/sci/ - Science & Math

I'm building a linear algebraic cryptosystem based on the non-existence of bases in certain vector spaces.

>>9632968
Not studying today because I ate a full 1kg carton of expired custard and my own breath is giving me nausae

>>9633004
nausea*

Spooky scary phantoms.

Working in ways to reduce computation time for certain processes by transforming the algebraic space before computing and using Hilbert space to simply multivariant equations.

What are the mathematics behind Planck lengths?

>>9633165
>Planck lengths
Not mathematics, try to ask the physicists.

>>9633175
>mathematics
This is not well-defined.

>>9632987
Tell me more.

>>9633180
>This is not well-defined.
Yes, and?

>>9632968
highschool algebra uwu

>>9633190
So "Not mathematics" is a meaningless notion.

>>9633205
Is a post stating that something meaningless is meaningless, meaningless?

>>9633165
Just learn about the "mathematics" behind made up things which don't exist. A good reference is >>>/toy/physics/.

>>9633283
You like a cute person desu, will you be interested in making a discord account joining few of us posters (very few) where it's comfy and we can discuss shit

>>9632968
Philosophy, specifically the theory of logic. You applied logicians wouldnt understand.

>>9632521
not that anon but one good argument is that nontrivial ideals can count as subrings

>>9633309
>Philosophy, specifically the theory of logic.
You're in the wrong thread.

"Classic control system" for my new job. Any one have a recommendation for a book or a reference?

>>9633165
>What are the mathematics behind Planck lengths?
Basic algebra.

I enjoy math trivia that relates to nature, like a trees tendency to sprout new limbs in a fibonacci-esque pattern, an ants ability to apply Fermat's principle, etc.

A more comprehensive resource on this theme would be excellent and much appreciated.

>>9634003
Natural transformations, natural equivalences. Start with these.

>>9632968
>What have you been studying lately, /mg/?

Physics

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>>9634079
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>>9634079
>>9634084
Are you okay?

s a physics engine that uses Manhattan distance possible?

What are the properties of a Manhattan version of Newtonian physics?

>>9634084
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>>9634089
Never been better.

>>9634094
Seriously, why don't everyone smoke cigarettes?

What is your excuse that you don't smoke and receive pussy over 9000 times a day?

So what was your excuse?? How does it feel to be neanderthalic?

It's a widely known fact that women are more interested in tough guys, and tough guys, of course, smoke.

Pros:

>tastes good
>smells good
>lightens you up
>makes you more relaxed
>gives social boost
>women are weak for you
>other men respect you
>looks cool anyway
>gives you something to do while waiting
>reason to get up in the morning
>good excuse to take a break from work

Cons:
>you might actually drown in pussy

To top it off, every night you guys make threads about how you don't have a girlfriend or some shit like that. Did it ever occur to you that maybe it's just solely because you don't smoke? I don't even want you guys to feel bad, but it's just so sad that you won't live your youth to the fullest to save a couple of bucks. Smoking cigarettes will end up cheaper than that crackwhore who you end up giving your virginity to.

>>9634099
>women
You don't need to smoke to get 2D women...

>>9632968
>high school wrapping up
>enjoyed calc way too much
>considering changing from double major linguistics/archaeology to pure maths
Any advice? I really enjoy math as of now, but I'm worried about how much use I'll get out of a degree, especially since I don't like engineering and the only physics that interests me is probably too complex for me to ever understand.
Not underage by the way.

>>9634107
This. And 2D always > 3D.

>>9634253
U r fucked. If you have to choose go math but you better get a PhD too

What's the point of studying maths, even if I do well in my undergrad years I am probably too dumb to publish any note worthy research and I don't want to be a professor. Yet this is the only field of study that I enjoy.

>>9634396
Why not study it as a hobby? That way you can give it your all, but still be ok with not publishing anything ever.

>>9634407
But then what would I study? There are no other STEM fields that I am interested in. I am probably just going to kms after I graduate desu.

>>9634412
>study math as a hobby
>don't know what you are studying
Math, obviously. But instead of being a try-hard, you'd be there for fun.

>>9634424
>study math for fun
>accomplish nothing and die and waste of life

>>9634424
Why would anyone not want to be a try-hard? That's a lot more fun.

>>9634396
I can hear you, just going to finish undergraduate studies in 4 months and feel the same exact way, but I can at least tell you that I don't regret any of this, the memoriez of algebra, topology, geometry, algebraic topology/geometry, model theory.. we might be brainlets but it does not mean it is meaningless to study. Then again, it is right to think what you are going to do in the future, but don't die over it.

>>9634432
I see no problem here, considering the fact that you will kill yourself after you graduate.

>>9634438
Why would it be more fun for z'ôm? Notice that z'ô already told us z'ô is too dumb to contribute to anything.

/mg/ is a /eg/ colony

>>9634448
>/mg/ is a /eg/ colony
What the hell is /eg/.

Daily reminder that enjoying moe shit anime is directly correlated with having a low IQ, multiple replies from the same anon trying to pose as multiple people will not change the truth.

>>9634491
>moe shit anime
Not well-defined.
>directly correlated
Sounds like some "statistics" (engineering) term. Take that elsewhere.

>>9632968
Would you rather be a girl that's great at math, or a guy that's terrible at math?

>>9634642
The second, since I can just become good at math in a short time if I have a male brain; much shorter than if I had a female brain.

A*[sin(x)/|sin(x)|] produces a square wave with amplitude A and 50% duty cycle. Why is it that when I integrate this I do not get a function that produces a triangle wave?

When you put a square wave through an integrator circuit like an op-amp with capacitor in feedback you get a triangle wave out. Why does the math not work?

>>9634642
A girl, but I assume you're saying really good at math. Not some IQ 130 bullshit. Like Noether

What are the prerequisites for topology?

>>9634781
The basics of set theory. Some analysis could help but it's not necessary.

>>9634253
>majoring in linguistics/archeology
>worried about maths employment prospects

I'm studying the Deligne-Mumford theorem on stable reductions and some basic theory on Metrized line bundles.

Thanks god there exists Liu book for the first topic, now for the second one wish me good look.

>>9634717
When you integrate it you do get a triangle wave.

>>9634717
What'd you get as a solution for the integral of that function? Maybe I got the wrong answer or something.

>>9634910
meant for
>>9634859

>>9634910
I don't know how to integrate the expression [math]\frac{\sin x}{|\sin x|} [/math] directly, but you can just write it as a piecewise function. Then the integral along an interval [math] [n\pi, (n+1)\pi [/math] is the integral of a constant, so a linear function as you would expect. I don't think there's a way around this, considering that the function you gave isn't even defined at [math]n\pi[/math], and can't be extended to a continuous function on [math]\mathbb{R}[/math] at all.

If you post what you tried to do, maybe I could point out the mistake.

>>9634928
I put in wolfram alpha because I didn't know how to integrate it either. I know representing a square wave as a piecewise function will result in a symmetrical ramp for the reasons you mentioned. I'm more interested in proving that integrating sin(x)/|sin(x)| will give the same result, at least for 50% duty cycle anyway.

>>9634939

>>9634939
>>9634941
Wolfram alpha is missing some of the subtlety involved. Remember that the fundamental theorem of calculus only holds for continuous functions. The function you got does differentiate to a square wave at most points, but is not differentiable at others. Same goes for a triangle wave. I guess this is a good example of why the word "continuous" really does need to be in the FTC.

In this situation, there is no global antiderivative, so taking an indefinite integral doesn't make sense. You can still take definite integrals, which is what an integrator circuit does, or what the piecewise approach does.

how do i calculate the binomial coefficient for a fractional power with a calculator. the nCr button is giving me a domain error (TI-34II) for (1/2)nCr(5)

How does it make sense to have a partial time derivative as its own term?

>>9635090
Use a computer or write a program for your calculator.

>>9635124
You could think of it as just abuse of notation, or you could think of the entire expression in brackets as being a differential operator. Either way, it means "distribute the stuff in brackets and you'll get an expression that makes sense".

Differential geometry is taking a toll on me. I try to understand the definitions, but after a while I end up ignoring how I'm taking a coordinate chart and were my functions go and just abuse notation.

>>9635194
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

>>9635224
I'm not saying I like that, but notation becomes cumbersome and I lose track of what is what. Im trying various aporoaches, intrinsic extrsinic bundles whatever but I still don't get it.

/mg/ team creme unite!

>>9635194
that's fine, differential geometry is not said to be the study of things invariant under notation for nothing

Joint diagonalization of matrices to speed up computation time in latent semantic indexing. Also some stuff with "almost commutative" matrices and how there exists approximations to those matrices such that you can get new matrices that do exactly commute

>>9634781
A good teached

>>9632968
holy shit learn how to photoshop that's terrible

>>9633201
third-world (sweden) posters are not allowed on this board, please go back to >>>/int/

What exactly makes a subject "geometric"?

>>9634642
Math women looks like effeminate men

>>9635490
Kek, that's a good one.

>>9635666
When a geometer (engineer) writes a paper on it.

>>9635775
>geometer
This is not well-defined.

Doing big formulas with big numbers in these pieces of shit is fucking difficult

>>9636237
Then don't you massive retard.

>>9636237
>japanese tech

You had one job, anon

>>9633292
Maybe. What type of stuff do you guys discuss?

>>9635666
When Thurston thinks about it for a whole 2 minutes of his time.

im gonna study math soon but i cant decide on what i should specialize in. set theory, complex analysis or topology?

>>9636440
Have you had any kind of Introduction to these topics?
Else making such a choice already is a pretty bad Idea.

>>9636440
>set theory, complex analysis or topology
But only one of these is even remotely related to math.

>>9634642
I'd rather be a girl regardless of being good or bad at math

>>9632968
Today, as break from mathematics, I will review some basic topology from James book, there are described the usual notions in term of filters, and there is also a chapter on uniform spaces which are new to me, at least this general definition.
Also there is this soft article ( https://arxiv.org/abs/1803.08851 ) that talks about Farey maps, I'm not familiar with Farey stuff but it seems incentered on classical modular constructions, (extended) upper half plane mod discrete groups of holomorphic automorphisms => Riemann surfaces, and the ending pictures are nice, but I didn't see the definition of the maps the article is talking about, will read this afternoon or tomorrow.
Anyway weak easter to all of you.

why so much weeb animeshit ?

>>9636440
In what sense 'specialize'? You can't just specialize on those basic topics. If you meant 'focus' then I guess it is up to you, maybe complex analysis and topology are the easiest to see direct results, but not anything new.

>>9636522
>4chan
>why animeshit
geez

>>9636462
>But only one of these is even remotely related to math.
Actually, none of them are.

>>9634396
Study math and choose electives in stochastic processes, probability and stats, then you get a comfy job where you will do math and earn 300k starting

>>9636530
Hi. The designated anime boards are
>>>/a/
>>>/c/
>>>/w/
>>>/cgl/
>>>/trash/
So please keep anime discussion in the appropriate place.

>>9636684
(You) started the anime discussion.

>tfw americans seriously need courses on how to learn to write proofs

>>9636782
>>tfw americans seriously need courses on how to learn to write proofs
Who are you quoting?

Let [math]A[/math] be a closed subset of a compact Hausdorff space [math]X[/math]. (note, these conditions might be irrelevant). Suppose [math]A[/math] is a retract of [math]X[/math], that is, there is a map [math]r:X\to A[/math] that is continuous and restricts to the identity on [math]A[/math].

Is the suspension of [math]A[/math] still a retract of [math]X[/math]?

Is the *reduced* suspension of [math]A[/math] still a retract of [math]X[/math]?

I believe only the latter is true.

>>9636791
i meant (reduced) suspension of [math]A[/math] still a retract of the (reduced) suspension of [math]X[/math]

>>9636791
Shouldn't that be trivial for functoriality of suspension construction? (do you have a counterexample for the first assertion?)

I hereby declare /mg/ to be a Team Creme only thread. Miniggers, Peepsters, Shitcolates, and Brainlet Butters should fuck off ASAP.

>>9636831
>Miniggers
Why the racism?

>>9636522
>>9636684
Anime will always be an indispensable element of these threads. Deal with it.

>>9636881
Because we Creme people are supreme.

>>9632968
Homotopy, specifically it’s applications in quantum theory

>>9633165
We don’t know. Will need a solar-system sized accelerator to,find out,

>>9632968
linguistic entropy

>>9636881
Because you're a bunch of green midgets.

>>9636883
Stop shitting in our thread please.

What's creme's genus?

>>9636320
Life, depression, cute animals and math pretty much, just comfy place we hang out in when taking break from studying :3

>>9636320
The topics include topological and categorical stuff spammed by an autistic faggot, suicide and how life sucks, occasionally culture, animals, anime etc. The general idea is to communicate in a friendly way with people, and you have been friendly to me in these threads, so you could fit in.
t. not >>9633292

>>9636466
Why?

>>9636936
Don't use my wife for shitposting, please, thank you.

I see posters here that are not creme gentlemen.

>>9636616
This is actually a good idea since I didn't want to limit myself with applied math. Thanks anon.

Why is counting so hard?

>>9637667
That's what happens when abstract stuff becomes too concrete. Sometimes I wonder whether all the abstraction is really needed, and then I remember how simple calculations can rape me.

>>9637680
I have the same problem. Could it be a working memory thing? Are there any meds that can boost your working memory?

>>9637693
Why would anyone take meds voluntarily? Just avoid counting and you're fine.

What would undergrad research even look like? Me and my professor are pretty friendly with each other but I am too scared to ask him if he's currently doing any research.

test

>>9637744
https://scholar.rose-hulman.edu/rhumj/
I imagine is mostly stuff like that. Only the aliens do actually impactful stuff while an undergrad, and a lof of martians don't do anything of this sort.

>>9636883
>m*e
>anime

>>9637772
see first part of >>9634516

>>9637714
Teach me your ways master! How does one avoid counting when doing c*mbinatorics?

>>9637779
Most simple: don't do combinatorics. Combinatorics is for supermegagiga autists. The reason is simple:
(1) you need to be beyond the rain man level to enjoy it,
(2) you need autistic computation power for the calculations.

>>9637779
One just avoids c*mbinatorics altogether or moves to some other thread to discuss it.

>>9632968
OFFICIAL MINI TEAM STRATEGY GUIDE, SPAM THIS EVERYWHERE

1. MAKE SURE TO ONLY RESPOND TO MINI THREADS AND ONLY REPLY TO MINI POSTERS

2. INCLUDE MINI SOMEWHERE IN EACH RESPONSE

3. HAVE A SLOW BOARD OPEN IN ANOTHER TAB AND TRY TO SNIPE NUMERALS AWAY FROM THOSE BOARDS

THESE ARE OUR STRATEGIES, ONE HAS TO WORK. GET WORKING MINI BROS!
>You know, anon, with great meme prowess comes great responsibility. Hiroshimoot called it "April Fool's Burden." Myself, I just call it as I see it: the responsibility of the Mini to discipline the lanklet.
>Anon looks seriously at the camera.
>"The Cremes, the Peanut Butters, the Chocolates, the Peeps...It's our responsibility to civilize them. And if we can't? Then they shall dangle from the tenth page. The Day of the Rope is near, Anon. We'll have every Creme in this board dead or in the archives in 10 minutes, and may God have me banned by a butthurt janny if I'm wrong. God bless the Mini Team."
CREME SLURPERS WILL NOT REACH 1000
WHERE THE FUCK ARE THE FUCKING CODEFAGS??????

https://www.youtube.com/watch?v=kuNixp-wvWM [Embed] [Embed] [Embed]
GO TO THE SLOW BOARDS YOU DUMBFUCK
TAKE THREADS COLONIZE THEIR ASS
SPAM SHIT GIVE OTHER MINIS (((YOU)))'S
GET GAINZ GO GO GO
>>>/h/
>>>/d/
>>>/c/
>>>/e/
>>>/cm/
>>>/o/
>>>/x/
>>>/fa/

>>9637772
>Zeta
>not shit

>>9637667
>>9637680
>>9637693
Anons realizing they aren't computers

>>9637845
zz was better but it's not anime so I had to post zeta instead

>>9636908
>Will need a solar-system sized accelerator to,find out,
Why? Where can I read more?

>>9638047
>zz was better
Patrician taste
>but it's not anime
True
>so I had to post zeta instead
False

>>9638059
it's the first image I could find okay, here have this instead

After graduating from electrical engineering and effectively wasting my time, I've decided to study mathematics, soon I hope to be in a masters' study, I've seen the nature of the exam and the courses and I'm fairly confident I'll do fine.

Still iffy on surface integrals so I'm studying vector calculus right now.

Does math have any comparison to a book that is what SCIP is to CS? Or even better comparable lectures?

>>9638880
>Does math have any comparison to a book that is what SCIP is to CS?
What would that entail?

>>9638884
Fuck. SICP I mean. Structure and Interpretation of Computer Programs is considered by many one of the greatest books when it comes to CS. It seems to be that gateway drug that is obsessive autistic love for computer science.

>>9638894
>Fuck. SICP I mean. Structure and Interpretation of Computer Programs is considered by many one of the greatest books when it comes to CS. It seems to be that gateway drug that is obsessive autistic love for computer science.
What are some features of it you'd want to see mirrored in a mathematics book?

Can someone give me some tips on how to stick this in my head? I failed the course twice now and I can't afford to do so again.

>>9635666
geometry = topology + additional local structure

does antihydrogen fall up or down?
...or sideways?

>>9639070
If you can't learn calculus on the first try you should go into the trades anon

>>9634448
There you go.

> https://arxiv.org/abs/1803.11448
> The theory of soft set is a new mathematical tool dealing with uncertainties, it is in-
troduced My Molodtsov [16] in 1999. This theory has several applications, for example:
economies, medical sciences, social sciences, engineering, (see [6, 15]).
> In this paper, basing at the approach of Chiney and Samanta [7], we have introduced
a definition of soft elementary compact set, and space. We have introduced also some
proprieties of the soft elementary compactness, and we have proved the main result,
which is the soft elementary version of Baire theorem.

>>9632968
Is 0 a natural number?

>>9639356
> /preschool/

>>9639393
>math general

>>9639356
>Is 0 a natural number?
No.

>>9639345
Do they have any good motivation to study those sort of parametrized sets? Any problem those things are taylored to simplify?

>>9637667
>>9637680
https://www.youtube.com/watch?v=AiosKUO7oqo

>>9639356
No.

>>9633310
And how is this a good argument?

Can you guys recommend a book on the history of math? I’m reading through Ball’s book now and liking it for the most part, but it’s pretty dated (1920s ish).

>>9639749
That's like asking for the history of music. If you consider a book from 1920 dated, then you seem to have something particular in mind.

babby-tier group theory

>>9639796
Come on, anon. It's quite fun!

>>9639820
It is! I just wish I could move on to the more interesting things sooner.

I was wondering if you can assign meaningful values to divergent integrals the same way you can with divergent series. For example, can you say an integral like [eqn]\int_{0}^{\infty} sin(x) dx[/eqn] has an actually finite result the same way [eqn]\sum_{n=0}^{\infty} n[/eqn] does? Think of Ramanujan summation and not the fact that [eqn]\zeta(1) = -\frac{1}{12}[/eqn].
I only know of Cèsaro summability, but that's just a coefficient dependent criterion for convergence, and not something that can assign values to integrals.
>>9639831
Don't let the weak dictate your learning speed. Just take a proper textbook and plough through it like the animal that you are.

>>9639796

babby-tier analysis. it's starting to come together though.

>>9639356
yes

>>9639836
Thanks for the encouragement anon!
I'll try my best.

>>9639847
>I'll try my best.
Weak.

>>9639860
Weak solutions are often the best.

>>9639945
Some weak solution is also strong.

>>9637767
The martians went extinct with Halmos

>>9639356
It depends on who you ask or what’s convienent at the time. I like to consider it a safe a natural, otherwise the set of positive integers = naturals, so it seems pointless to have two sets denoting the same thing.

>>9639749
Look into Stillwell’s work in bot his history of mathematics texts and my favorite, Elements of Mathematics: From Euclid to Godel (which isn’t exactly history, but good nonetheless - along these same lines, see Mathematics: It’s content, methods and meaning” by the Russians).

>>9640150
>The martians went extinct with Halmos
Had a quick read on the matter, had a good chuckle. Thanks anon.

I'm revising some linear algebra and there's one thing I don't quite get.

Say that you have some symmetric matrix A. Then range(A) and kernel(A) form orthogonal subspaces. Define P and Q as the projections onto range(A) and kernel(A), and take some other symmetric matrix M.

Shouldn't it be true that M = PMP + QMQ? That is, M can be decomposed into parts living in the range of A and in the kernel of A, since they are orthogonal subspaces.

I ran this in Python and got something different, so I'm not sure what I'm not understanding.

Sludging my way through Spivak after completing Stewart’s take on calculus. The first two chapters destroyed my weaknesses in algebra that were overlooked throughout calculus

I just purchased pic related and it's more of a door-stopper than I expected. I mostly care about the applications of ODEs. Has anyone gone through this book before? Any recommendations of which chapters are essential and which aren't?

>>9640175
By the way, I did take an ODEs course at a community college but it was pretty bare bones.

>>9640175
"elementary"
Beware these words OP

>>9640206
I thought it would be a simple guide to ODEs :(

I can't bring myself to work on my,calculus project... It was due last week but I might be able to turn it in still since I know the professor hasn't gotten through them yet. I have lost all motivation and don't know why.

https://web.archive.org/web/20150423201942/http://www.amazon.com/gp/richpub/syltguides/fullview/r1ge1p236k3ysv

Is this guide a meme?

>>9640173
Well unless A and M are related, there is no reason why M should map the kernel or range of A to itself (which would be implied by the identity M = PMP+QMQ).

>>9640323
Same with me - probably one just can't be creative the whole year... Even a colleague of mine - who is extremely advanced - has her "lazy" months...
Of course, if you have a deadline (do you?) then that's quite shitty...

>>9640401
I am generally against calling things a meme, but this guide was written by someone who clearly had not done an undergrad in mathematics.

A good idea is looking at university course requirements (e.g. MIT or Harvard or whatever school you like) and then looking at the suggested course textbooks for each course. Then doing this in order like you were doing the courses yourself, just at home. This should be sufficient.

Also, there are like 5 math.stackexchange questions per topic for "best references for first course in <topic>". So everything is easily accessible.

Tensors. I want to kms.

>>9640175
This is more a reference to ODE techniques then a book to work through.

>>9640614
Tensors aren't scary [math](\ ^\otimes \smile ^\otimes )[/math]

Why are these threads always filled with smug weebs?

>>9640704
>why are there smug weebs on a website explicitly targeted towards smug weebs

>>9640704
sorry anon, but >>9640710 is 100% correct.

>>9640614
They are extremely simple.

A matrix is bilinear map whose numerical representation is an [math]n_1 \times n_2 [/math] array.

A tensor is a multilinear map whose numerical representation is an [math]n_1 \times n_2 \times \dots \times n_m [/math] array.

>>9634253
>linguistics/archaeology
>math
Hard choice, but patrician choices anon. I respect you for following your interests; Im going the Material/ChemE for employability, but my true passion lies in a more pure logos: math and linguistics.

>>9640710
>a website explicitly targeted towards smug weebs
[citation needed]

if this is tricky to me, should i switch my major from app math to somethin else?

>>9640721
Doubt your definition is good

>>9640805
Then use a proper book fucking retard

>>9640806
No no. There is no "then". You were just wrong. End of dialogue.

>>9640805
I did not state definition I stated the representation which comes about by the existence of basis theorem. You can just read an algebra book yourself and this will become very obvious.

>>9640806
please stop pretending to be me.

>>9640848
>please stop pretending to be me.
you might want to fuck off back to r*ddit

>>9640853
so toxic anon. can't you just [math]Enjoy\ Mathematics?[/math]

>>9640848
>representation
Wut

Definition gives ALL the information about a mathematic object. There is no room for any "representation" bullshit.

Is knot theory fun? If it is, what is a good textbook on it?

>>9640885
>Is knot theory fun?
no

>>9640883
I respect your opinion, but it is not correct. Let me give an example to show the manner in which this is the case.
A vector's numerical coordinates with respect to a basis is not literally that vector. The vector itself is simply an abstract object obeying a number of mathematical axioms.

Definition alone also does not give everything one might want to know about some mathematical construction. Consider the definition of the Real numbers under an axiomatic setting, (as is done in undergraduate level Real Analysis.) Such a definition does not illustrate how one might construct that set from the set of rational numbers, and so there is some aspect of the mathematical object which is not classified under immediate definition.

For further example, consider the definition of a vector space. The set of vector space axioms could be written in terms of groups, or we could write the algebraic laws directly. 2 definitions yield a different perspective, but are still equivalent. Continuing with the example, we can also notice that the definition does not mention dimension, but yet dimension is an intrinsic quality which me might want to know about a vector space.

I hope this post was helpful.

>>9640885
Are you an undergrad? The Knot Book is a good start if you don't know a bunch of topology. Knots by Burde and Zeischang is good if you know a bit more.

>>9640917
I do know some general and algebraic topology, but I'm stupid. What's a good book that would mansplain the knot stuff to me like I was retarded but still cover things properly?

>>9640765
Work on specific examples for a while and the general properties should make more sense. Hopefully you have exercises to work from.

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

>tfw finishing a PhD in math but still struggle with literally any exercise in an undergraduate textbook
how the fuck does this happen
why am I like this

>>9640323
Discipline yourself and you stop relying on motivation, weak willed faggot

>>9640998
funny thing really, turns out you forget things over time if you don't keep up on them.

>>9640998
are you making any significant contribution in your phd?

>>9641017
I feel like I never really understood them well in the first place, which is the more depressing part.

I guess that's what I get for doing a PhD in England, where you're expected to do research straight out of undergrad where they teach you nothing.
>>9641018
got a few reasonable application-oriented publications.

>>9639836
How do I plough through textbooks?

>>9641024
what kind of examples are you dealing with?

>>9641003
>faggot
Why the homophobia?

>>9641040
Why the homophobia-phobia?

Trigonometric functions

>tfw I'm only in pre-calculus

>>9640765
stick with it. dont just quit things because theyre hard.

>>9640998
did you not do any teaching during your phd years ? it's the best way to keep practicing the basics

>>9641053
trigonometric functions are a spook.

>>9641037
I did stuff related to quantum computing. it's pretty comfy because it's just lots of linear algebra

>>9641059
when you only have 3 years to finish your PhD, teaching feels like a bit of a waste of time

>>9641076
I guess, most people I know teach though, even though they're all in your situation (fellow europoor here)

>>9633251
Actually, the post is quite in the reverse direction of meaningless: it is quite meaningful.

>>9640944
>>9641056
thanks for the responses but im fine with the computation part

in that example, i dont understand why the author chose to take the time derivative of u(t)e^(-at). i understand that the result is to show that u(t)e^(-at) is a constant but how did he think to do that in the first place? it amazes me

the book is hirsch and smale btw

>>9640442
>this guide was written by someone who clearly had not done an undergrad in mathematics.

Why do you say that?

>>9633251
touché

>>9640758
spineless

>>9640765
you should quit if you are truly so weak willed

Should I learn a proof assistant like Coq? Is it useful ? My professor brought it up as an option that some mathematicians tske to help get really solid proofs .
As background I have some programming and my key interest is theoretical computer science. Not sure how much that matters

>>9641601
>Should I learn a proof assistant like Coq? Is it useful ?
Yes and yes. Current mathematics publications are plagued by "proofs" which are more like rough heuristics than actual rigorous proofs, and Coq is a cure for this disease.

>>9641601
>>9641608
I'm uncomfortable with saying Coq so I think I'll abstain

>>9641601
Is it possible to make a career of hiring myself out to a mathematician and programming up/ using proof assistant to verify their proofs? A lot of mathematicians hate programming or are unwilling / lack the time to really get into something like Coq

>>9640885
They're not just fun, anon, they're fucking amazing. Just consider their complements in [math]\mathbb{R}^{3}[/math] if you don't believe me.

>>9641124
If you take the derivative of a constant function, you'll get zero as the result. It's just that.

>>9641028
The same way you do with women: with masculine fury and determination to prove your worth as a member of society (mathematical society in this case).

>>9641076
>I did stuff related to quantum computing
Don't leave us hanging like that, spill some beans man.

>>9641608
>Current mathematics publications are plagued by "proofs" which are more like rough heuristics than actual rigorous proofs
What do you mean exactly? Any illustrative examples?

>>9641816
How do the complements make them amazing? Sure, they have non-trivial (co)homology, but you get non-triviality at n=1 by removing a line too.

Studying Foucault-like relativistic moral truth systems derived from communist-like power structures and their applications to algebraic geometry.

>>9641878
>Not knowing about the geometrization of knot complements
What meme uni did you attend?

>>9641919
A uni that doesn't teach knots at all. All the focus is on the anal side and the algebraic side of things is completely neglected.

>>9641923
And what sort of meme self-learning on knots are you doing?

>>9641930
None, I guess.

>>9641935
Then you should read Master William Thurston's Bible and start your path to enlightenment, instead of caring about a sad smug posting weeb's opinion on memes. 'Cause seriously, that last answer sounded sad.

>>9641970
I don't think any book can help if calling my self-learning a meme was enough to demoralize me so badly I could hardly even get to the grocery store, and when I did I didn't buy anything because I was too scared of the people standing in front of the vitamin pills I was trying to get. I'm a failure, but at least I tried.

>>9641979
Awww i wish i could hug you. Don't feel sad , buddy! Everyone is different, and you shouldn't take everything others say to heart!

>>9641979
Do you want to learn together? I made it sound like I know a lot about the topic, but I actually don't. The topic of my Bachelor's thesis is related with this stuff, but my actual understanding isn't very deep.

>>9642008
I guess.

>>9642011
Thanks for the offer, but nah. I'm not a social being.

>>9642022
The social component of mathematics is really important, you know?

>>9642043
What do you mean?

>>9642047
It's not just about doing mathematics, it's also about sharing it with others, which helps one have a better understanding of their own work. We're in this thread because talking about mathematics is cool, and learning is no different in that regard.

>>9632968
Topological Vectorspaces

>>9641979
>I don't think any book can help if calling my self-learning a meme was enough to demoralize me so badly I could hardly even get to the grocery store, and when I did I didn't buy anything because I was too scared of the people standing in front of the vitamin pills I was trying to get. I'm a failure, but at least I tried.
cringe

>>9642050
Fag.

>>9642050
Well, I'll think about it. I'm not sure if I can keep up with your pace etc.

>>9633004
>>9633011
Why the fuck anon?

>>9642069
You don't even know my pace though. You just want to avoid having to make a decision now and hope that we'll both forget about this because you're insecure, but you don't want to admit it (at least not to me) so you just say that "you'll think about it".

>>9642065
How do macho men like you do mathematics?

>>9642065
>Fag
Why the homophobia?

>>9642077
I would like to try it, but I just don't think I can. If you want a straight answer now, then take a no. I know I'm insecure about things, and I don't have to admit to you explicitly since it's obviously visible in my post.

>>9642091
>but I just don't think I can
Wouldn't you rather know?

>>9642094
I've already wasted enough of your time. Do you think I want to waste more of it?

>>9642099
go get laid pussy

>>9642102
?

>>9642099
You're not the one who decides whether I've wasted my time or not, it's me. And I've been all the fucking morning on my bed, so you can guess hoow much of an impact you "wasting" my time would have on my productivity.

>>9642108
Oh, I forgot it's only morning in the US now. Time zones are too hard for me, I'd just waste your time. That is my final answer.

>>9637151
cause I could be an heterosexual slut

>>9639836
>∫∞0sin(x)d
t-the answer is 0

>>9640721
kill yourself

>>9640614
https://www.youtube.com/watch?v=CliW7kSxxWU

>>9642128
It feels like I'm talking to myself in a bad day. How did you get to this point?

>>9642155
It's a long process of me hating myself and living in a hostile environment, but at the same time trying to justify my existence by trying to be good at at least something for once. My parents would like to see me get a PhD, but I don't know if I'm capable of even getting in anywhere. I can try, but I don't know if I can handle my potential failure, and I can just forget the whole thing and live the rest of my life in the shame of giving up and without doing the only thing I've ever been decent at. I guess I appear smart to those who don't know uni math is really like since everyone is telling me I'll make it and other stupid shit like that, but I only see a trail of failures behind me. You seem nice, and I don't want to drag you to the bottom with me.

>>9641028
reading books is for nerds

>>9642011
I'll learn with you anon anytime uwu

>>9642200
>Notices Spanish
OwO ¿Qué es esto?
>>9642179
It's too easy to be nice to someone so similar to me, and I have the same fears. It helps me read about famous mathematicians' life and the problems they faced. Weierstrass is quite a tragic example:
http://www-groups.dcs.st-and.ac.uk/history/Biographies/Weierstrass.html

>>9632968
College algebra

>>9642223
That was an interesting thing to read. I didn't know anything else than the obvious two things: (1) he was a German, (2) he contributed a lot to analysis. Why are you afraid?

>>9642227
Hate artists who upload exclusively to twitter.

>>9642269
I want a sense of belonging, and I feel the only way I could ever achieve it is by proving my worth and convincing everyone that I deserve to be wherever I end up, especially to myself. But I'm the kind of person who's not made for those feelings, and I'm scared for my future.
This one's also good:
http://www-history.mcs.st-andrews.ac.uk/Biographies/Green.html

>>9642284
Have you been doing well so far, though? The feeling of alienation is really crushing.

>>9642311
I have if you ask anyone but me.

>>9642321
Could it be that you are wrong, and you actually can make it if you just understand you are wrong?

>>9642326
Could it be I'm the only one constantly inside of my own mind, who can see me for what I am?

>>9642370
Could be. But it could also be that you neglect the exterior perspective, and thus fail to see the big picture in which you are not a loser.

>>9642085
Fag.

>>9642179
>>9642223
Why is everyone like this? I mean here. What the fuck is wrong with you?? I'm starting to think that French(?) guy who also posted animes really did kill himself last week. Fucking weebs man. This is so depressing.

>>9642284
>>9642311
>>9642321
>>9642326
>>9642370
>>9642383
Why is everyone here so depressed???

>>9642509
>>9642516
Mathematics is a surrogate activity and therapeutic for us on the brink of kyssing our'shelves, as it doesn't itself force us to operate with people (who I am horrible with) but instead with things people have created (such as textbooks and papers etc). Or that's my perspective.

t. >>9642179

>>9642509
>I'm starting to think that French(?) guy who also posted animes really did kill himself last week.
Can't find it on the archives.

>>9642523
The guy who wanted to donate money.

>>9642521
How do you even do math when you're so damn depressed tho? Your brain isn't working properly when you're depressed.

>>9642542
I do what I can. Eventually I get too anxious with the book and drop it. That's why I don't know much more than the basics of anything.

>>9642516
because you're in a general, and one that doesn't even really need to exist at that.
Go to any general on any board and you'll find a bunch of pathetic fucks desperate for attention.

>>9636237
Dude just script your own calculator in python or your language of choice.

>>9642552
What's wrong with that?

>>9642645
It's not healthy.

>>9642650
Why?

>>9642645
>what's wrong with being an obnoxious faggot

>>9642655
Yes: your supposed discomfort aside, what's wrong with people talking about their problems here? I am asking in earnest. Please give me a serious answer.

>>9642662
This is the science and math board, not the melodramatic whining board. Your shit belongs on /r9k/.

>>9642668
This is a community of people interested in science and mathematics. An imageboard is nothing without its users.

>>9642674
not an argument

>>9642679
Sure it is. People don't go to pubs just to drink alcohol and burn a fag. Likewise, people don't come to /sci/ or /mg/ merely to read or post about science or mathematics. You seem to be confused about how social spaces work.

If you want /mg/ to be stringently about mathematics you've come to the wrong place. Try a journal's editorial board instead.

>>9642674
>2018
>coming to 4chan for "community"
Desperate and pathetic. Don't you have some d*scord you should be ERPing in?

>>9642705
How cute.

Does anyone here have the ability to vouch for an account on arxiv and is willing to do it for an anonymous fellow like me? I swear I'm not a crank.

>>9642655
>>what's wrong with being an obnoxious faggot
Who are you quoting?

Math is for chads. Anime retards and autists shouldn't be accepted into any serious program.

>>9642780
Have you ever been on a math campus?

>>9642783
Yes, it's disgusting. Autists that only care about manipulating symbols and tedious proofs. What it is it's not what it should be.

>>9642788
Can you please get a trip?

>>9642798
Not my problem that you are an autistic nerd who doesn't understand proper intellectualism os ultimately pure chad.

>>9642806
>proper intellectualism
cringe

>>9642808
>he doesn't know

>>9642815
>>he doesn't know
I'm not a "he".

>>9642806
Who hurt you anon? How can I help you?

>>9642816
Please follow "the rule".

it's time to retire this thread

9

8

7

6

5

4

3

2

>>9642895
Stop.

1

>>9642897
Ok.
>>9642860

>>9633175
That is is string theory