🧵 /mg/ - math general
Anonymous at Mon, 24 Mar 2025 21:02:19 UTC No. 16627609
Badly-formatted information edition
Previous thread is: >>16589624
Talk mathematics
Anonymous at Mon, 24 Mar 2025 21:19:56 UTC No. 16627628
>>16627609
Your fractal fandom and cellular automata fandom are swapped. (Also, is it possible to prove that universe is NOT a simulation ran on rule 110)?
Anonymous at Mon, 24 Mar 2025 22:25:11 UTC No. 16627680
Why don't we apply proof by "it's fucking obvious ffs" more often?
At least half of the Millennium Prize Problems could easily benefit from this. And there are plenty of others, like the Mertens conjecture, or the Jordan Curve Theorem
Engineers really have figured it all out
Anonymous at Mon, 24 Mar 2025 22:59:09 UTC No. 16627705
>>16627680
you stole this method from me in a different thread. I'm watching you buster
- Kenny G
Anonymous at Mon, 24 Mar 2025 23:55:55 UTC No. 16627760
>>16627609
I love mandelboxes
Anonymous at Tue, 25 Mar 2025 00:21:34 UTC No. 16627814
>>16627609
For >>16627561
Response: >>16627804
Anonymous at Tue, 25 Mar 2025 01:55:28 UTC No. 16627904
My TA gave a bonus problem that has nothing to do with the rest of the course and I don't know where to begin. How do I approach this:
>Without reference to whether or not any such p can be found by brute-force methods, prove that if pi is normal there must exist infinitely many prime p such that tan(p) > p!.
Anonymous at Tue, 25 Mar 2025 02:36:14 UTC No. 16627923
>>16627609
What's a good "intro" resource for someone getting filtered by computational Geometry? I've been getting my ass kicked by Gallier's Geometric Methods book as a self-study tool and wondering if anyone has something quick to work through as an undergrad friendly "quick" resource.
Anonymous at Tue, 25 Mar 2025 03:13:44 UTC No. 16627951
>>16627923
https://gamemath.com/book/intro.htm
Anonymous at Tue, 25 Mar 2025 17:22:58 UTC No. 16628314
>>16627628
>rederived modern math
do you think this is really possible for a singular person given enough time
Anonymous at Tue, 25 Mar 2025 18:58:57 UTC No. 16628360
absolute retard here, where can i go to start practicing combinatorics ?
Anonymous at Tue, 25 Mar 2025 19:23:55 UTC No. 16628385
>>16628360
khan academy
Anonymous at Tue, 25 Mar 2025 19:41:08 UTC No. 16628397
>>16628360
>absolute retard here, where can i go to start practicing combinatorics ?
https://courses.csail.mit.edu/6.042
https://doc.lagout.org/science/0_Co
Anonymous at Tue, 25 Mar 2025 20:02:30 UTC No. 16628418
>>16628385
>>16628397
much appreciated
Anonymous at Tue, 25 Mar 2025 20:41:18 UTC No. 16628454
>>16627904
What does it take to make tan(p) really really really really really really big?
Anonymous at Wed, 26 Mar 2025 09:04:32 UTC No. 16628874
What's the smallest set of binary numbers 0->255 (0000_0000 -> 1111_1111) where any binary number in the space (0->255) can be produced by XORing some two elements in the set?
I can do 0->15 (0000->1111) with 8 elements
0000
0001
0010
0100
1000
0011
0111
1111
but the pattern doesn't scale up unfortunately
Anonymous at Wed, 26 Mar 2025 09:20:49 UTC No. 16628877
>>16628874
Just realized 0000 is redundant, so 7 elements for 0000->1111
Anonymous at Wed, 26 Mar 2025 09:55:34 UTC No. 16628883
>>16628874
>>16628877
please disregard this I suck cocks. it's just the entire range of the lower portion and the same shifted left.
00_01
00_10
00_11
01_00
10_00
11_00
Anonymous at Wed, 26 Mar 2025 12:11:16 UTC No. 16628942
If you were a prime in Z and you were to go into the ring of integers of a Galois extension of Q, which kind of prime would you be?
>Inert
>Split
>Ramified
Anonymous at Wed, 26 Mar 2025 14:50:52 UTC No. 16629032
>>16628314
Sure thing. Modern math was derived the first time around by millions of people. Step 1: mathematically derive the psychological behavior of two agents interacting to learn more about their environment (game theory, discourse theory, transactional analysis)
Step 2: increase n to the required population
An immortal human who doesn't go mad or suffer from entropy decaying the environment they move around in could do the first step within a couple hundred years and scale it up sufficiently in only a few trillion more.
Anonymous at Wed, 26 Mar 2025 16:33:01 UTC No. 16629081
>>16627951
Thank you. The first few chapters seem a bit too basic (I already have done a typical calc sequence, linear algebra, probability, real analysis etc.) but the later stuff might be helpful.
Anonymous at Thu, 27 Mar 2025 09:54:01 UTC No. 16629696
>>16629613
It's fairly straightforward to use induction to show the answer is always n.
Anonymous at Thu, 27 Mar 2025 13:46:03 UTC No. 16629845
Anonymous at Thu, 27 Mar 2025 22:11:03 UTC No. 16630221
>>16629613
>>16629696
Just do it directly.
Sum[x^m / (1-x^m) * 1/(1-x^m+1)]
= Sum[x^m (1 / (1-x^m) - x/(1-x^m+1))/(1-x)]
= x/(1-x)^2 = Sum[ n*x^n]
The answer is n.
Anonymous at Fri, 28 Mar 2025 04:25:42 UTC No. 16630524
Anyone here an actual working mathematician? Or at least a graduate student working toward a PhD? I feel alone among you niggas. What research are you anons working on? Any other quantum group enthusiasts?
Anonymous at Fri, 28 Mar 2025 04:43:11 UTC No. 16630535
>>16630524
I work in so niche a topic that I risk doxxing myself with specifics, but I got a paper published in a good journal this year and am working on more
Anonymous at Fri, 28 Mar 2025 05:01:33 UTC No. 16630548
>>16630535
Well, this can't be too long of a list.
>you'll know it's me because I use a refrigerator prank
Anonymous at Fri, 28 Mar 2025 10:45:44 UTC No. 16630755
>>16630221
I have no idea what you are summing there or how it answers the question.
different Anonymous at Fri, 28 Mar 2025 14:10:14 UTC No. 16630872
>>16630755
"In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series."
Anonymous at Fri, 28 Mar 2025 18:10:34 UTC No. 16631077
>>16630535
My subject is also niche so I don't wanna expand on it either. Nice job on the pub anon
Anonymous at Fri, 28 Mar 2025 18:23:45 UTC No. 16631097
How doable is for me, an advanced applied math undergrad, to do all the questions in Verbitsky's trivium in one week (maybe less)?
Anonymous at Fri, 28 Mar 2025 18:39:43 UTC No. 16631119
>>16631097
100%, in fact if you can't then you're ngmi
Anonymous at Fri, 28 Mar 2025 19:02:59 UTC No. 16631152
>>16631097
V. Arnold's trivium would be more appropriate given you background:
https://physics.montana.edu/avoront
Anonymous at Fri, 28 Mar 2025 21:55:27 UTC No. 16631307
>>16627609
How to learn math faster
I am an undergraduate student and a very slow learner . I want to learn math deeply in a faster pace than I am right now
Any method to increase speed
Anonymous at Fri, 28 Mar 2025 22:50:53 UTC No. 16631357
>>16631307
Keep at it for years. You'll speed up.
Anonymous at Fri, 28 Mar 2025 23:52:37 UTC No. 16631397
>>16630755
I enumerated all possible sums of the form required then made a histogram of the sum values.
Then number of sums summing to n is stored in the coefficient of x^n
Anonymous at Sun, 30 Mar 2025 18:38:45 UTC No. 16632964
I'm looking for a good differential equations textbook. Anyone have any good recommendations? I prefer pre 2000 textbooks I think they're formatted better. Thanks in advance.
Anonymous at Sun, 30 Mar 2025 21:34:11 UTC No. 16633154
is there a roadmap for learning math? i want to start from scratch. interested in moving onto physics and cs but i was a terrible student and skipped classes and stuff. and i think building upon math would be a great idea? idk please spoonfeed me. how do i even learn this thing?
Anonymous at Sun, 30 Mar 2025 21:36:12 UTC No. 16633156
>>16633154
look up hung hsi wu, he's got all you need for the basics.
Anonymous at Sun, 30 Mar 2025 21:39:32 UTC No. 16633159
>>16633156
oh thanks for your help anon i appreciate it can you also look up blue waffle? thanks
Anonymous at Tue, 1 Apr 2025 04:28:26 UTC No. 16634602
>>16633159
He wasn't trolling
Anonymous at Wed, 2 Apr 2025 06:27:50 UTC No. 16634795
>>16632964
What level of differential equations are you trying to study?
Anonymous at Wed, 2 Apr 2025 22:03:35 UTC No. 16635475
>>16634795
ode, then eventually pde and integro-differential equations
Anonymous at Thu, 3 Apr 2025 17:22:28 UTC No. 16636212
Would anyone be interested in reading a math blog post I wrote? In it I provide a proof that the signature homomorphism is well defined using exterior algebra in a non circular way.
Anonymous at Thu, 3 Apr 2025 17:26:32 UTC No. 16636215
>>16629613
Wtf I thought putnams were hard?
Anonymous at Thu, 3 Apr 2025 17:31:36 UTC No. 16636222
How do I REALLy learn math? I’m going back to school now and while I passed the majority of the math sequence I needed to graduate (got filtered by abstract Algebra) I was unable to really get an intuition for any calculation I was doing without a clear visual (that’s probably why I was able to get through the analysis sequence and PDEs but not algebra)
What do I do? I thought I’d be able to understand stuff better this time around but I just feel like I’m pushing around definitions and until a proof finishes itself but I barely have any grasp on the objects I was working with!
Anonymous at Thu, 3 Apr 2025 17:32:46 UTC No. 16636223
>>16636222
You keep thinking about stuff you learned in new ways and seek out new perspectives on it. What do you not understand?
Anonymous at Thu, 3 Apr 2025 17:38:09 UTC No. 16636235
Phone posting so excuse me not replying directly: I don’t know what I don’t know. I have vague intuitions and sometimes that’s enough to get me through what I’m working with but other times I’m left there after finishing a proof and am like “what the fuck did I just prove?” The isomorphism theorems are a good example: I can state them and tell you when to apply them for example problems from the text but to me it’s a bunch of giberish. I have no intuition as to why they should be true and just accept that they are after being able to memorize proofs of them
Anonymous at Thu, 3 Apr 2025 17:41:08 UTC No. 16636240
>>16636235
Isomorphisms theorems are pretty fundamental. Have you tried looking at a lot of examples of them in action? Have you considered simpler cases like vector spaces or the case of the integers?
Have you tried proving them on your own, in a new way perhaps?
It's really hard for me to understand what you mean because they're so obvious and intuitive to me. Like how would you explain the first isomorphism theorem in your own words?
Anonymous at Thu, 3 Apr 2025 17:49:09 UTC No. 16636247
I know that they’re fundamental and that’s why I failed the class in the past. For the first one we have that if you take a group homomorphism and take out all the stuff that maps to the identity, you’re left with the image of the homomorphism. I can tell you that. I can give you a symbolic representation of it. It just feels foreign to me. I get that I’m supposed to use linear algebra as my examples for this stuff but I never develop great intuition for properties of vector spaces either (I know I’m a terrible student lol). Idk I don’t think I’m too stupid to learn this stuff but it just hasn’t clicked yet. It’s like I’m learning a foreign language and am repeating what the teacher tells me but it doesn’t feel natural to me
Anonymous at Thu, 3 Apr 2025 17:51:13 UTC No. 16636251
I have not tried nor been successful at proving them in a different way yet. Maybe that would be a good idea but I don’t know how I’d start. How would I think of another way they’re true? Just starte at the definitions and look at examples until it occurs to me randomly?
Anonymous at Thu, 3 Apr 2025 17:59:06 UTC No. 16636260
>>16636251
These are the images that come to mind when i think of the first isomorphism theorem.
You're not removing the elements that map to identity. You're saying two elements are the same if they differ by an element that maps to identity. I.e. if they map to the same thing.
G/kerf is taking G and saying two elements are the same if they map to the same thing in f. So in a sense you squash G to make it fit into the map f better. You're not removing anything.
Does this make sense?
Anonymous at Thu, 3 Apr 2025 18:02:54 UTC No. 16636263
I’ve never thought of it that way thank you! I’ll have to mull it over for a bit to see if it makes it stick but that’s certainly a new perspective. I have really high verbal IQ and decently high spatial reasoning but I have terrible adhd so my working memory and therefore abstract reasoning/computational understanding is dog shit and the only reason I’ve gotten this far in math is that I’ve had really nice professors who really care and want me to learn. Are there more images like that for the other isomorphism theorems?
Anonymous at Thu, 3 Apr 2025 18:10:51 UTC No. 16636266
>>16636263
Yes actually.
Anonymous at Thu, 3 Apr 2025 18:12:23 UTC No. 16636269
Can I pay you to tutor me or something? I’ll keep posting here but I really need a PhD to do the work i want and that means conquering these abstract formalisms no matter how much I hate them
Anonymous at Thu, 3 Apr 2025 18:33:23 UTC No. 16636294
>>16636269
I dont offer such services. But if you ask questions on here or on /sqt/ I might reply.
Anonymous at Thu, 3 Apr 2025 22:11:08 UTC No. 16636640
>>16636269
Sure. 100$ per problem, money first.
Anonymous at Fri, 4 Apr 2025 05:54:48 UTC No. 16637008
Why are there so many women in my statistical learning theory class? It's unusual.
Anonymous at Fri, 4 Apr 2025 06:54:41 UTC No. 16637027
>>16637008
autistic women like statistics
its a lot of structure and they can pretend its relevant to people
Anonymous at Fri, 4 Apr 2025 11:02:31 UTC No. 16637163
When I am at infinity I am a king, when I am at 1 I am in New York, when I am at 2 I am a bird.
What am I?
Anonymous at Fri, 4 Apr 2025 13:03:44 UTC No. 16637215
>>16637214
from Billingsley, Convergence of Measures.
Anonymous at Fri, 4 Apr 2025 13:06:49 UTC No. 16637217
>>16637214
What is there to fix?
Anonymous at Fri, 4 Apr 2025 13:23:34 UTC No. 16637225
>>16637217
Nothing. I was just joking.
Anonymous at Fri, 4 Apr 2025 14:02:36 UTC No. 16637250
No one got it? >>16637163
Anonymous at Fri, 4 Apr 2025 16:39:30 UTC No. 16637416
Fuck it, the answer to >>16637163 is the Lp norm.
p = infinity gives the distance between two points for the king in chess, p = 1 is the Manhattan distance, 2 is the Euclidean distance (birds don't have to abide by streets and can fly directly in a straight line).
Anonymous at Fri, 4 Apr 2025 23:16:27 UTC No. 16637690
According to my TA there is a bijection between the uncomputable reals and the set of all orderings of the natural numbers, but it doesn't matter to any real-world math since it's impossible to construct the latter set.
Is the bijection part always true or does it depend on some crap about the continuum?
Anonymous at Sat, 5 Apr 2025 06:55:37 UTC No. 16637877
>>16637690
>the continuum
probably just making a point about cardinality
Anonymous at Sat, 5 Apr 2025 15:03:45 UTC No. 16638207
I'm feeling socially isolated studying math. I thought for sure I would make some friends in graduate school but that didn't work out, there's only a few other students here and I hate their guts. I also tried joining twitter and following accounts that seemed cool but it turns out they are all larpers who will avoid conversations with you if you bring up something they cant feign knowledge of.
Sorry for making an off-topic post I just hope someone will know what I can do
Anonymous at Sat, 5 Apr 2025 15:38:28 UTC No. 16638215
>Was looking through the real numbers the other day
>Find weird set of numbers that is bigger the the naturals
>ok.jpg
>But it's smaller than the reals
>mfw
guys please help. there's a black van outside my house now and I keep getting calls from numbers I don't recognize.
Anonymous at Sat, 5 Apr 2025 15:49:57 UTC No. 16638220
>>16638207
you're living while contradicting your identity. either live in isolation or dumb yourself down to your surroundings. life goes on no matter what
Anonymous at Sat, 5 Apr 2025 16:28:24 UTC No. 16638241
What you guys think of numerical/computational math? I'm thinking of doing my master thesis in that area.
Anonymous at Sat, 5 Apr 2025 16:42:10 UTC No. 16638249
>>16638241
what do you think is interesting in that area?
Anonymous at Sat, 5 Apr 2025 17:54:33 UTC No. 16638288
>>16638207
I'm in a similar boat. While I haven't found a solution, I guess I can give some thoughts.
Math shouldn't be done solitarily. Almost no researcher works this way, and even when studying from a book I find it goes much faster (and is more fun) with multiple people, filling gaps in each other's understanding.
Still, that's mostly how I do it, and whenever I get tired of being stuck / alone, I'll switch to a different hobby for a while. I think the "change of scenery" helps keep it all interesting.
I also have a small job tutoring high schoolers, which helps somewhat with social isolation in general. It's nice to help with basic stuff like negative numbers, and sometimes there's the chance to answer an interesting question they have, or change some myopic viewpoint their teacher or textbook provides.
I don't know of any worthwhile online spaces for talking about / studying math, unfortunately. Talking to people online has, as you say, mostly been disappointing.
Anonymous at Sat, 5 Apr 2025 19:27:45 UTC No. 16638338
>>16638249
Combination of application and theory!
Anonymous at Sat, 5 Apr 2025 20:36:27 UTC No. 16638385
Phone posting so sorry I can’t reply directly to the loneliness posts: research is supposed to be a collaborative process. I’m sorry you’re having a tough time anon. Life is lonely if you don’t reach out and I find math most beautiful when I can share the ideas with others. Have you considered joining an industry research group? They work together and might be more fulfilling
Anonymous at Sat, 5 Apr 2025 20:40:15 UTC No. 16638388
Another response to that: if I keep posting understanding questions here for anons would you mind helping me? I’m not very smart (or at least I don’t think I am) but I find math very beautiful and wanna keep understanding it.
I’d like to get through Dummit and Foote over the summer and while I know I really struggle academically, I’m stubborn enough to have not given up on trying to learn math yet. The pictures that were shared for the isomorphism theorems were very helpful, thank you!
Anonymous at Sat, 5 Apr 2025 20:54:45 UTC No. 16638405
Any good suggestions for a good field and galois theory book that goes in depth upto stuff like transcendental extensions ,kummer theory, Hilbert 90 and more
Anonymous at Sat, 5 Apr 2025 22:09:20 UTC No. 16638466
>>16628314
0. 0
i. 0+-i -> diverge into "make shit up"
1. e**0 -> diverge into Peano/number theory
-1. e**(i*pi) -> diverge into complex analysis
D. e**(i*2*pi) -> diverge into elliptic curves
Anonymous at Sat, 5 Apr 2025 22:10:39 UTC No. 16638468
>>16638388
Grigori Perelman is the only logically coherent mathematician is all you need to know. The rest is simplicial homotopy
Anonymous at Sat, 5 Apr 2025 22:31:08 UTC No. 16638472
Do any other anons here experience Mathematics as a war with your mind? It tries to beat you down with its obtuseness but every day you show up and fight and engage with the material, you’re winning. If you do that enough times, you eventually make progress
Anonymous at Sat, 5 Apr 2025 22:45:33 UTC No. 16638477
Is there a typo at the bottom equation? An extra "*a)"?
Anonymous at Sat, 5 Apr 2025 22:51:01 UTC No. 16638478
>>16638477
>Is there a typo at the bottom equation? An extra "*a)"?
It might be easier to reply if you attached that equation. (Verification not required.)
Anonymous at Sat, 5 Apr 2025 23:35:54 UTC No. 16638491
>>16638472
Sounds like dialectics, are you sure you're not a philosopher?
Anonymous at Sun, 6 Apr 2025 00:02:43 UTC No. 16638504
Vitali sets have a cardinality strictly between the countable and the continuum.
I will not elaborate.
🗑️ Anonymous at Sun, 6 Apr 2025 00:57:15 UTC No. 16638532
Anonymous at Sun, 6 Apr 2025 01:00:58 UTC No. 16638535
>>16638472
Applies to beautiful math too
Anonymous at Sun, 6 Apr 2025 03:46:42 UTC No. 16638598
>>16638478
I'm a fuckin idiot.
e is identity
Anonymous at Sun, 6 Apr 2025 07:33:55 UTC No. 16638672
Learning about orbits in phase spaces it's occurred to me that you could just make a phase space for the human brain.
>1 vector for each neuron's connections
>More vectors for every kind of sensory input (eg color cells in the retina or pressure-sensing cells in the skin)
While this object would be computationally intractable with modern computers, is it possible to check whether there are inescapable attractors in that phase space?
Anonymous at Sun, 6 Apr 2025 09:11:19 UTC No. 16638720
Can anyone here recommend a good homological algebra book for commutative algebra (mainly need Tor and Ext)
I know basic category category from first few chaps of MacLaine
I found rotman strange as he assumes too much algebraic topology to motivate stuff
Any good book/notes to get comfortable with Tor, Ext, Snake Lemma etc stuff
Anonymous at Sun, 6 Apr 2025 23:18:43 UTC No. 16639179
>>16639094
Try seeing whether you can prove the commutativity of t
Anonymous at Sun, 6 Apr 2025 23:33:29 UTC No. 16639191
>>16638504
Vitali sets are just a different incoherent definition of irreducebility.
Anonymous at Sun, 6 Apr 2025 23:34:30 UTC No. 16639192
>>16638672
Here's the real trick: we can just model all of knowledge as a phase space instead and thus recover the theory of everything, simple as.
Anonymous at Mon, 7 Apr 2025 00:53:00 UTC No. 16639253
Hey, is a non genius IQ enough to get a PHD in math? I was convinced that I was too stupid to study math and that’s why I got poor grades in undergrad but I finally got my IQ test back and I got 128 non verbal, 120 pictoral nonverbal and 130 for geometric nonverbal. I was told those are the scores most closely related to mathematical performance (unless I misunderstood). Those aren’t genius level but I’m certainly not stupid. If I’m not stupid, am I capable of doing research? What do I have to do differently if I struggle in school to do well in graduate school and academia as a whole? If I could I’d wanna do research in stochastic processes
Anonymous at Mon, 7 Apr 2025 03:21:35 UTC No. 16639359
>>16639253
How are your math classes going so far and where are you currently as an undergrad?
Anonymous at Mon, 7 Apr 2025 04:34:16 UTC No. 16639386
Have there any recent examples of scientific discoveries by natural scientists inspiring new maths or is all modern maths now stuff that is sitting in the waiting room for its future scientific application?
Anonymous at Mon, 7 Apr 2025 06:59:54 UTC No. 16639443
>>16639386
https://www.quantamagazine.org/neut
Anonymous at Mon, 7 Apr 2025 08:53:43 UTC No. 16639478
anyone know of a good introduction to integrating in motivic Hall algebras?
Especially when working with moduli stacks of quiver representations
Anonymous at Tue, 8 Apr 2025 01:05:45 UTC No. 16640138
One of my students has a strange attitude to theories. He thinks that every multidimensional model that isn't about literal geometric objects "must really be a single spectrum".
This isn't a higher algebra topic, alas. If it's a two-axis graph he compresses everything to a single diagonal line. He even thinks the political compass is a psyop to keep people from realising that things are one dimensional. I tried using the prisoner's dilemma to depict a 2-axis scenario and he started arguing that it was impossible for any event other than either cooperate-defect or defect-cooperate to occur.
Is there a name for this crazy belief?
Anonymous at Tue, 8 Apr 2025 01:13:55 UTC No. 16640143
>>16640138
It sounds like autism. I've seen plenty of strange autistic beliefs about math. Just look at the knots people twist themselves into over finitism.
Anonymous at Tue, 8 Apr 2025 05:14:25 UTC No. 16640233
>>/sci/#16589624
Anonymous at Tue, 8 Apr 2025 05:56:30 UTC No. 16640268
>>16638504
No such cardinality
Anonymous at Tue, 8 Apr 2025 17:07:23 UTC No. 16640568
Say something obvious but make it sound important
>for every pair of nonzero integers x and y, there is a prime p such that x and y are inverses of each other mod p
Anonymous at Tue, 8 Apr 2025 17:17:09 UTC No. 16640576
>>16640568
There is a formula phi(x,y) in the language of set theory so that for any set A, there is a unique set B with phi(A,B). Furthermore, one can ensure that B is equal to A
Anonymous at Tue, 8 Apr 2025 20:16:48 UTC No. 16640714
How do I get into a math PhD if my GPA is horrible?
Anonymous at Tue, 8 Apr 2025 22:53:37 UTC No. 16640817
>>16640714
Do a master's degree somewhere first. Master's programs are usually easier to get into, will give you a chance to improve your academic standing, and give you a taste of what actual research is.
Not everyone needs to do a math PhD (or a PhD generally). A master's will give you an opportunity to see if that life really is for you.
Anonymous at Tue, 8 Apr 2025 22:59:54 UTC No. 16640819
>>16640817
PhD in applied math will get you any job you want 300k starting
Anonymous at Tue, 8 Apr 2025 23:19:15 UTC No. 16640831
>>16640819
Yeah, okay.
Anonymous at Tue, 8 Apr 2025 23:26:35 UTC No. 16640833
>>16640817
Can I teach in university with a masters?
Anonymous at Wed, 9 Apr 2025 01:31:38 UTC No. 16640893
>>16640833
Depends on the school. A lot of the state universities in the USA do allow non-tenure track professors to have a masters rather than a PhD. Generally if your long term career plan is to be a professor, you need a PhD, but it's not a 100% rule like it used to be.
Anonymous at Wed, 9 Apr 2025 06:53:11 UTC No. 16641033
e ~ 2.718281828459
claim:
The next e day is on Sunday 13 April 2025.
proof:
round(100×(e – 2)) – (3×28 + 29)/4 – 31 = 12 + 3/4
Thus in leap years, e day is on April 12th.
And in other years, it's on the 13th.
Anonymous at Thu, 10 Apr 2025 01:39:37 UTC No. 16641987
so what exactly is the free group
there is a homomorphism of a free group of rank n to any group, so what is the image/kernel of that
Anonymous at Thu, 10 Apr 2025 15:51:52 UTC No. 16642452
If you can turn any differential equation like y=x(y'-y''+y''') into a functional equation like f=xg, is there a next step up the chain that you can use to generalize functional equations?
Anonymous at Fri, 11 Apr 2025 00:59:57 UTC No. 16642764
Anyone have a good source for an n-categorical analogue of K-theory? Or where one should go in developing a theory like it? Lurie has his infinity shit but I would be behooved if I could do some sort of "2-categorical k-theory" nicely. If not I'll invent it.
Anonymous at Fri, 11 Apr 2025 06:51:12 UTC No. 16642946
>>16641987
<a_1,...,a_n>
Anonymous at Fri, 11 Apr 2025 19:28:30 UTC No. 16643390
Red circles have the same radius and so do the orange circles. They are arranged inside a square, being tangent to the two lines like shown in picrelated.
If the number of orange circles is N, what is the ratio between the areas of one orange circle and one red circle?
Anonymous at Fri, 11 Apr 2025 20:55:03 UTC No. 16643450
>>16643390
assume square side is one, given the small height of bottom left, solve for orange diameter using ratios, solve for the two orange sub-segments that make up the small height separated by the tangent of the orange circle using brahmagupta's formula, solve for the length of the two red sub-segments that make up the hypotenuse tangent between the orange and red circle using these two orange sub-segments and the orange radius while including that there are n oranges, solve for the red radius using heron's formula, solve for the ratio of the squares of the orange and red radius for n oranges
Anonymous at Fri, 11 Apr 2025 20:57:54 UTC No. 16643451
>>16643450
forgot to mention to solve for the length of the hypotenuse tangent between the orange and red circles was found using ratios
Anonymous at Sat, 12 Apr 2025 01:13:08 UTC No. 16643645
Some interesting combinatorics nuggets here
https://www.youtube.com/watch?v=_sE
Might connect some dots
Anonymous at Sat, 12 Apr 2025 01:30:53 UTC No. 16643662
>>16643390
If N = 1, then (r/R)^2 = infinity.
If N = 3, then (r/R)^2 is depicted.
If 3 < N < 13, then (r/R)^2 is very complicated.
Anonymous at Sat, 12 Apr 2025 03:38:56 UTC No. 16643731
Good video resources for permutations & combinations, probability(right from elementary to advanced level) and statistics with loads of good problems(atleast as homeworks with written solutions in pdfs)? It also shouldn't exceed 70 hours
Anonymous at Sat, 12 Apr 2025 08:29:51 UTC No. 16643852
looking for the entirety of mankind's knowledge of mathematics in video form (including future discoveries) ideally under 10 hours (12 at a push)