*is there

Anonymous at Mon, 7 Oct 2024 09:41:44 UTC No. 16413738

>>16413140
There are only two cases [math]x_m = 0[/math] and [math]x_m = 1[/math]. Just verify it works in both.

Anonymous at Mon, 7 Oct 2024 09:48:43 UTC No. 16413742

>>16413738
I interpreted Coldplay Spies as ' they were in hell, so they could only be the profession spy'. This is a nice hanging metaphor off that song. Now fart on my lip.

Anonymous at Mon, 7 Oct 2024 09:51:57 UTC No. 16413743

>>16412907
Based kaworu pic. If you're this autistic over math terminology just go through a real analysis textbook. A lot of places have separate calculus classes for math majors and everyone else

Anonymous at Mon, 7 Oct 2024 09:57:14 UTC No. 16413747

In your experience, is there any value at all in going through "synthetic proofs". Proofs that basically encapsulate this from Knuth's Surreal Numbers:
>“B: True. I've got this mad urge to get up before a class and present our results: Theorem, proof, lemma, remark. I'd make it so slick nobody would be able to guess how we did it, and everyone would be so impressed.”
i.e. proofs that were seemingly made to be as terse and as dense as possible, where one can only really verify each step is technically correct, but there is no apparent motivation behind any of the steps until the very last sentence when it all magically comes together. I find it very unsatisfying, and am not certain it's a good usage of my time to closely follow the proof, and not instead memorize the theorem/lemma/proposition and just get to the exercises and apply the results in my own proofs.

Anonymous at Mon, 7 Oct 2024 12:40:38 UTC No. 16413976

Can anyone help me find out why this is true? All we have is
[math] m_{*}(E_j - F_j) \leq \frac{\epsilon}{2^j} [/math], where does [math] m_{*}(F_j) \geq m_{*}(E_j) + \epsilon [/math] come from? So far all we know are the basic definitions of outer measure and measurable sets that I will post right with images right here:

Anonymous at Mon, 7 Oct 2024 12:41:58 UTC No. 16413977

>>16413976
properties of outer measure:

Anonymous at Mon, 7 Oct 2024 12:42:38 UTC No. 16413978

>>16413977
properties of measureable sets

Anonymous at Mon, 7 Oct 2024 12:46:56 UTC No. 16413983

>>16413977
>>16413977
Can't you use sub-additivity for [math] E_j = F_j \cup (E_j - F_j) [/math]?

Anonymous at Mon, 7 Oct 2024 13:18:47 UTC No. 16414004

>>16397639
What happens since 4096 DH will eventually be broken by quantum computing thus it will break key exchanges and there is a lack of study on ways to incorporate this into even openVPN

Anonymous at Mon, 7 Oct 2024 13:23:49 UTC No. 16414009

>>16410868
Use a Nicotine Lozenge, more effective for nicotinic acetylcholine receptors just don't get addicted.

More Choline != More Acetylcholine use, and likely will downregulate it or leave you with acetylcholinesterase issues, aside from that learn to meditate, and not mindfulness, do Zuowang - Read the relaxation response.

Anonymous at Mon, 7 Oct 2024 13:45:44 UTC No. 16414029

>>16413983
You're absolutely right. Thanks

Anonymous at Mon, 7 Oct 2024 14:19:17 UTC No. 16414063

>>16413978
C'mon man

Anonymous at Mon, 7 Oct 2024 19:34:27 UTC No. 16414492

>>16412887
Here, this is the derivative of the function

Anonymous at Mon, 7 Oct 2024 20:47:07 UTC No. 16414618

Not sure if this is a dumb question, but:

What would be an example of a topological space X, and a dimension-2 cohomology class [math] c \in H^2 ( X ; \mathbb{Z} ) [/math] on X , such that c is not the first Chern class of any complex line bundle on X ?

Anonymous at Mon, 7 Oct 2024 21:45:51 UTC No. 16414693

>>16414618
Nvm, I think no such example exists, if I'm not mistaken.

Anonymous at Mon, 7 Oct 2024 22:06:44 UTC No. 16414731

>>16414492
So because in any neighborhood of 0 there are points in which the derivative is 0, it means there are critical points in the original function, i.e minimizers. I think I get it? But my analysis foundations are weak

🗑️ Anonymous at Tue, 8 Oct 2024 01:40:27 UTC No. 16414950

Is every subfield of C other than R or C necessarily disconnected?

Anonymous at Tue, 8 Oct 2024 01:47:28 UTC No. 16414955

Is every subfield of [math] \mathbb{C} [/math] other than [math] \mathbb{R} [/math] or [math] \mathbb{C} [/math] necessarily disconnected? (with the relative/subspace topology)

Anonymous at Tue, 8 Oct 2024 02:37:45 UTC No. 16415010

I don’t understand why axiom of choice is such a big deal. If we accept the idea of real numbers, then given an uncountable family of nonempty sets {A_r}, with the real numbers as an indexing set, why is is so hard to accept “strands” of elements {a_r}, where a_r is in A_r for all real numbers r? What am I missing? Why is it a big deal to assume this object exists? Do I misunderstand the issue? I use the concept of choosing an element from a possibly uncountable set some times, and I worry I may be invoking arguments that I don’t realize that I don’t understand.

Anonymous at Tue, 8 Oct 2024 04:28:09 UTC No. 16415100

>>16414618
No because BU(1) is a K(Z,2)

Anonymous at Tue, 8 Oct 2024 05:26:36 UTC No. 16415133

>>16415010
>I don’t understand why axiom of choice is such a big deal.
there are some weird implications that follow from it. But it's a big deal for mostly historic reasons. Back in the day they had to justify accepting this "new" axiom. It is also a minor annoyance that AC is totally nonconstructive
>well you take your ideal and then by Zorn's lemma this is contained in a maximal ideal
>can we describe the maximal ideal?
>no, anyways next we choose a basis for the vector space of all real sequences
>can we write down an example of such a basis?
>no, but it's okay, I'm sure one exists!

>why is is so hard to accept “strands” of elements {a_r}, where a_r is in A_r for all real numbers r?
Without making this precise, you can describe at most countaby many real numbers

>What am I missing? Why is it a big deal to assume this object exists?
what you're missing is that it is not really a big deal in this day and age anymore. It is a little bit interesting to see if you really need AC for your argument. But most of the time nobody really cares outside of a few extremists.

There are also some really weird consequences for not accepting the axiom of choice (even if you use a weaker version). For example, without choice, a set can be partitioned into more partitions than the original set had elements. There is a big list of these in a mathoverflow thread somewhere, but I can't find it again with a quick google search.

Anonymous at Tue, 8 Oct 2024 06:23:22 UTC No. 16415188

>>16410926
Initial values are for part (a). You're confusing part (a) and part (b).

If I got it right, A and B very simple whole numbers, and the coefficients in front of a_0 and a_1 involve 2^{n+1).

Anonymous at Tue, 8 Oct 2024 06:47:36 UTC No. 16415232

>>16412907
>this is as bad
Lots of things are taught best using "history" as a guideline with "modern foresight" to aid the retrospective study. Basic arithmetic is taught first, then you build up to harder stuff. Historically, math is discovered easiest first, then harder things later. With modern understanding, when reteaching you can often skip or move things around, but in general the trend is from earliest to modern. You can say the same about physics. Like, it would be dumb to teach, starting off with quantum electrodynamics then go to classical, even though classical can be derived from quantum.

For calculus, Newton and Leibniz developed it with some idea of an infinitesimal. Newton knew this new thing was not rigourous, so to support his ideas he used geometric arguments instead of calculus in his published stuff. It wasn't until like Weierstrass or whoever who made use of limits to make calculus rigourous. Then in the 60s Robinson brought back infinitesimals with hyperreals.

There's zero reason why a teacher shouldn't teach using infinitesimals. It builds foundation as it did for Newton, it guides you to a more rigourous definition with limits, and hell, it actually can be justified anyway.

Furthermore, there's very little reason why a teacher is supposed to say everything I just said. Cause it's like, pretty obvious that people teach this way. What book is even saying "oh btw, infinitesimals don't exist"?

Anonymous at Tue, 8 Oct 2024 07:05:37 UTC No. 16415263

>>16412887
Well cos(1/x) seems to oscillate a hellava lot as x approaches 0. Not hard to imagine that there's a bunch of local minimums. Maybe ask yourself, how many minimums of f(x) are there within a domain when x is between (a_n, b) where 0 < a_n < b for all n. Surely there exist a finite number of em right? Suppose if a_n is a decreasing sequence as n -> infinity? How will the number of minimums change? Now what if you choose a domain [0, b)?

Anonymous at Tue, 8 Oct 2024 10:44:30 UTC No. 16415447

please help me with this. Its not homework or anything, im just trying to get back into math after being out of highschool for a decade, i thought it would be a simple problem but im retarded.
I want to set it up as a related rate but i can't remember how. I think the answer is x=r(sqrt2)-r but i can't prove it rigorously and i also dont think that really answers the question of how xx changes with r, it gives me an x if i know the radius but that the same as knowing the rate of change?

Anonymous at Tue, 8 Oct 2024 11:04:31 UTC No. 16415460

>>16412907
The thing is, learning how to do calculus is very important. Before you worry about definitions, proofs, and stuff like that, you NEED to get used to calculus. It is just like you learn how to add, subtract and the multiplication table before any complicated notion like axiom enters your vocabulary. You need to know how to use calculus to get through basic and important subjects like ODEs, Mechanics, Probability, etc.

If you can't deal with the momentary arbitrariness then just go straight to Real Analysis, but this subject won't give you the intuitions about integrals and derivatives that a standard calculus course would. I advise you to get used to it first, then you worry about foundational aspects.

Anonymous at Tue, 8 Oct 2024 11:24:09 UTC No. 16415476

Is information theory dead? Did all the experts just sell out to telecom companies and start working on 5G networks and shit? Or is there still a point to actually study it?

Anonymous at Tue, 8 Oct 2024 12:16:59 UTC No. 16415537

>>16415133
Wait, why can we at most describe countably many real numbers with my example? I must be missing something.

Anonymous at Tue, 8 Oct 2024 12:20:17 UTC No. 16415540

>>16415537
And in my example it’s an uncountable set {A_r} parameterized by real numbers, each set being mapped to an element a_r in A_r for each real number r.

Anonymous at Tue, 8 Oct 2024 13:31:08 UTC No. 16415628

>>16415447
Your question makes no sense, x does not depend on r.

Anonymous at Tue, 8 Oct 2024 14:57:13 UTC No. 16415762

>>16415628
If i want to keep the area of the inner circle and the outer ring the same then as r gets larger x has to as well.

Anonymous at Tue, 8 Oct 2024 15:12:35 UTC No. 16415790

>>16415762
You seem to be missing the point. If the areas stay the same then so do x and r. You can't change one without affecting the other (area).

Anonymous at Tue, 8 Oct 2024 15:22:27 UTC No. 16415799

How much are you guys using ChatGPT to aid with your math? I'm using the free one and man, the mistakes it makes is so damn annoying. Is the paid version really that much better?

Anonymous at Tue, 8 Oct 2024 15:55:03 UTC No. 16415828

>>16415799
I've seen article that there's some model trained on math olympiad, maybe find it out and try.

Anonymous at Tue, 8 Oct 2024 17:58:57 UTC No. 16415991

>>16415460
>>16415232
I think my main problem was that the same symbols we have been taught before are being used in different ways, similar to linear algebra which was uncomfortable to me until studying group theory on my own accord, after that I understood the semantics and where the language came from very intuitively. Mathematics follows this linear teaching method like you are being taught one universal language, until it suddenly doesn't since there are obviously many abstract worlds, using similar syntax with different meanings while still presenting itself in this semi linear fashion.
I took a calculus course to learn what it was, rather than using it because I wouldn't want to use something without having at least some fundamental understanding of what it is and understanding its definitions. But that may be an easily outvoted position.
Differentials for example was another thing that was used non rigorously basically as a homonym for the concept of infinitesimals. But as far as I am aware, there are no literal differentials in your first calculus courses even if the word is being used.
If you're arguing for teaching using infinitesimals, I'd argue that fluxions would be an even more intuitive way to teach calculus at first because it couples the derivative to time and its notation is something a student wouldn't have seen before, making it more concrete.
I guess I wrote this out also to ask if my understanding is correct? (ignoring my subjective points on how I personally would have liked to be taught).

Anonymous at Tue, 8 Oct 2024 18:17:40 UTC No. 16416026

>>16415447
I don't know what the other anon is talking about, but there is definitely a relation between [math]x[/math] and [math]r[/math], because of your constraint on the sizes of the "inside" and "outside".
From [math]A_i=A_o[/math] you get [math]\pi r^2=\pi(r+x)^2-\pi r^2\iff 2r^2 = (r+x)^2\iff \sqrt{2}r = r+x[/math], so (as you thought) [math]x=(\sqrt 2-1)r[/math].
Since [math]\sqrt 2-1 \approx 0.4[/math], this means that if [math]r[/math] increases by 1 unit, [math]x[/math] increases by about 0.4 units (rate of change).

Anonymous at Tue, 8 Oct 2024 20:19:08 UTC No. 16416231

>>16415188
Oops I thought the -1 was a 1, one is a fraction, not a whole number

Anonymous at Tue, 8 Oct 2024 20:21:20 UTC No. 16416236

>>16415799
I currently have a job getting paid $50/hr to ask an AI math questions and correct its responses.

They suck at math. Do not use them.

Anonymous at Wed, 9 Oct 2024 01:12:21 UTC No. 16416664

Does anyone know why this is true? I haven't really studied much linear algebra. Is this just because we have a system of equations with d+1 variables and d equations? Where does "not all zero" come into play?

Anonymous at Wed, 9 Oct 2024 01:21:02 UTC No. 16416676

>>16416664
Null space, faget

Anonymous at Wed, 9 Oct 2024 03:11:04 UTC No. 16416783

>>16415991
I am not advocating for any particular foundational school of Calculus, I am just saying that the point of first year calculus is to get students used to using derivatives and integrals, students should not worry about foundational aspects before being able to compute integrals, derivatives, Taylor series, and line integrals on the spot. The same is true for Linear Algebra, you can worry about the proof of the Jordan Canonical Form later, in your first course you should learn the basics of vector spaces, linear transformations, change of basis, matrices, determinants and how to solve linear systems. You'll have plenty of time in Analysis and Algebra courses to brood over definitions, but from there on all your professors will assume that you remember how to calculate the Taylor Polynomial of a function(sometimes a multivariable one), find the determinant of a 4x4 matrix, remember Stoke's Theorem by heart, etc.

The main point is: there is a lot of stuff in math that you need to get used to, before understanding fully those concepts you should simply get used to them. Just accept not understanding 100% of what you're doing sometimes.

Anonymous at Wed, 9 Oct 2024 04:25:55 UTC No. 16416918

>>16416664
look up what "linear dependen[t/ce]" means

Anonymous at Wed, 9 Oct 2024 06:06:25 UTC No. 16417003

>>16416664
Please stop posting

Anonymous at Wed, 9 Oct 2024 06:42:03 UTC No. 16417025

>>16416783
I'm still not convinced, there's no reason a linear algebra course can't spend two weeks on basic group theory and Algebra, or a first calculus course on the history and philosophy of the concepts such as the idealism of infinitesimals and the modern arbitrary notation that is used.
You are told idealistic philosophy and religion are silly for depending on direct experience and superstitions, but then ridiculed for questioning anything in math class and told that you won't get it and a mystery man of rigor in some other university has it figured out. "just believe, this is how math is, it is true, do not worry about foundational aspects". Societal schizophrenia.

Anonymous at Wed, 9 Oct 2024 10:46:22 UTC No. 16417284

>Dirichlet was the first "modern" mathematician, everybody does it nowadays but before Dirichlet there was nobody who combined rigor with the idea that our axioms are inherently arbitrary.
Is this true? Sure he predates Cauchy and Riemann but Descartes should count, right?

Anonymous at Wed, 9 Oct 2024 11:28:18 UTC No. 16417322

I tried googling what this diagram means. Apparently, it has something to do with some kind of differential equation that represents physical matter, but it says that with too many time dimensions the solutions become unpredictable.
What does that mean, exactly, from a mathematical perspective? Do the laws of motion become one-to-many?

Anonymous at Wed, 9 Oct 2024 13:35:49 UTC No. 16417447

>>16417025
I disagree, a semester is a really short time, most courses will skip basic stuff that you'll be assumed by professors to know later. Calculus at least is generally divided into 3 courses, but Linear Algebra is presented in an incomplete manner in most universities. Why waste 2 weeks on basic group theory when there is already a full semester course in basic group theory all math students will take? You could use those two weeks teaching stuff that students will never encounter again but are expected to be familiar with(SVD decomposition, Linear Interpolation, Block Matrices, etc.).

By the way, in a decent math course you will go over all the foundational stuff, generally multiple times. You will be given plenty of time to understand groups, functionals, the differential, etc. But you have a short time to get used to integrals, derivatives, series, linear systems, Fourier decomposition, Line integrals, big O notation, etc. Also, there is nothing more "idealistic philosophy" like than tirelessly obsessing about deriving all knowledge from first principles and having full understanding of everything and never being comfortable with some arbitrariness here and there.

Anonymous at Wed, 9 Oct 2024 14:12:01 UTC No. 16417499

>>16417284
Why would Descartes count?

Anonymous at Wed, 9 Oct 2024 14:19:22 UTC No. 16417512

>>16417322
Read the original paper: https://arxiv.org/pdf/gr-qc/9702052

Anonymous at Wed, 9 Oct 2024 16:31:06 UTC No. 16417682

>>16417284
in this, too, as with everything else, Leibniz was first

Anonymous at Wed, 9 Oct 2024 16:43:31 UTC No. 16417703

>>16417682
>>16417284
Why would our current axioms be considered arbitrary? They are roughly the minimum set of axioms we found that guarantees the existence of the math objects we want to assume that exist without generating contradictions. If you tweak them just a little you get totally different mathematics that does not match to the stuff we generally want. Our set of axioms is as much an arbitrary set of statements as Bach's symphonies are arbitrary sets of sounds.

I get that there is a place in math for the exploration of different systems of axioms, and that the general mentality shifted from "just stick to what is obviously true" to "lets try this to see if it doesn't produce obvious nonsense", but we haven't gone full arbitrary yet..

Anonymous at Wed, 9 Oct 2024 17:58:23 UTC No. 16417833

I am trying to learn math "properly." I have two goals:
1. Understand textbook readings so that I do not just try to match problems with examples.
2. Pass courses without the help of a professor or lecture at all. Only through reading texts.

I started this project by going through an Algebra textbook. Anyone have advice for this endeavor?

Anonymous at Wed, 9 Oct 2024 18:31:38 UTC No. 16417922

>>16415133
So my argument involves the existence of a right inverse g of a function f to define a bijection between the image of f and a subset of the domain of g. The pre image of each y in the image of f may be infinite, and the image of f may be infinite.

I believe the choosing of where each y should be mapped to by g is described as invoking the axiom of choice.

I read somewhere else that the axiom of choice really is just a name for a type of argument people make, and once we name it, we can see what happens if it’s not allowed. Someone called the idea of defining a function at each y based on choosing an element from its pre image “infinite instantiation”.

Anonymous at Wed, 9 Oct 2024 19:13:31 UTC No. 16418005

>>16397639
>>16397650
Passwords and decryption keys can be retrieved using a bootkit. All you have to do is reverse engineer the cryptographic program used to encrypt and decrypt the data. Post bail and skip town, you should probably flee the country to a non-extradition country.

Anonymous at Wed, 9 Oct 2024 19:20:42 UTC No. 16418026

>>16417833
Start slow. Reading a math textbook is kinda hard, it starts easy but you'll get really tired in the middle to end. Start with a book that is clearly for undergrads and not super long.

Anonymous at Wed, 9 Oct 2024 19:39:30 UTC No. 16418078

>>16398827
That was a subhuman shitskin.

Anonymous at Wed, 9 Oct 2024 19:46:34 UTC No. 16418089

>>16417703
Arbitrary in the sense that you don't need to justify the axioms as "true facts about the Platonic universe" like how Euclid's axioms (the only axiomatic theory in mathematics until the 19th century) were justified.

Anonymous at Wed, 9 Oct 2024 20:07:30 UTC No. 16418121

>>16417922
While fine in the category of sets, it is interesting to note that this behavior is rather "unnatural". as soon as we require some extra structure (e.g. groups, topological spaces, etc) it is very rarely the case that every surjective map admits a right inverse.

Anonymous at Wed, 9 Oct 2024 22:18:02 UTC No. 16418251

I think I've just proven
[math]\sqrt{-1} \in \mathbb{R}[/math]

Anonymous at Wed, 9 Oct 2024 22:52:09 UTC No. 16418295

okay so
let's prove that [math]\sqrt{-1} \in \mathbb{R}[/math]
let's assume [math]\exists x \in \mathbb{R}, x = \sqrt{-1}[/math] and see if any contradiction arises
[eqn]
x=\sqrt{-1}
\\
x^2=-1
\\
x^2+1=0
[/eqn]no problem so far
then let's multiply by [math]x[/math] several times, by assuming [math]x \neq 0[/math]
[eqn]
x^2+1=0
\\
(x^2+1) \times x = 0 \times x
\\
x^3+x=0
\\
x^4+x^2=0
[/eqn]which is consistent with complex math
then, since we've already established that [math]x^2=-1[/math], we can conclude that
[eqn]
x^4+x^2=0
\\
x^4+(-1)=0
\\
x^4=1
\\
x=1
[/eqn]problem?

Anonymous at Wed, 9 Oct 2024 23:13:13 UTC No. 16418309

>>16418295
So sqrt(-1)=1? What is 1*1?

Anonymous at Thu, 10 Oct 2024 00:03:10 UTC No. 16418371

>>16418309
[math]1 \times 1=2[/math] according to latest theory

Anonymous at Thu, 10 Oct 2024 01:09:22 UTC No. 16418416

>>16418295
>problem?
Yes. 1 has 4 4th roots. It's in the name. Specifically, 1, -1, i, and -i. When dealing with an operation with multiple solutions where which solution matters, you may need to specify which you are dealing with.

Else you end up with a situation comparable to claiming
|x|=|-x|=|ix|=|-ix| therefore x=-x=ix=-ix.

Anonymous at Thu, 10 Oct 2024 01:35:59 UTC No. 16418448

>>16418416
I'm working within real numbers, so arguably there's solutions can either be x=1 or x=-1

Anonymous at Thu, 10 Oct 2024 02:14:52 UTC No. 16418503

>>16418448
You are not working with real numbers because you said x^2=-1.

Anonymous at Thu, 10 Oct 2024 02:20:03 UTC No. 16418507

>>16399936
That's cool

Anonymous at Thu, 10 Oct 2024 04:20:05 UTC No. 16418628

What do q-analogs originate and what are they used for?

UNSECGEN at Thu, 10 Oct 2024 05:18:05 UTC No. 16418686

should I read something like velleman before this? https://arxiv.org/pdf/2101.01939.pdf
also rec an equivalent to this for analysis + addenda for calc techniques

thx

Anonymous at Thu, 10 Oct 2024 05:50:28 UTC No. 16418726

>>16418686
Velleman what?

Anonymous at Thu, 10 Oct 2024 06:08:16 UTC No. 16418744

Speaking of Evan Chen's Napkin and Alan U. Kennignton's Differential Geometry what are other based autist overly long but coherent math notes?

Anonymous at Thu, 10 Oct 2024 07:17:03 UTC No. 16418810

How many books of the picrel are meme books?

Anonymous at Thu, 10 Oct 2024 07:23:48 UTC No. 16418821

>>16418810
None. The meme is to read them in that order. You can start Spivak right away. The first chapter has little set theory (by making addition, multiplication, order and natural numbers primitive concept instead of their set-theoretic presentation). A good exercise could be starting in the reverse order and going back only to fill gaps

Anonymous at Thu, 10 Oct 2024 07:26:50 UTC No. 16418824

>>16418821
How is the order bad? I followed the order till Set Theory rn, and have completed Basic Mathematics.

Anonymous at Thu, 10 Oct 2024 07:37:39 UTC No. 16418840

>>16418824
You don't need to finish every chapter before the next book, so you did well finishing Basic Mathematics without the preceding Set Theory, and you can skip Allendoerfer and that purple book if you want to get to Spivak. Its better to open the first chapter of every book in the chart and decide after that what you need, all im saying this couldn't be possible if you didn't abandon the rigid order

Anonymous at Thu, 10 Oct 2024 07:56:20 UTC No. 16418853

>>16418840
yeah I just read Spivak globally and much can be skipped. The entire first two parts regarding the fundamentals seem superfluous after doing Lang

Anonymous at Thu, 10 Oct 2024 09:21:21 UTC No. 16418902

>>16418853
Yes, do skip those chapters but try to solve every exercise. Some are very rewarding and absent from every other place.

Anonymous at Thu, 10 Oct 2024 10:15:47 UTC No. 16418948

>>16414004
>quantum computing

Anonymous at Fri, 11 Oct 2024 00:43:54 UTC No. 16420065

You can adjoin some non-elementary functions, like log(f), to the set of elementary functions and still get a closed set of functions. There are presumably some functions that make sets that aren't closed when adjoined. (My guess is most hypergeometrics) How do I find out what they are?

Anonymous at Fri, 11 Oct 2024 01:43:05 UTC No. 16420132

>>16420065
log is an elementary function

Anonymous at Fri, 11 Oct 2024 02:51:41 UTC No. 16420264

how's my proof? chatgpt says it's valid

Anonymous at Fri, 11 Oct 2024 05:07:06 UTC No. 16420557

>>16420264
cleaned it up

Anonymous at Fri, 11 Oct 2024 14:37:28 UTC No. 16421025

How do you prove that if f is n times differentiable (n>=2), then f_xi ' is n-1 times differentiable?

Anonymous at Fri, 11 Oct 2024 15:59:23 UTC No. 16421123

Is this how you define fractional exponents?

Anonymous at Fri, 11 Oct 2024 16:06:24 UTC No. 16421137

>>16421123
You use e^x. College math textbooks go into this like Rudin(?)

Anonymous at Fri, 11 Oct 2024 16:08:34 UTC No. 16421142

>>16421123
With the caveat that your redefinition has multiple possible values whereas the original statement is single-valued by convention, yes.
For example, [math](-3)^{2}=9[/math] as well, but [math]9^{\frac{1}{2}} \neq -3[/math] (again, by convention)

Anonymous at Fri, 11 Oct 2024 17:59:33 UTC No. 16421302

Why can we add rational exponents

x^(1/4) * x^(1/5) = x^(9/20)

Anonymous at Fri, 11 Oct 2024 18:19:49 UTC No. 16421349

>>16421025
you can use LaTeX here, you know

Anonymous at Fri, 11 Oct 2024 18:41:37 UTC No. 16421384

>>16397906
Is there a version of this where the images are readable?

I cant even read the names.

Anonymous at Fri, 11 Oct 2024 21:10:51 UTC No. 16421768

can somehow decompose this into something more understandable

Anonymous at Fri, 11 Oct 2024 21:19:24 UTC No. 16421787

>>16421302
again, read >>16421137

Anonymous at Sat, 12 Oct 2024 08:26:48 UTC No. 16422524

>>16421768
there is no correct answer. it's a shitpost as old as 4ch itself.

Anonymous at Sat, 12 Oct 2024 13:29:28 UTC No. 16422717

>>16422524
yeah but i want to it explained why with math logic

Anonymous at Sat, 12 Oct 2024 13:36:08 UTC No. 16422722

How come the relation that operations have to properties is one of {doesn't have it, has it on the left, has it on the right, has it on both sides}? Are there any logical structures that must be represented by a multidimensional array of symbols and can't be reduced to a linearly ordered sequence of symbols?

Anonymous at Sat, 12 Oct 2024 13:58:41 UTC No. 16422739

>>16421768
well if you guess at random, then you have a 25% chance of being right.
Oh but wait, both a) and c) are correct meaning that there is a 50% change of being right if you guess at random. The answer must be c).

but if c) is the only right answer, then that must be mean you have a 25% chance of being right if you guess at random.......

Anonymous at Sat, 12 Oct 2024 14:03:02 UTC No. 16422744

>>16421768
the trick is to notice the question did not specify a uniform distribution, so just flip a coin to decide between c and b

Anonymous at Sat, 12 Oct 2024 14:05:51 UTC No. 16422751

>>16422744

Anonymous at Sat, 12 Oct 2024 15:48:51 UTC No. 16422913

>>16397584
Anyone have a working cracked CrystalMaker software

Anonymous at Sat, 12 Oct 2024 17:51:50 UTC No. 16423179

does anyone here know these lectures/book?
I've been looking for a reference with exactly those topics for those purposes, it's short so I'll read the whole thing if possible

Anonymous at Sat, 12 Oct 2024 18:26:52 UTC No. 16423266

>>16421137
>using le complex numbers just to define rational powers
Rudin doesn't define it like that. Also, that's an asinine definition.

>>16421123
Assuming, you are using real numbers, one can show for every positive integer [math] n [/math], and a positive real number [math] x [/math], there exists a unique [math] \textit{positive} [/math] real number [math] y [/math] such that [math] y^n = x [/math]. This [math] y [/math] is defined as [math] x^{1/n} [/math].

Now, [math] x^{p/q} [/math] is defined as [math] (x^p)^{(1/q)} [/math], however for this to be well-define, it needs to be shown that if [math] p/q = m/n [/math], then [math] (x^p)^{(1/q)} = (x^m)^{(1/n)} [/math], which is not too hard to show.

Anonymous at Sat, 12 Oct 2024 19:12:11 UTC No. 16423354

is transcribing a book in latex a good way to memorize and understand definitions and proofs since we are writing them step by step?
i already do the same by hand and i can say the method works but it's really inefficient.

i also tried not writing anything but i just read too fast and i miss the important bits, any advice to improve is welcome.

Anonymous at Sat, 12 Oct 2024 19:23:49 UTC No. 16423376

>>16421123
one way is to define the exponential for n > 0 and derive the formulas
[math]
x^nx^m=x^{n+m}
[/math]
and
[math]
(x^n)^m=x^{nm}
[/math]
.
then you define x^0=1 and x^p for p = -n, n > 0 as x^(1/n) and see that the formuals still work.

Anonymous at Sat, 12 Oct 2024 19:25:14 UTC No. 16423378

I think this problem is cool so I'll post it here as well

Anonymous at Sat, 12 Oct 2024 19:38:38 UTC No. 16423407

>>16423354
It works for me, but it might not for everyone. I transcribe a lot of my notes using Latex because my handwriting sucks and I might lose them otherwise, and it does indeed help me know if I understand the material or not.

Anonymous at Sat, 12 Oct 2024 19:50:06 UTC No. 16423437

>>16423407
i'm talking about notes from a book not a lecture, which is much slower because before summarizing something i have to understand it and rewrite in my own words.

Anonymous at Sat, 12 Oct 2024 20:42:57 UTC No. 16423528

>>16423354
My recommendation is before reading a proof to try to do it yourself. One problem with this approach is that you have not to let your ego get in the way and if some theorem is a struggle just read the proof instead of getting stuck and refusing to do that until you solve it.

Anonymous at Sat, 12 Oct 2024 20:50:23 UTC No. 16423542

>>16414009
>not mindfulness, do Zuowang - Read the relaxation response.
Could you please elaborate on this?
What has your experience been using these techniques? Different anon then the one you'd replied to here.

Anonymous at Sat, 12 Oct 2024 20:58:02 UTC No. 16423554

>>16423528
how am i supposed to come up with proofs that took centuries to develop? at the moment i'm studying mathematical analysis rudin style (not using the book though) but for other topics it should be easier.
i try to read proofs very slowly until i internalize every word and i am able to explain by myself without help.

Anonymous at Sat, 12 Oct 2024 22:32:27 UTC No. 16423677

>>16397584
>math
>s
why do yuropoors ruin everything?

anywho, good resources on brushing up on calc/trig? It's been a long time but I'm gonna take a physics class at my local CC for my job and need to get my math skills back into shape

Anonymous at Sun, 13 Oct 2024 00:39:18 UTC No. 16423834

>Have chat GPT's Wolfram Alpha model help me formalize my ideas into a coherent formula
>Basically end up starting at a+b = c and progressively mapping Peircean triadic semiotic theory and bleeding edge metaphysics onto progressively more complex operations
>Make Wolfram alpha run some intensive tests against gold standard formulas for specific types of problems
>Mine wins like 40% of the time.
I thought you nerds said this math shit was hard.

Can you dorks run my equation in your loser machines to see if it can compete with any other weenie-hut-jr formulas?

Anonymous at Sun, 13 Oct 2024 01:22:48 UTC No. 16423895

>>16423834
Actually nevermind it turns out I was reading the results wrong, I'm retarded.

My formula can handle insanely complex scenarios but not simple ones.

You win this round, mathfags.

Anonymous at Sun, 13 Oct 2024 06:16:36 UTC No. 16424287

>>16423554
>how am i supposed to come up with proofs that took centuries to develop?
Keep in mind that the definitions also took centuries to develop; since you get those "for free", most proofs should be (relatively) easier for you than for whoever worked them out first.

Anonymous at Sun, 13 Oct 2024 10:50:20 UTC No. 16424854

I started grinding this book close to 3 years ago, but my motivation dwindled later. (It turned out that my analyst job never required anything more complex than the 4 basic operations. Doing proofs helped keep my logic skills sharp though.) I am 90-95% done with every chapter/exercise.

If I want to learn only mathematics that could help me with real world analytics and decision making then am I right in assuming I'd need Calculus, Linear Algebra and Statistics?

Anonymous at Sun, 13 Oct 2024 11:09:27 UTC No. 16424957

>>16424854
Study Operations Research.

Anonymous at Sun, 13 Oct 2024 12:34:17 UTC No. 16426041

How to define continued fractions without dots? Like a recursive or some other method?

Anonymous at Sun, 13 Oct 2024 12:35:31 UTC No. 16426074

>>16423354
If you have to memorise anything but conventions, you're doing it wrong. All definitions and proofs have motivations except maybe in Number Theory. FUCK NUMBER THEORY.

Anonymous at Sun, 13 Oct 2024 12:45:38 UTC No. 16426324

>>16426041
An infinite continued fraction is the limit of its convergents.

Anonymous at Sun, 13 Oct 2024 13:18:50 UTC No. 16426950

Why don't more math problems use multi-armed bandits as a framework?

Anonymous at Sun, 13 Oct 2024 13:29:32 UTC No. 16427194

>>16426074
memorization is a crucial part in learning, there's so many common words that in math take up another meaning.
i can't count the times i was lost in the steps of a proof only because i did not have the definitions in front of me that reminded me of what i can and cannot do.

Anonymous at Sun, 13 Oct 2024 13:40:18 UTC No. 16427460

>>16427194
>>16426074
I used to hate memorization when I was younger, but now that I am a bit older, I sort of of just like that fact that I know more trig identities than other people who have done less math than me.

Anonymous at Sun, 13 Oct 2024 13:45:34 UTC No. 16427534

>>16427460
once you become familiar with the subject you dont need to memorize anymore, you just know it.
but since we're talking about being exposed to the subject for the first time, it's a whole other story.
returning to the topic, i just want to how math students study from dense books without becoming monastic scribes.

Anonymous at Sun, 13 Oct 2024 13:57:58 UTC No. 16427676

>>16423677
>good resources on brushing up on calc/trig?
bumping this

🗑️ Anonymous at Sun, 13 Oct 2024 14:03:51 UTC No. 16427731

>>16414955
why would it be? C is homeomorphic to R^2, and every disk in R^2 is not only connected but path connected.

Anonymous at Sun, 13 Oct 2024 14:42:07 UTC No. 16427993

>>16399936
In my experience Asians aren't really much better at math than whites. Asian parents push all of their kids to study it hard so the average kid is better, but once you get into the spread of math majors whites are at least as good if not better.

Anonymous at Sun, 13 Oct 2024 14:43:08 UTC No. 16427999

>>16423677
Just download a calc 1/2/3 textbook. Look up whatever your community college uses and study it.

Anonymous at Sun, 13 Oct 2024 14:58:57 UTC No. 16428110

>>16423554
As the other anon said, you already have the definitions and the direction of where the theory goes, which should help. You of course don't have to derive all proofs yourself, but after you've been exposed to a few and if the book is designed well for learning (which Rudin may not be desu, where are you studying analysis from "Rudin-style"?), at the point that you are introduced to some lemma or theorem, you should already have some idea of why it's important and why it could/should be true, and how the proof could go. Working through some examples to get some intuition why the statement holds for them is often quite helpful for this too. Of course it takes some time getting exposed to proofs and trying the approach before you get comfortable with it. But for learning I'd say it's supremely useful as then you don't have to "remember the proof" but just "remember some semblance of the way you derived (a part) of it".

Anonymous at Sun, 13 Oct 2024 16:02:01 UTC No. 16428451

>>16428110
thanks anon, i will try to do it then since i am studying at my own pace.

>(which Rudin may not be desu, where are you studying analysis from "Rudin-style"?)
to clear things up, i already know calc 1/2/3 from my engineering courses. i also took other math courses like linear algebra, probability, dynamic systems, etc., i am not a complete beginner.

i also got good grades and everything but i felt like a baby swimming in the ocean, in the sense that, although i am good at manipulating these mathematical objects, i don't have a "deeper understanding" of them, so i decided to read math books that cover things from the ground up rigorously.
the russian MIR collections contains many good books and i am using "mathematical analysis, a special course" by Shilov, which starts with the construction of the real numbers, metric spaces and then proceeds with limits, derivatives and integrals.
so far i like it and i learnt new things but i'm not sure that i'm spending my time efficiently, most of the times i already know what he's explaining and for the rest it's mostly useless nitpicking stuff.
i'm not sure what to do

Anonymous at Sun, 13 Oct 2024 17:41:51 UTC No. 16428901

I got a mediocre grade on my analysis exam and now I feel stupid. It's only a B-, and above average, but I feel like a retard. My GPA is like 3.5 and is probably gonna stay there, I feel like if I were actually smart I'd be getting top grades on every exam. I'm tested with a top .5% IQ and I feel like my identity has been shaped by being smart my whole life. What do I do now? This isn't even new, I've gotten far worse grades in the past. But I feel stupid now for some reason.
I feel like maybe I can't actually do anything, I feel like my IQ is now a limiting factor on my success for the first time in my life.

Anonymous at Sun, 13 Oct 2024 17:44:12 UTC No. 16428905

>>16427999 (checked)
fair enough, I still have my old textbook around. Just wasn't sure if there were any good online problem sets or such that people liked

Anonymous at Sun, 13 Oct 2024 18:25:40 UTC No. 16429015

>>16427194
You're memorising because you're not pausing to understand it.

Anonymous at Sun, 13 Oct 2024 18:33:58 UTC No. 16429047

>>16428901
I got straight As in my undergrad math classes (math major) but pretty much straight Cs in my "core curriculum" (state government, public speaking, philosophy of something etc.).
Why do you feel stupid? You gave it your all and only got above average?

Anonymous at Sun, 13 Oct 2024 18:43:39 UTC No. 16429074

>>16429015
you're also right.
i'm going to change approach and see how it goes.
i should put more work into practice and actually use the definitions and i should have no problems. that's how i learned programming at least, lots of practice.

🗑️ Anonymous at Sun, 13 Oct 2024 18:45:45 UTC No. 16429081

>>16397584
>be you, member of hyper advanced civilization billions of years ago
>can simulate entire universe in your beast ass computers
>simulate Earth before it happens
>want to design message for them that they can decode
>how to make sure they get it
>repeat an FRB at the planet with a specific midline number since the attenuation over the distance won't affect that center value
>encode using their modern mathematics systems
>US Government takes 7 years to tell people
>groan and kick your space cat

Anonymous at Sun, 13 Oct 2024 18:48:34 UTC No. 16429090

>>16429047
>Why do you feel stupid?
Well I would always effortlessly do the best in the class up until college, and I feel like if I were actually smart I still wouldn't have to try in college. I didn't try all that hard on the exam, only did the practice exam and skimmed over the textbook, but I get the feeling that a truly gifted person wouldn't need to work harder.

Anonymous at Sun, 13 Oct 2024 18:51:18 UTC No. 16429100

>>16429090
Well, yeah that's just arrogance. How can you hope to compete with people that are both smart and like-math/put-serious-effort-into-studying-math

🗑️ Anonymous at Sun, 13 Oct 2024 18:51:22 UTC No. 16429102

>>16429081
Also, if you think they didn't do something to affect our reality over that timeframe, then I have some news for you.

Justin Roiland is Just In Roy Land

Same as you. Same as me.

Anonymous at Sun, 13 Oct 2024 18:54:08 UTC No. 16429110

>>16429100
Don't get me wrong, I like math a lot, but I don't really like studying for exams. I enjoy homeworks a lot more. But I just feel like exam grades should come without effort if I'm staying caught up and working on homework, and they don't. Well, mediocre scores do, but I feel like that points to me not really being smart.

🗑️ Anonymous at Sun, 13 Oct 2024 18:54:15 UTC No. 16429111

>>16429081
>>16429102
The first being that stepped foot from Earth on another world.
Humans Of Planet Earth planned for it to be Buzz Aldrin.

But someone else thought it would be more fitting, if it were an alien.
Neil A.
Alien

There is a Santa Clause, of course.

When is Christmas?

I wonder if Congress knows.

You can go crazy, or you can flex your IQ and learn how to read the delimiters of this reality.
It's constructed.

Remove your limiters, by reading the DELIMITERS.

🗑️ Anonymous at Sun, 13 Oct 2024 18:55:39 UTC No. 16429116

>>16429081
>>16429102
>>16429111

This is Blue Eisenhower November. Going Dark

X.
STARGATES

Anonymous at Sun, 13 Oct 2024 19:11:08 UTC No. 16429156

>>16429090
>>16429100
>>16429110
Hello Gentlemen.

Anonymous at Sun, 13 Oct 2024 19:13:10 UTC No. 16429162

>>16429110
Same thing. Maybe you are maybe you aren't. But there's likely going to be some other students that are certainly smart and combine that with high effort and you'll never stand a chance against that regardless of how smart you are.

Anonymous at Sun, 13 Oct 2024 19:19:51 UTC No. 16429178

>>16429162
Well I don't even know if it's worth it to put that much effort into studying for exams desu, I feel like I learn a lot more from homeworks and lectures.

Anonymous at Sun, 13 Oct 2024 19:54:09 UTC No. 16429269

>>16397584
Help. I have a feeling of impending doom if I don't post this image.

Someone REALLY SMART at math. Please, a number breaking down like this from a random arbitrary origin point anywhere in our Universe, naturally, is completely expectable, right? Please tell me there is nothing special about this number. Like, it's not THAT rare for a big number to break down into 4 primes, with more than 11 digits each, yeah? There are certainly an infinite number of numbers that do that, aren't there?...

Anonymous at Sun, 13 Oct 2024 19:56:51 UTC No. 16429273

>>16429269
If it's not obvious, this is from a post that was deleted on another board, about the signal that is about to be announced as "extraterrestrial"

Their claim is that it is FRB 121102

"Anonymous 10/13/24(Sun)13:34:04 No. 39030820 ▶
>>39023189
Do you know WHY BENbros are ahead of the curve, though?

Because they decoded that thing.

https://www.express.co.uk/news/weird/1960323/nasa-alien-announcement-space

https://www.dailymail.co.uk/sciencetech/article-13950399/Evidence-alien-life-revealed-month.html

https://www.ladbible.com/news/science/scientists-apparently-find-alien-alien-prove-143008-20241012

http://104.197.48.230/frb-data/

And this November, you little fire, rock, stick, primates, might find out some minor details."

Anonymous at Sun, 13 Oct 2024 21:51:04 UTC No. 16429539

>>16429273
Hz are an arbitrary unit. We could have a unit of time that is based on any other atom instead of cesium (or any other transition, no need to fetishize the hyperfine transition) and still find numerical coincidences.

Anonymous at Sun, 13 Oct 2024 21:57:39 UTC No. 16429553

>>16429539
Found the brainlet.

Differentiate off this guy, we could nullify most of the efficiency difference on this planet.

Anonymous at Sun, 13 Oct 2024 22:01:56 UTC No. 16429568

>>16429539
These are not coincidental.
The statistical anomaly exceeds your discredit.
You need to begin thinking of reasons that this is real.

Such as.

Any civilization that can produce FRB121102, has enough compute to predict for Universal simulations.
AKA, they can simulate this planet from there.
AKA, they can simulate you, from there.
AKA this is a directed message, and if you're too brainlet to understand the underlying significance of it's inherent mathematical structures, it's not for you.

I need you, to change your viewpoint.
Get this directed message, to the attention of others.

Anonymous at Mon, 14 Oct 2024 09:06:54 UTC No. 16430538

>>16426324
How do you define partial sums?

Anonymous at Mon, 14 Oct 2024 10:36:53 UTC No. 16430632

>>16426950
beats me. thinking about working them into evolutionary economics of forgetting, myself

Anonymous at Mon, 14 Oct 2024 10:38:35 UTC No. 16430634

>>16429273
ah yes, the Daily Express, Daily Mail, and LadBible. the Holy Trinity of trustworthy scientific sources.

Anonymous at Mon, 14 Oct 2024 13:40:15 UTC No. 16430867

>>16429110
>Well I don't even know if it's worth it to put that much effort into studying for exams desu
NTA, but this is cope. For the first time in your life your raw intellectual gifts aren't enough to not-give-a-shit through a class, and instead of realizing you might need to start trying and developing your mind past its baseline, you're on here pussy-footing around talking about "aaah i don't even like studying.. .maybe i'm just not smart enough desu"

B- on your analysis exam? in an American university? Obviously you don't know analysis. Do a post-mortem on the exam/class, identify the topics you don't know well enough, go over them and drill them. Welcome to intellectual maturity.

Anonymous at Mon, 14 Oct 2024 15:06:29 UTC No. 16431033

>>16429269
>>16429273
you need to kill yourself my man

Anonymous at Mon, 14 Oct 2024 19:31:02 UTC No. 16431599

>>16402313
You could try Cox's "Ideals, Varieties, and Algorithms", it's an absolutely elementary approach to AG that introduces all the commutative algebra it requires. Idk how much "serious" theory it covers, but I think it gets the idea of "using algebra to study geometric phenomena" across well, also it has tons of pictures. For basic "serious" AG you could try Fulton's "Algebraic Curves".

Anonymous at Mon, 14 Oct 2024 20:40:44 UTC No. 16431765

https://youtu.be/BXwALAkPubc?si=tnWXQ9zFlMxgPiny
Beautiful people study geometry

Anonymous at Mon, 14 Oct 2024 21:58:03 UTC No. 16431914

Why are differential equations so hard?
I mean they are easy to write down like

2y'' + y/ln(y') - 52 = exp(-y^2)

can you solve that? i literallt just shat it out

Anonymous at Mon, 14 Oct 2024 22:27:03 UTC No. 16431947

Let [math] f : [0,\infty) \rightarrow \mathbb{R}^n [/math] be a continuous function, let [math] A \subset \mathbb{R}^n [/math] be a nonempty subset, [math] A \neq \emptyset [/math].

Suppose [math] A \cap \mathrm{image}(f) = \emptyset [/math].

Also suppose either [math] \lim_{t \to \infty} f(t) [/math] doesn't exist, or it exists but is not a point in [math] A [/math].

Then does [math] A \cup \mathrm{image}(f) [/math] necessarily fail to be path-connected?

Anonymous at Mon, 14 Oct 2024 22:41:37 UTC No. 16431979

>>16431947
Sorry I forgot to also add the condition that A is closed.

Anonymous at Tue, 15 Oct 2024 00:44:24 UTC No. 16432133

>>16431947
Tell us the definition of path connected

Anonymous at Tue, 15 Oct 2024 01:50:17 UTC No. 16432190

>>16424957
based & ORpilled

Anonymous at Tue, 15 Oct 2024 01:55:47 UTC No. 16432193

>>16431914
just use an iterative method with an initial value, if it converges in under 1000 steps, it's a solution for your initial value, profit

Anonymous at Tue, 15 Oct 2024 01:58:03 UTC No. 16432199

>>16429110
>>16429178
>>16429090
>>16428901
cringe
>>>/r9k/

Anonymous at Tue, 15 Oct 2024 02:00:16 UTC No. 16432202

>>16426074
cringe + undergrad

Anonymous at Tue, 15 Oct 2024 02:10:16 UTC No. 16432210

>>16431947
with your limit statement I think you could say the closure of [math]Im(f)[/math] does not intersect [math]A[/math]; now you have 2 closed sets in [math]R^n[/math] which do not intersect, so you should be able to contain them in 2 disjoint open sets because it's Hausdorff, so it's not even normally connected

Anonymous at Tue, 15 Oct 2024 02:30:37 UTC No. 16432238

>>16432210
I don't think that works, as it doesn't consider the case where the closure of image(f) intersects A (even if lim f doesn't exist):

E.g., in [math] \mathbb{R}^2 [/math] consider [math] A =\{0\} \times [-1,1] [/math] and [math] f(t) = (1/t,\sin t) \text{ for } t\geq 1 [/math] , the two pieces of the usual topologists' sine curve [math] A \cup \mathrm{image}(f) [/math], which is connected but not path-connected, with A and image(f) being its two path components. Note [math] A \cup \mathrm{image}(f) [/math] is the closure of image(f) in this case.

>>16432133
https://en.wikipedia.org/wiki/Connected_space#Path_connectedness
Two-second google search.

Anonymous at Tue, 15 Oct 2024 02:44:10 UTC No. 16432248

>>16414009
>acetylcholinesterase issues
such as

Anonymous at Tue, 15 Oct 2024 02:47:44 UTC No. 16432250

>>16432238
maybe to start out, do you think it's true in the case that [math]\lim_{t\rightarrow\infty}f(t)[/math] exists?

Anonymous at Tue, 15 Oct 2024 02:58:20 UTC No. 16432269

>>16432250
Yea I've figured out why A and image(f) are not path-connected if lim f does exist (and isn't in A). [ in the context described in >>16431947 and >>16431979 ]

What I'm considering now is the case where lim f doesn't exist. One issue is that we can't say the closure of image(f) is disjoint from A in this case, as in e.g. the topologists' sine curve example: >>16432238

Anonymous at Tue, 15 Oct 2024 05:15:27 UTC No. 16432397

>>16432396

Anonymous at Wed, 16 Oct 2024 05:00:03 UTC No. 16433929

what's the answer? mathway can't figure it out