/sci/ - Science & Math

is this accurate?

>>11002602
Not really. Was this made by a CS sophomore or something?

>>11002602
Kurisu is a physishit, so how would she know?
(I love her though)

The graph is also pretty much bullshit, ignore it.
There is so much wrong with it...

If you roll a dice 10 times, what are the odds you get exactly three 3s, two 2s and one 1?

How do I brute force myself to study all day long?

Is this all or is there something missing?

>>11002774
Nah.
Algebra is
>technically speaking complete
But that's only because of how much stuff you can fit in abstract. Adding universal would be best.
Analysis lacks harmonic, hypercomplex, geometric and Clifford at the absolute least.
Discrete is weird.
Geometry needs convex, complex analytic, synthetic differential, discrete differential, tropical and projective.
Fuck if I know what's missing in number theory.
Topology needs piecewise-linear, point-set and pointless. Maybe topos theory. There's also specific stuff, like symplectic and contact topology, but you can sort of slip it into one of the others.
Fuck if I know the rest.

>>11002799
I forgot p-adic in analysis.

>>11002774
It’s just very general.

But eg. I can not find measure theory, but you might consider that part of another theory.

>>11002681
something along the lines of
(10choose1,2,3,4)*((1/6)^6)*(1/2)^4

>>11002826
double checked, should be right
note that the answer would be the same for any three different numbers rolled 1, 2 and 3 times.

>>11002799
>>11002800
thanks!

>>11002826
solved using a different method
((10choose3)*(7choose2)*(5choose1)*3^4)/6^10

got the same answer ~1.6%
so it should be correct.

>>11002774
Around 2010 I tinkered with partitioning of disks and other figures into slices and made a word clouds with info like that. There's the Mathematica question how to do that on SE if someone's interested, or I can dig it out (although by now there's millions of web app if you just want the result).
For a finer grained division of math subjects into topics within the fields as well, there's the subject classification for papers etc., there's the MSC2010
https://mathscinet.ams.org/msc/pdfs/classifications2010.pdf
It has thousands of items.

>>11002602
>is this accurate?
Why don't you try it and find out?

>>11002618
>CS
not science or math

>>11003858
>deRham cohomology
>topological QFT
>modular arithmetic
>noncommutative algebra
>cartan geometry

>>11002758
>How do I brute force myself to study all day long?
What have you tried?

Threadly reminder to work with physicists.

>>11003903
Re-reading the textbook. Doing sets of problems until mental exhaustion where even basic arithmetic is difficult. I mean what else is there to do? Flash cards? Remember steps by writing them down? Talking to a duck?

>>11003901
Not sure what you're getting at but I should probably recompile it again. Also has quite a physishits bias when I look at it today.

I just digged out the source and saw that I trimmed the following

Microlocal Analysis
Deformation
Quantum Groups
Fourier Analysis
Topological Groups
Representation Theory
Special Functions
Module Theory
PDEs
Lie Groups
Harmonic Analysis
Wavelet Analysis
Potential Theory
Integrable Systems
Turbulence
Chaos Theory
Dynamical Systems
Metric Spaces
Stability Theory
Optimal Control Theory
Ergodic Theory
Calculus Of Variations
Optimization
Bifurcation Theory
Measure Theory
Stochastic
Fuzzy measures
Bayesian Inference
Statistics
Martingale Theory
Regression Analysis
Probability Theory
Estimation Theory
Game Theory

Here's the full list, I'm happy for comments (best in that file right there)

https://gist.github.com/Nikolaj-K/502bf35e1fb818df85f33de47668a793

>>11003981
Anything with fuzzy in the name is shit.
But I genuinely can't comprehend why you included modular arithmetic but not PDEs.

>>11004336
it's the 9th one down

>>11002676
imagine dating another mathematician. fucking ungodly.

Outside of Misha's curriculum, what does a proper differential geometer needs to know?

>>11002774
Where's Measure Theory?

>>11005152
probability?

>>11002602

Presently I am unable to determine whether flat modules are "justice".

>>11004603
Besides your typical differential geometry and riemannian geometry courses, some algebraic topology, some structure theory of lie groups and lie algebras, some functional analysis, some PDE.
This should be plenty for foundation, then it really depends on what you are interested in.

What do you guys think of applied mathematics?

>>11005250
misha's thing includes everything u mentioned except maybe structure theory. it is an actually complete undergraduate curriculum

>>11005177
But measure theory is enormously important in analysis too...

>>11002548
Which public uni is a go-to for rigorous Math? Exclude UCs

>>11005674
http://www.ams.org/notices/199701/from-reclass.pdf

Anything in group 1 is generally considered a "good" math department, and with a handful of exceptions most of them are much stronger than good. The best non-UC one in terms of reputation on that list is probably Michigan.
But honestly it doesn't matter that much in undergrad, especially once you scratch off all the super-prestigious private schools. Obviously it does matter somewhat (it's easier to get more famous recommendation letter writers at better universities, which matters, and if you come from a no-name campus you might need to score higher on the GRE since they don't know how much they can trust your GPA), but plenty of people get admitted to top 10 programs each year after doing their Bachelor's at mediocre universities.

who of you did this? I am dying https://www.youtube.com/watch?v=SYWaQe0qmNI

Because all sections on trivial vector bundles [math]M\times \mathbb{R}^n[/math] are of the form [math]s(p)=(p,s^*(p))[/math] with [math]s^*:M\to \mathbb{R}^n[/math], I'm asked to prove that the map [math]ds[/math], with the differential being applied to [math]s^*[/math], is a connection of the vector bundle. The definition I'm given is the first one here https://en.wikipedia.org/wiki/Connection_(vector_bundle).. I'm having trouble with the precise definition of the connection. My first thought was to write the map as [math]ds=ds^*\otimes s[/math], but it seems to have some issues with lineartiy, because when you apply it to the sum of two sections you are going get mixed term in the tensor product because of the bilineartiy. Going by linear algebra, to inject a given linear map into the tensor product, you multiply it by the identity, but I really have no clue if this makes sense for sections, even on trivial bundles. Sorry if I'm saying retarded shit, I'm pretty new to these formulations of Diff Geo.

>>11002676
She's a neuroscientist you dumb fuck.

>>11004538
Yep, physicists in my experience are cuter.

remind me a site with a shitton of links to math books downloads, please

>>11004603
What's misha's curriculum?

>>11006349
>Libgen
>Type "springer" on pirate bay

>>11006299
>a long symbolic manipulation proof with tensors where the only result you use is the product rule
That's the kind of stuff you should just leave to physicists.
>>11006351
That one autistic curriculum that's posted here every now and then.

>>11006317
Why the homophobia?

>>11006359
>Libgen
thanks a lot, i was not able to recall this combination of letters

>>11006368
The one that has some pretty underground stuff in its "deepest" level?

>>11002548
Why aren't infinite products as common and as important as infinite series?

>>11006614
They are pretty important https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem They are just much more ill behaved and there are plenty restrictions on the convergence so they appear on much more particular situations. You also can define infinite series on any vector space with a norm, while Infinite products require further algebraic structures, which require a commtative product (most examples of them are either C or R).

How would you rigorously prove this?

>>11004336
I'd love to disagree, but I also never got warm with fuzzy math. If you look at library stacks, it's clear that there was a lot of hope around the 80's and 90's, but I suppose it's not much more than another way to look at things already treated otherwise. I'd love to be wrong on that too.
I don't know why modular arithmetic made it there. Just like BRST-Cohomology. As I said, it had a physicists bias.

>>11006614
I suppose there's also no such a nice and handy formula as the Taylor expansion for products.

At one point I also found that (unless something goes very wrong I guess), you have that

[math] \prod_{k=0}^\infty b_k = \prod_{k=0}^{M-1} b_k + \sum_{n=M}^\infty(b_n-1)\,\prod_{k=0}^{n-1}b_k [/math]

That's derived in video on the channel I linked above somewhere, but the clip is not PG13.

I do think there must be a point of speaking more often in terms of the Gamma functions product representation (in terms of rationals).
There's also the Weierstrass expression with the exp upfront and I couldn't get warm with it yet.

I'd be interested to see what your building up of algebra looks like if you e.g. use

[math] \dfrac{1}{1-x} = \prod_{n=0}^{\infty}\left(1 + x^{2^n}\right) [/math]

instead of

[math] \dfrac{1}{1-x} = \sum_{n=0}^{\infty} x^n [/math]

Also there's

[math] \lim_{N\to\infty} \prod_{n=0}^{N-1} \left(1+\frac{x_n}{N}\right)=
\exp\left(\lim_{N\to\infty}\frac{1}{N}\sum_{n=0}^{N-1}x_n\right) [/math]

and you get to those expression a lot in QFT.
Similarly (more exotically),

[math] \lim_{\Delta x \to 0} \prod{f(x_i)^{\Delta x}} = \exp\left(\int_a^b \ln f(x) \,dx\right) [/math]

and other product integrals.

Now, to guess "why" more morally from an exotic (topos theoretic) standpoint, it's maybe worth pointing out that [math]\sum[math] resp. [math]\prod[math] (just like [math]\exists[math] and [math]\forall[math]) arise from...

>>11006776
...
Now, to guess "why" more morally from an exotic (topos theoretic) standpoint, it's maybe worth pointing out that [math]\sum[/math] resp. [math]\prod[/math] (just like [math]\exists[/math] and [math]\forall[/math]) arise from looking at projections [math] p : E \to X [/math] which for discrete and countable objects end up counting volume of fibrations resp. it's section space. I.e. there [math]\sum_X[/math] ends up collecting all the volumes of the fibres and [math]\prod[/math] the amount of sections (from the base X into the individual fibres). And combinatorics as we do it is just not too much concerned with counting the amount of legal functions, but rather items in a space. If you want the amount of items in over each point in X, you just add them up by summing over X. But if we were to describe a space X and were interested in how many functions s on X there are that map into a space with certain conditions, then you'd naturally take products over X (you take one a in X, collect the legal values functions can take, then you take another one, b, and all the values, and by counting functions, you need to multiply - if that makes sense).

>>11006774
https://en.wikipedia.org/wiki/LogSumExp

I don't know what I was thinking when I enrolled into an applied maths major. I guess I was even more of a mathlet than I am right now.
>no topology, number theory, differential geometry, algebraic topology, less algebra and geometry
I'm definitely switch to pure maths next year.

>>11006614
because of integrals. infinite products don't have as obvious of a physical meaning.

>>11006800
actually well-written post, makes sense

If the set of all sets which do not contain themselves can be described as a 'paradoxical' set, is there such thing as the set of all 'paradoxical' sets?

>>11006776
How do I understand the pic in your post?
t. Learning analysis

>>11007080
Does the set of all paradoxical sets contain itself?

>>11007086
That's category theory on the image, son...

If I have a connected manifold with an affine connection, I know that between two points, there is always a smooth path connecting them. So if we generate an arbitrary basis at the tangent space of a particular point, couldn't we generate a global frame by parallel transport? I suppose the crux would be in showing that it must be smooth. The problem I have asks me to construct this when the parallel transport is independent of the path, but I don't see were it comes into play.

>>11004603
How did he ended in Brazil?

>>11007153
> So if we generate an arbitrary basis at the tangent space of a particular point, couldn't we generate a global frame by parallel transport?
Obviously fucking not, but I can't draw the reason right now. Think of the circle in R^2.

>>11007170
The circle is parallelizable bruh.

>>11007153
https://en.wikipedia.org/wiki/Parallelizable_manifold
[math]K[/math]-theory provides an obstruction to this.

>>11007171
That's not the point.
If you have something with non trivial holonomy (that is, parallel transport depends on the path) you hit the wall very fast with antipode-like points that are approached by many of the paths you're using to construct the frame.

>>11007173
Based Touhou posting differential geometer

>>11007180
O shit yea, I see it know, thanks.

>>11007158
Brazil is hardly a mathematical shithole (at least as far as geometry and pdes go). Impa also tend to attract high visibility foreigner researchers by offering high pay (Grothendieck lectured there for a while too)

>>11007158
Brazil is part of the 5* countries for mathematics and is one of the leaders in the Dynamical Systems field.

>>11007196
>differential geometer
H-haha yeah

>>11007211
No problem lad.
>>11007287
You know, I don't get why you seem concerned with stuff like going into a postdoc. You aren't Neumann, but you seem to have a pretty tight grip on what you need to know and related fields.
Is competition actually that bad in the U.S.?
Should I start feeling concerned I've only picked up symplectic geometry in my sophomore year?

>>11007311
I'm Canadian. While the competition is not exactly fierce, there's only a handful of institutions that has a dedicated mathematical physics research group.

>>11002602
its accurate but vague

still better than 99% of the "/sci/ guides" I've seen

>>11007455
thanks I made it myself after talking with a few anons.

>>11006337
Are physicist GFs real?
I'm so alone.

>>11007523
What? Who's talking about girls?

>>11007531
.....oh.
I mean that's cool. I don't have a problem with sucking her penis.

>>11007439
Why is mathematical physics not that popular? There is a deparment on my uni, abd I literally just had to show interest for me to get a research project.

>>11002602
My wife.

>>11007523
It is, the physics department in my Uni is full of cuties. I even fell in love with one of them, even though we only talked once, but unfortunately she decided to study abroad.

>>11006337
If I wanted to date a schizo I'd go to the social science department
I want a engie gf to suck my superior cock, and violently sexually abuse her.
>>11006381
big anime tibbies is bestest
post more you tranny Yukari poster that's always in the math general.

>>11007580
I'm so happy.
We can do math together and snuggle.

>>11007569
Don't get me wrong, every major university has a few people doing it.
The point is that there aren't many major universities around, and PI isn't exactly short on post-docs.

>>11007580
>fell in love
...
>he was the one in love
>she didn't love him
>HE LOVED A GIRL AFTER TALKING TO HER
a-anon I...
>>11007588
physics girls deserve rape.

>>11007607
>physics girls deserve rape.
t. virgin engiefag

>>11007602
Any universitys/groups you can recommend for somone planning to do their phd in mathematical physics (even though they only have a master in pyhsics)? is there a chance they would take me?

And unrelated, who is the guy in the op?

>>11007614
>who's the absolute lad in the OP
Oka-kun. Relevant in several complex variables and analytic geometry.

>>11007614
UoT, Lisa Jeffery is amazing.
>is there a chance they would take me?
Have you taken math courses and shown tangible interest in the relevant math?

>>11007607
No, it wasn't immediately after talking to her. I actually forgot about her after that, but then her facebook profile appeared to me and I started reading about her and it all made me fall in love, I made several plans and situations that would make us closer, but in the end I was too shy to try anything and then I learned she was studying abroad.

Suppose I have a minimal bandwidth graph ordering. Using the knowledge that the vertices are already ordered to mininize their bandwidth, how do I find the largest cliques contained in the graph?

I have a paper to write about why Greece developed their mathematics they way they did. Any suggestions on potential factors that influenced it?

>>11006351
>What's misha's curriculum?

>>11007624
i have taken most of the standard math, like functional analysis, measure theory, analysis on manifolds, and a variety of other stuff (abstract harm analysis, lie groups and algebra, microlocal anlysis, algebraic topology). I guess my algebra background is a bit weak.

>>11007609
>rape = dating
cringe
>virgin engiefag
>me a math major
>a math major = a virgin peon engineer filth
kek, it's almost funny.
Look at pic related she's probably thinking about getting raped by a big, hairy, swarthy mathematician.
>>11007636
bro, I know you're not a math major.
don't you know how simple it is to just met underclassmen female in engineer classes and tutor them in smooth brain math, then during a private session you rape them?
I don't understand you, why would you love something you just saw? I've never loved anything in my life. Because nothing loves me. Sex is fine, but distracting.
tell me anon, what is love even? I hear it all the time in movies and books, but what could it mean?

>>11007671
>math major
Ew. The only math major I've ever met with an ounce of masculinity was my father's old jewish accountant with 8 inch long armpit hair that hung out of his wifebeater.

>>11007668
Then you'll be fine on that front. It'd also really help if your masters project has a decent math slant.
It really depends on the faculty and university (UoT is especially tough) but as long as you show genuine interest and competence then you should stand a pretty good chance.

>>11007639
>Using the knowledge that the vertices are already ordered to mininize their bandwidth, how do I find the largest cliques contained in the graph?
What have you tried?

>>11007668
Then you should be fine on that front. It'd also really help if your masters thesis has a decent math slant.
It really depends on the faculty/uni (UoT is especially tough), but if you show genuine interest and competence you should stand a pretty good chance.

Im so fucking lonely

>>11007671
I'm math major, but I'm a brainlet, lad, I bombed Calculus, Computation, Physics, Linear Algebra and Geometry so far. I'm in no position to tutor anyone.

I don't actually know what I felt for her, but I would call it love, I just wanted to be with her, to ne her partner, I even envisioned our lives together in the future, I envisioned a lot of cute moments in my head, it's so sad that I could never talk to her, I had an entire semester to confess my feelings but I was too shy to do so, and now it's impossible.

In mathematical terms, I would say love is undefined.

>>11007678
desu, my master project was kinda garbage and not very interesting from a math point of view (and probably not interesting from a physics point of view either).
guess i have to try and see.

Unrelated again, does nobody here know who the dude in the op is?

>>11007691
Stick to your major.
It's the new tribe.
Find a nice girl from your major to snuggle with.

>>11007701
engineering girls are either roasties who drop out after 3 semesters or autistic beyond belief

>>11007704
>no autistic engie gf to show the superiority of your physics major dick.

>>11007676
yes well I also read philosophy. I exercise my body to practice discipline and to keep the vessel of my mind at top condition.
How could I possible spend hours reading math if I'm some scrawny or fat loser that gets tired from getting out his chair.
So yeah, I'm not the epitome of masculinity, I strive for the appearance of a thinking man. Why would I indulge in flesh endlessly? my body simply needs to be aesthetic, not grossly animal like.
I'm not a jew, I'm mixed.
I've only had sex once and don't intend to practice it more, it's distracting. I wanted to explore what it was like to be a plebeian scum bag that sucks women all day. It was thrilling, but that's what I fear. I fear I'll lose my love of math and pursue trivial and mundane acts of savagery.
keep your homophobia to yourself, uncivilized faggot.
look she's still thinking about big math cock.

>>11007680
Initially I thought I could just take the two vertices with maximal bandwidth as the interval bounds of the clique, but it turns out it's more complicated than that if the minimum bandwidth exceeds the size of the maximize clique.

>>11007700
Yep, no harm in trying, except for the $150 application fee lmao

>>11007691
I understand, my friend. Loneliness is a hard thing to live with. However, you learn to survive.
practice discipline. If you are bored then that must mean there is nothing else to be known, so inform me on all the knowledge of all things, I'd love to know.
>>11007695
Improve your foundations, with bad ones it'll just get worse. It might feel hard to go back, but it's less intelligent to ignore where you fail. Yes when I was 10 I realized I needed a better foundation after having trouble with notation in a Linear Algebra book, I then learned logic, set theory, a more rigorous approach to algebra, and proofs. I did much better with a more mature mind.
Calculus seemed trivial, and analysis was a breeze.
Sounds like you had some severe delusions about this girl. Don't show emotion for a gash of warm meat, it may feel great but in retrospect it's just sticking a meat rod into a meat bag, and your brain tells you it's better than breathing.
>>11007704
>autistic
easy to take advantage of
>roastie
easy to take advantage of
are you even trying?
try girls that are easier to take advantage of

Is it possible to make contributions to physics by learning and using only math without studying physics? I mean, there's a mathematical formulation of quantum mechanics, so technically it's possible to take these as axioms and start building from there, right?

>>11007730
Yeah, I've been thinking of becoming a reclusive, living only for studying, I might even build my own monastery so others like me can gather to study in peace and live among their equals.

>>11007723
> $150 application fee lmao
welp
anyway, thanks for the help

>>11007739
Depends on what you mean by contributions _to physics_.
You can make a contribution to mathematical physics, but actual physicists aren't going to be the ones that give a shit.

>>11007742
That sounds incredibly based.
I'd join. Fucking math monk life.

>>11007745
Contributions to physics as in solve the Yang mills mass gap problem. Who give a shit about their approval? I only care about /sci/'s approval.

>>11007759
https://arxiv.org/abs/1502.04135

When looking at universities for (math) undergraduate study, what qualifications would you guys consider important? The general consensus from my professors is that it does not really matter as long as the institution has a good reputation but I'd like to hear from people more active in the field.

>>11007756
Good to know, I was afraid no one would like to join since most people who think abput living as a monk would rather study humanities.

I think if I don't find a wife before I turn 35, I'll jist buy a piece of land somewhere far away from any city and build that place.

>>11007767
Thanks I guess

>>11007739
A whole bunch of mathematicians have made great contributions to physics without any knowledge of it. Just focus on your area and become an expert in it.

>>11007767
>wombs_sleep.jpg

>>11007767
If I edited a journal I would desk-reject anybody who sent me stuff formatted in this two-column bullshit.
It's so fucking ugly. It needs to die.

>>11007772
There's almost no specifically mathematical advice worth giving to somebody entering undergrad. As long as you aren't at an absolute meme-tier university (I mean REALLY meme-tier, even average state unis are fine) your foundations will be basically the same. Name prestige does help, especially if you end up applying to jobs and not grad schools, but name prestige has nothing to do with the math department.

Find a medium-large math department, but err on the larger side if you have to. The only downside to a huge school is that it's harder to connect with profs. At a small school there may not be that many profs worth connecting with at all, there may not be many/any extracurricular math events, there may not be enough students to run a reasonable selection of upper-division and grad courses for you to take, etc.. A small department will hamstring you if you're trying to do math seriously.

Make sure you're happy with the location too. A lot of people don't think enough about the fact that they have to live there for four years and end up at Cornell despite hating the cold or Notre Dame not realizing they're headed to fucksville nowhere or stuff like that. Try to visit first if you can.

>>11007806
All of that is fairly consistent with what I've been told so far so that is a good sign. Unfortunately I don't think I will have the opportunity to visit any universities due to class constraints.

I've got to take a math placement test for the first class in my new major, which will be calc 1 with analytical geometry. I'm super stressed. I haven't used math in about a year because my previous major was in the humanities so I didn't bother.

It's a general purpose test that covers everything from radicals to functions to systems of equations. I have a month, so, how do I best prepare?

>>11007828
elementary geometry and algebra will make it trivial.

>>11007828
I wouldn't worry, people have it worse.. I'm going back into last 3 semesters of mathematics to finish my degree I haven't done anything in 2-3 years. Should be fun..

>>11007828
Imagine not using math every single day of your life and being this behind. Might as well just start from the beginning. No point in trying to cheese it.

>>11007840
Okay. Right now I spent a few hours on it today and went through the whole algebra 1 section on khan academy. I have a month so I plan on using Khan to just review every subject at least 5 or so times. That should nail it in there.

I've got geometry, algebra 2, trig, and precalc to do starting tomorrow.

>>11007845
You poor soul. Good luck

>>11007851
I was a poli sci major. I do, as stated before, intend to start from the beginning in a way. With hard work I will make it. I'm pretty quick with these things so it should be easy.

where do you draw the line between formal and practice proof?

>>11008297
practical*

>>11007700
>unrelated again
I've literally already told you it's Oka.

>>11007650
They had plenty of time and nothing better to do.

>>11007910
uh oh. I wouldn't recommend khan at all. that's smooth brain stuff.
read some good shit like geometry revisited and euler's elements. just to name a few.
if you had more time I'd even say to read understanding analysis by abbott.
>intend to start from the beginning in a way
do you have a background in proofs, set theory and logic? those are pretty good to start with.

How do physicist manage to produce any results given that they so often appear to have no clue as to what the underlying math is about? I have a friend who is in physics grad school now, and he uses a book by Howard Georgi called "Lie Algebra in Particle Physics", and nearly all of it looks something like what's shown in the picture in terms of how material is presented. The entire topological aspect of the subject is never even mentioned and all but most basic of results are never motivated nor proved. And yet they go on to use this book as a segway into QFT and whatnot. I'm just surprised that someone can use those tools without hardly any understanding of the actual ideas behind them. And if you don't believe me just grab the book I mentioned and see it for yourself. I'd say it's literally impossible to properly learn any lie theory using it.

>fell for the Tao Analysis and Hoffman Linear Algebra meme

what level are these books, what else is necessary to learn for a core math degree, and what comes after?

>>11008297
what is the point of this vague question? how the answer will help you?
>>11008339
physicists are retards, what do you expect from them?
>>11008344
you need to learn "proof logic" that is, you should be able to write formal computer verificable proofs, know how to make new definitions and check for typization (that is related to stuff like "1/x when x is zero"). Google keywords such as "First order logic, Fitch style, Definitorial expansion) Also you will need some basic set theory not because it's interesting or something but because it provides all the tools necessary to make the rest of the mathematics formal and precise. For example you can formally write down and formalize Euclidean algorithm in polynomials as a theorem with a simple strong induction or define Gauss elimination by a finite recursion theorem. Having logic and set theory by your side you path basically opens to the rest areas of mathematics where you can start from the beginning: linear algebra, analysis and introduction to topology.

>>11008339
Physical intuition can replace deep knowledge of maths to some extent, I would guess

>>11008497
>what is the point of this vague question?
because formal proofs aren't always practical proofs.

>>11008297
What is a "practical proof"?

Can someone give me a quick intuition on what the [math]\preceq[/math] relation means in this context where it compares two linear spaces? I know that the definition of poset states that its an ordering relation that you can equip a space with, which makes sense if you want to compare elements of that space. But I dont see how that would apply to spaces themselves. Is there an underlying "superspace" that contains the three given spaces as elements and then is equipped with the poset?
For this exercise I mostly just used it kinda like [math]\subseteq[/math] in that it shows that one space is (possibly) bigger and contains the other and it sorta works and makes sense but I dont know if thats just always the case or just happens to be what it means here.

>>11008339
Would like to know this as well. Im pretty decent when it comes to proving theoretical physical theorems, but Im hopelessly lost with pure maths and lag behind a lot there.
I feel like most of the times intuition just happens to be right and every physicist is just too afraid to be called out on his poor maths understanding to actually question when someone says "well that thing just obviously works out to be that other thing", but I think a lot of that is wishful thinking and most physics profs I have talked to usually can easily rigorously prove theorems if you ask them.
I guess also if its just a book on intro to QFT they probably just omitted proofs if they thought it would lead to far from what they actually want to teach in that book if they detailed every single aspect of every proof.
Reading over it doesnt sound too bad to me either. They dont really say much though and I feel like it just explains the definition of smoothness but very possibly my own idea of smoothness is just not very rigorous so any actual mathematician would be disgusted if they were to hear me explain it like that to someone...

>>11008805
>error you are banned
>banned for a post on a board youve never visited
>your ban expired june 6th
>you have to refresh the page, paste your text and forget to upload your image
t-thanks 4channel

>>11008811
Pretty sure it means Y is subspace of X.
Of you are taking direct sums and factoring the original space

What's the best book to start studying analysis, lads? Apostol or Rudin? And I want justifications for which one to study from.

>>11008334
>do you have a background in proofs, set theory and logic?
Not sure, remember doing logic in my super special elementary school gifted class but beyond that idk.

>>11008828
Rudin is tougher, that means that it will help you develop more maturity. Francis Su's lectures in video might help if you're having trouble.
Apostol is easier, but lots of people don't like Apostol's writing style, so keep that in mind.
Both books are good, and whatever one you grab and study will teach you.

>>11008820
So [math]Y \preceq X[/math] is actually just [math]Y \subseteq X[/math] but for spaces instead of sets? and it has basically nothing to do with posets? Or does the definition of poset straight up imply that one space is a subspace of the other when talking about subspaces in a "superspace" or set of spaces or whatever. Thanks a lot anyways though!

>>11008864
That symbol is often used for a "generic" partial order relation when you don't want to use <= for any reason.

>>11008867
Ok I see. So pretty much just have to know what the context is and then apply it intuitively. I dont think Ive seen it in any other context during this class so I guess "one thing contains the other completely and possibly also the other way around" will suffice for my exam...

>>11008828
abbott: Understanding Analysis, you'll get through the book. Rudin has pretty great exercises, however.
I hear a lot of good stuff from pugh: Real Mathematical Analysis

>>11008874
wait do you think of "A subset B" as "B contains A completely and possibly the other way around"?

>>11008828
Read Apostol, do the problems out of Rudin.
It's a good thing to realize as soon as you can that studying anything from exclusively one source is for brainlets. There is no such thing as a single "best" book to learn from, since learning anything from a single source both limits your breadth (since you only know the things a single author decided to include) and restricts you to only the one explanation your author chose, where there might be half a dozen ways of explaining any given topic.
Any time you try to learn anything you should be using minimum two resources, preferably even three or four (note they don't all have to be books; you might be attending physical lectures, you can listen to online open courseware lectures, you can be talking to a supervisor, etc.)

>>11008999
You can interpret the statement as saying that [math]Y[/math] is a (not necessarily proper) subspace of [math]X[/math].

>>11008999
Kinda yeah? Am I missing something with that interpretation of subset? Im only a physicsfag so if the only deviation from that idea is in some highly abstract realms of pure maths Id be lost on it anyways. Or I just never properly understood it, which would explain why Im shit at maths...
Either way Id appreciate a better interpretation if mine is lacking.

>>11009034
why would they use a different symbol for subset? the answer is literally above you >>11009019 it means that Y is a subspace of X
I would give you some advice on learning but you seem like a lost cause so I won't

>>11008339
You look at it from the wrong angle - not being rigorous can be an advantage by making room and time for other ideas to work on. In the end, a physicist does QFT to predict physics, not to prove theorems about QFT as a mathematical theory.
Consider how physicists/engineers are introduced to Fourier transforms a year or more earlier than mathematicans. Because they use it. They will get a PhD without quite having a correct picture of functional analysis, but that's also not the point of it.

If f(x) is bounded by some M, does that necessarily imply that M is in the range of f?

>>11009034
It's not just a subset, it also inherits the vector space structure from the parent set [math]X[/math]. Not every subset of a vectors space (when viewed as a set) is a subspace, a subset has to satisfy some conditions related to addition of vectors and scalar multiplication for it to be a subspace of a vector space.
For example, [math]\left \{ (0,1),(1,1),(1,2)\right \}[/math] is a subset of [math]\mathbb{R}^{2}[/math] when viewed as a set, but it's not a subspace of the vector space [math]\mathbb{R}^{2}[/math].

>>11009062
sin(x) is bounded by 2, i.e., |sin(x)| <= 2

Why not read the first two sentences of the "Bounded function" wikipedia article to answer your question?

No, the function sin(x) on the reals is also bounded by M=7.

>>11009066
hello, my sin(x) minded friend

>>11009062
No, you can investigate under what condition do [math]m=inf \left \{ f(x) :x\in A\right \}[/math] and [math]M=sup\left \{ f(x) :x\in A\right \}[/math] belong to the range of a bounded function [math]f[/math] with domain [math]A[/math].

>>11009069
>>11009075
>>11009066
I guess I meant the minimum bound, but you guys bring up a good point. Thank you.

>>11009078
>least upper bount
Weierstrass extreme value theorem is the most useful one for this. If it doesn`t give you the extreme value you need, you`ll need to invoke specific properties of the function.

>>11009078
>minimum bound
It achieves it if f is continuous and the domain is compact. Otherwise it might not.

>>11009065
>a subset is not just a subset
Sorry but what? I though we were talking specifically about subsets, not subspaces? We may be missing each others points here...
Either way I can see how a subspace has to inherit the structure of its parent but not necessarily all of its field (I think) or whatever that space is based on. But for subsets what I wrote should hold, shouldnt it?

How is this stack for starting at undergrad level?

I'm not sure what would come after (Munkres' Topology?) - I imagine you could also add in Enderton for Set Theory and Logic.

>Tao - Analysis I & II
>Hoffman & Kunze - Linear Algebra
>Feller - Probability I & II
>Knuth - Concrete Maths

>>11009148
>probability
I'd recommend waiting until you have a solid grasp of measure theory, and I don't know what it is that Tao covers, but Donald is good. It has this kino red cover with measuring tape.
>concrete maths
That sounds like a meme.

Also, ask this sort of babby stuff in sqt.

>>11009148
Why don't you try and find out?

>>11009147
>one thing contains the other completely and possibly also the other way around
This is good enough of a interpretation of a subset, nothing really wrong with it

>>11009164
try to prove with this definition why the empty set is a subset of the empty set

>>11009157
concrete maths is essentially the maths required for the Art of Computer Programming volumes (so some discrete stuff, but only a meme if you don't complete TAOCP afterwards)

>>11009180
>nothing contains nothing
What's the problem here?

Assume I don't know any linear algebra. Which book would you foremost recommend? Opinion on Linear algebra done right by Axler?

>>11009276
how can it contain something if it contains nothing?

>>11009378
Linear algebra and its applications by Gilbert Strang

>>11009148
The problem with making yourself "curriculums" is that you're trying to make yourself a math degree without knowing what a math degree contains so you just pick out a bunch of titles that sound cool, and end up jumping from basic linear algebra to a 900-page comprehensive probability treatise from 50 years ago to an introduction to combinatorial methods in computer science.
Just pick up a book you want to read and read it. If you find yourself missing prerequisites, then you go and learn them.

>>11009480
Thank you, i hope it's not too heavy. I have difficulty reading math textbooks

How do I avoid the trap of wanting to be a generalist? Every time I think to myself that I'm going to focus on a particular textbook (or two, or three) I keep adding more and more because I don't want to feel like I'm missing out on some other potentially cool topic. I want to make sure I at least learn some of the most accessible stuff, as in anything interesting that is within the scope of an introductory graduate level course.
In a typical grad program what is the minimum each student will do from each of the major topics (algebra, analysis, topology, etc)?

>>11009571
>In a typical grad program what is the minimum each student will do from each of the major topics (algebra, analysis, topology, etc)?
Quite a bit of algebra and analysis is generally expected. At least two semesters of each is pretty normal. Topology expectations are lower, most students only take a single algebraic topology course and some unis don't even make this a requirement (although they really should).
If you want to get a pretty good handle on what the average PhD student is "expected" to know, most major programs publish syllabi for their qualifying exams and past exams. The purpose of these is to more or less prove that you weren't jacking off for the first year and deserve to stay in the program, and roughly speaking you can say that they cover the minimum everybody is supposed to know.

>>11009551
It is better to read it as an additional book, that is, if you already have general picture in mind because he likes to focus your attention on not so necessary details. So you should look for other book/books as a main book

>>11009148
Knuth defined the discrete maths most computer science degrees everywhere teach their students (he's only missing graphs, and rightfully so. Graph theory should br treated as it's own subject).
The book is good, but very hard. Although the difficulty decreases as you move forward.
Also, his introduction to finite difference calculus is too brief, and if you get interested in that you'll need to look somewhere else.

>>11002774
Where is the homotopy theory?

>>11009905
In algebraic topology.

Will I ever start to understand or pick things up faster? I've been studying math for a couple years and I'm still pretty slow to have passable comprehension with some things.

>>11010362
Nope, it'll only get slower as you age.

>>11010190
Neither our subject nor its interaction with other areas of inquiry is widely understood. Some of us call ourselves [math]algebraic~topologists[/math], but this has the unhelpful effect of making the subject appear to be an area of topology, which I think is profoundly inaccurate. It so happens that one way (and historically the first way) to model homotopical thinking is to employ a very particular class of topological spaces. Today, the praxis of homotopy theory interacts with topology no more often than it does with arithmetic geometry and category theory, and the interactions with areas like representation theory are growing rapidly. [math]Homotopy~theory~is~not~a~branch~of~topology.[/math] This is important, because as long as homotopy theory is classified under the umbrella of topology, there will be errors of judgement in who is considered competent to judge our work; the results of this at journals, on the job market, and in funding is real and lasting.

>>11010605
>maps the nerve of your categories to simplicial sets
>uses Brown representability on your homotopy spectra
Heh, nothing personnel...

>>11010622
In my opinion, homotopy theory is closer a branch of category theory than a branch of topology, although neither is accurate.

>>11010659
>homotopy theory is closer a branch of category theory
It's the other way around.

what is the most fruitful field of research in math right now? what is the most interesting recent discovery?

>>11010775
At least at our current level of knowledge, higher category theory in the sense of (n,k) categories with k>1 cannot really be said to be just a subset of homotopy theory. I would agree that it is not fruitful to try to draw a line between (infinity,1)-category theory and homotopy theory.

This is a reasonably pointless argument, however. In hindsight, to avoid this, the post you are replying to should have said
>In my opinion, homotopy theory is closer to category theory than to topology, although it is not equal to either.
I am not trying to say anything negative about any field, I am only objecting to the description of homotopy theory as just part of algebraic topology. They are both vibrant and beautiful fields, but they are distinct.

>>11010802
>what is the most fruitful field of research in math right now?
In what sense? If you mean by an objective metric, such as which field gets the most funding, then presumably the answer is something like PDEs (or a branch of applied math, if that counts as an answer). If you mean by a subjective answer, then the answer would be subjective.
>what is the most interesting recent discovery?
The most interesting recent discovery to someone in field X would most likely be a discovery in field X that is only of marginal interest to someone in field Y. Of course, there are exceptions, with certain theorems transcending these boundaries, but they only come once every some number of decades.

/mg/ is the worst general out of all the generals I have seen on 4chan

>>11010867
I see you've never seen the kpop general.

>>11010816
>if that counts as an answer
Why would it?

>>11010885
Obviously I don't know, which I why I put that in a parenthetical. Do you have any less inane comments to make?

>>11010867
>/mg/ is the worst general out of all the generals I have seen on 4chan
>>>/reddit/

>>11010899
>I don't know
Why did you ask then?

>>11010979
Thanks for answering my question with a solid NO.

>>11010982
I didn't even read the entirety of your post, so I don't know what you're referring to. Can't be bothered wasting my time on inane garbage like that.

Anyone help me with this problem? I tried a few answers but got it wrong and I only have 1 more chance.

Probability = number of wanted outcomes/number of possible outcomes

So from seat 2 we can possibly go to (4,5,6). i think to find m/n, I want to multiply the probability of 4, times probability of 5 times probability of 6. but this is where I am confused.

At p4, i have a 1/3 chance of landing on 1 (1,2,6), at p5 i have a 1/3 chance of landing on 1 (1,2,3) but at p6, our only possibilities are (3,4,5) so wouldn’t that give me 0/3 chance of landing on 1?
Am i looking at this incorrectly?

>>11010867
y

>>11011189
you can write E_i for the expected time if you start in seat i and want to end up in seat 2
then you get equations like this:
E_1 = 1 + 1/3( E_3 + E_4 + E_5)
basically the equation says if you want to go from 1 to 2, then you either go from 1 to 3, 4, 5 and continue from there
do the same for other starting points, this leaves you with linear system of 5 equations which you can easily solve.
There is also a subtlety: this system will have a solution, but also E_1 = ... = E_5 = +inf is a solution, considering the wording of the problem maybe you can ignore it, but normally you should think which case is right

>>11010867
then you've never been on /tv/

>>11011375
ty anon, this helped me a lot and i got the correct solution now. I was going about it all wrong, i didn’t even realize linear algebra was what I needed

>>11010867
>>11010867
/mg/ isn't even the worst general in /sci/.
Hell, it's the best general in /sci/.
>guys my foot feels funny what's going on
>I've got a mechanical engineering degree how do I get a fucking job
>help me with homework
>I FUCKING LOVE ELON
>excel spreadsheets
>climate change generals

TLDR: YOUR 2 CENTS CAN HELP A LOCAL AUTIST HOW TO SELF-LEARN MATH BECAUSE THE FUCKING UNIVERSITY SYSTEM IS NOT WORKING FOR MY ADHD MIND AND I STILL HAVE AN ABSURD AMOUNT OF MATH TO GO

>Started going to tutoring for math recently
>Tutor is actually able to get me to understand the material
>I am fucking swallowing it up
>I don't fucking see how calculus will help me learn programming--especially since it's been my hobby for years and Calculus has not come up one goddamn time--but alright.
>Think back to highschool
>9th grade: Middle-aged male teacher who hates children, yet, still reeked of pedo. Constantly yelled at that one black kid who actually never did anything wrong (most students struggled)
>10th grade: Middle aged teacher who hated kids except he ripped on everyone equally for not being able to understand "such simple math" (Most students struggled)
>11th grade: Angry lesbian yelling about algebra and trig at 7:30 AM (90% of students dropped out or failed)
>12th grade: The return of the lovehandled pedo (Students struggled)

Literally one person passed my freshman Algebra II final... With a C. Everyone else was D and below, we . I fucking swallowed up trig with my other professor, they knew how to teach.

Whatever my current professor is doing is not helping me learn but I need this for my degree. My tutor has taught me some organizational shit and I heard about RPN and it is so much fucking easier to read, but I still need some help.

>>11011922
Elon musk is a retard

>>11010867
/mg/ been the worst general in 4chan is precisely why I’m here. Been around dummies like all of you make me feel smart.

>>11007624
Based Yukari-poster, do you make these mathphys manga edits yourself?

>>11011973
I'm not sure how much I can help, but you can add me on discord and ask me questions there if you wish.
I'm a grad student so I should be able to guide you through entry level material.

>>11011973
Jesus, you've had some bad teachers.

>>11011990
What's your discord?

>>11012015
michiru#6658

>>11009148
Use this instead of Feller

Sid Resnick's A Probability Path

Olav Kallenberg's Foundations of Modern Probability
And this before Tao for Measure Theory.
http://measure.axler.net/

This for complex analysis
complex analysis gamelin

>>11011211
The people in these threads are insufferable assholes who only come here to posture about being more intelligent than everyone else. See: the replies to my post.

>>11002602
It's only 300k starting if you get a job at a top quantitative hedge fund or Google Brain / Deepmind.

>>11012059
t. cope seethe dropout failure beta bitch mathlet never gonna make it physishit stupid popsci redditor

>>11012059
>>11012288
Fuck off.

>>11012059
>assholes who only come here to posture about being more intelligent than everyone else
>implying that's in any way a bad thing instead of absolutely hilarious

>>11007739
what book is that?

>>11011986
No, these are excerpts from the manga "Wild and Hausdorff Hermiticity".

>>11007523
Girls in my Physics department are all ugly.
I'm dating a qt tranny from Math department

>>11012466
gay

>>11012455
did someone actually make a full edit of wild and horned hermit or are you joking around
if the former, i'd love to read it. WaHH was kino.

>>11012455
>>11012515
I need it too...

>>11012515
>>11012535
I don't know anon, am I joking around?
Don't forget to check out Funtorial Scrollery too

>>11012537
>Funtorial
Functorial*, yikes

>>11012537
Seen that there are no results in google for any of the two, I would say that you are joking around

Can I get a recommendation for a rigorous upper level *introductory* algebra book. What I mean by this is a book that assumes a great deal of maturity on the reader's part, but is otherwise mostly self contained.

>>11012573

>>11012584
Grillet's Abstract Algebra is my *personal* recommendation. Pirate it off libgen.
Lads here constantly shill Aluffi's Algebra Chapter Zero.
There's also Lang's Algebra and Rotman's Advanced Algebra, but those are dogshit.

>yukariposter will never fuck me in the ass

>>11012600
>talking shit about Rotman
fight me

>>11012584
Aluffi or Dummit/Foote

>>11012537
I haven't gotten to that page in normal FS yet. Seems important.

>>11012584
Look mom, he posted it again!!! Everyone recommend Aluffi!!!
Sometimes I wonder if this is Aluffi himself just trying to get off over the fact that everyone eats up his dogshit book.

>>11012627
Have you read Aluffi? What's wrong with it?

>>11012602
Why the homophobia?

>>11012627
what's so horrible about aluffi ?

>>11012627
mup da doo muh categorical viewpoint
>defines functors on page 500

>>11012606
>just looked up Rotman
anon, I...

>>11012635
>>11012643
>>11012646
Oh yeah! Okay! Hahaha!!! Let's all just dogpile on the innocent guy stating his opinion! You fucking morons are pathetic. Nothing to defend yourselves. BURDEN OF PROOF YOU IRREDEEMABLE SHITS! None of you have a future in mathematics, that's for sure. Pathetic, just absolutely pathetic.

>>11012667
are you being serious ?

>>11012584
https://www.math.ens.fr/enseignement/archives_pedagogiques.html?type=1

>>11012640
because you're a deranged schizo

>>11012584
Jacobson, Basic Algebra.
Don't listen to the fags telling you alluffi/bourbaki/lang. Those are not good books to learn from.

>>11012640
theres no homophobia
I want to be with you

>>11012679
Not sure I understand what the alternative would be? Lmao.
Stupid post, you're outing yourself.

>>11012753
>Have you read Aluffi? What's wrong with it?
>what's so horrible about aluffi ?
that's a legit (and politely stated) question, answer it

>>11012667
Tone down the paranoia. If you're gonna call a book dogshit, you better explain why that is. Else everyone will think you're a hipster hating on things because they're popular.

>>11007086
sorry for the bad audio

https://youtu.be/fTBL4TmZNRo

>>11009571
Oh God I have this problem too. I always feel like I'm missing out. I know your pain anon.

Can someone who isn't a circle jerker, tell me why I shouldnt read allufi? I really want to know what the advantages/disadvantages of his approach are.

>>11013062
read it and find out

>>11013062
Depends on your goal in life.
>why should I go to a music concert
Well why not. It's nice to consume other peoples work if it's well crafted. That's always the answer for me anyway.

>>11013062
it's better to read something than to keep worrying about what to read. the book is okay, just start reading and see for yourself.

>>11012455
>>11012537
>>11012597
I just can't imagine the levels of autism necessary to have both enough knowledge in mathematical physics and a drive to make touhou manga edits with actual research level mathphys content that kinda makes sense.
Like, I'm actually envious.

>>11013099
It's a variant of the "rubber ducky" method programmers use, really. I make these memes to organize the fundamental ideas and make sure what I've written down actually makes sense. Then I refine them once more and transfer to TeX notes.

>>11007742
sounds fun, sign me up senpai

>>11013063
>>11013081
>>11013091

I'm interested in abstract algebra, and category theory, seems from what I'm gathering at the slight hints in this thread, that he talks about abstract algebra through a category theory lens? If so, that would be cool, I would definitely pick it up. I'm mostly looking for a refresher on groups/rings/fields/ because it has been awhile since I took an algebra course.

Is that enough context for someone to give me a fucking straight answer dickheads?

Has anyone here tried to read something that is barely comprehensible to them at their level? Would this be a good way to increase maturity?

>>11013136
That's cool. Your works are probably the highest tier meme content coming out of \sci\, lol. But that's enough asslicking for today. Wish you all the best, anon.

>>11013178
When I was a student I generally read some books there were a year or so ahead of me. It helped.
But I also sometimes got things like K-theory and didn't get much out of it.

>>11012739
>>11012640
Yukariposter please respond to my feelings.

>>11013272
Be advised that I do not post things such as "I'm not a 'he'" or "why the homophobia", or any other general comments that do not contribute at least a little to the mathematical content of the thread. Whoever replied to you is not me.
I am nevertheless unable to reciprocate your feelings, however, as I am already spoken for. Sorry to disappoint.

>>11013285
Im going to fucking hang myself. Why does love hurt so much?

>>11013302
If you think yukariposter is a good partner, you've set your expectations way too low. Try punching higher with some confidence. You can have some of mine I won't need it.

>>11013321
how dare you talk about the man I love like that?

>>11013358
You're sweet. but must die emotionally to be unblinded.
this is the way it must be.
you're treated this way by others for a reason.

Could you lads at least shitpost about maths instead of homoerotic feelings?
>>11013178
Yeah, I just gave up and came back later.
No point to reading stuff where you don't know half the constructions and definitions.

>>11013167
Pretty much all modern graduate algebra textbooks use categories when appropriate. The only difference with Aluffi is that he turned his categories into a marketing gimmick and then did a shitty superficial job of using them.

>>11013099
>actual research level mathphys content
nigger one of the comics you're replying to is like halfway through a semester of Lie theory at most
fucking circlejerkers

>>11013178
>Has anyone here tried to read something that is barely comprehensible to them at their level?
Yes. It was horribly frustrating and unproductive and I barely learned enough to squeak by (since I was only reading them because I needed to).
>Would this be a good way to increase maturity?
No. There is a sweet spot of difficulty you need to hit.
When you read stuff that's way too advanced what tends to happen is that your understanding becomes very atomic; in order to make any progress at all you have to break the text down line-by-line, and with a lot of hard work you can understand each individual sentence in isolation, but you will find it almost impossible to piece those together into anything that resembles actual understanding of the subject.

>>11012584
The absolute best way to learn abstract algebra is to spend weeks or even months not actually learning algebra but fretting over which way is optimal because the vast swathes of information and ratings you have easy access to on the internet have left your mind anxious about doing anything any other way than what the hivemind tells you is the 'best way'.

True algebra masters can go years without ever learning a single theorem in algebra. Honestly mate you're best to just keep downloading dozens upon dozens of beginner algebra textbooks, never reading them, never starting them, and continually posting on /sci/ to find out which is the best way because you DO NOT under any circumstances want to spend 10 minutes doing anything in a way which is anything less than the best way. Better to spend months doing nothing instead.

>>11012584
>rigorous
How rigorous are we talking? When I landed in college I took a class on logical proof and greatly enjoyed it. I had a bit of a knack for doing proofs quickly in my head. Are you of the same intellectual stature?

What are some cool things about sets with one element?

>>11013369
I'd do whatever it takes to win his love

>>11013634
>his

>>11013634
why do you deserve it?

>>11013659
Presumably because she's a cute physishit?

>>11013659
Im devoted.
>>11013644
?
>>11013695
I am not a female.

>>11014054
you'll take the pronoun that he assigns you.

>>11014056
Yes, but only if he instructs me to do so. Not you.

>>11013167
Aluffi is a great book, I only truly understood Algebra after reading it. I think what some people don't like about the book is the level of the exercises or the fact that Aluffi puts some "jokes" randomly on the book. Theorywise though the book is top tier.

For high level exercises use Jacobson.

>>11013596
A topological space being T_1 iff singletons are closed comes to mind.

>>11003905
but why

Yup, I just decided the areas that I will specialize in:

Several complex variables
Category theory
Mathematical logic
Analytic number theory
Algebraic topology (thinking)
Complexity theory (*)
Quantum field theory(*)
Philosophy of mathematics(*)

(*) Just as hobbies

What do you guys think of my character build?

>>11015092
>Mathematical logic
>Philosophy of mathematics
Just pick this. The rest is unnecessary.

>>11012762
>>11012765
>I don't understand you! You're on trial!
Autism. Fine, I'll share my objective criticism. The exercises are obnoxiously difficult and poorly expressed, and the wording and presentation of material is awkward and confusing. After I got an A in my Abstract Algebra class with Fraleigh I feel as though I should be the last one having a tough time understanding an introductory level Abstract Algebra text, so it seems to me objectively to only be possible that the book is written for morons.

>>11013386
>homoerotic
I'm not a "he."

@11015154
>obnoxiously """"difficult""""
>written for morons
lmao

>>11015092
>several complex variables
Absolutely kino.
>category theory, mathematical logic
Wastes of time.
>analytic number theory
Not my cup of tea.
>algebraic topology
Not optional, you need quite a bit of it for several complex variables. Specially sheaves. Several complex variables lives and breathes sheaves.
>the entire remainder
Dogshit.

>>11015408
Why is Category Theory a waste of time? It's constantly shilled here and looks really nice, I have a thing for very abstract areas.

Thanks for the info on algebraic topology. Anything more I should know?

>>11015092
>Several complex variables
Well, have you decided which ones?

>>11015408
>Category theory is a waste of time. You gotta learn some useful topics, like sheaves.

>>11015707
I pick the nome [math]q = \exp \tau[/math] desu.

>its another "feeling suicidal because you don't feel competent" episode

Stop just feeling and finally act it out. The world would be better without literal scum like you constantly defiling it.

>>11015798
Talk to an MD and start exercising and give yourselves 3 months to decide if you want to or not

>mg devolves into circle jerking, avatarfagging, and general homosexuality

It was just a matter of time I suppose..

>>11013272
>>11012739
>falling in love with squat mongoloids on the internet

you're serious aren't you?
that's amazing.

>>11015798
itsnot going away better deal with jt

>>11013695
that doesn't answer my question. Cringe and retarded.
>>11014054
>Im devoted.
worthless answer.

>>11015974
>Cringe
Refer to >>>/r/eddit/.

>>11015154
>>I don't understand you! You're on trial!
:D

>>11015988
dilate

Does anyone know the name of of the channel of a young guy who makes videos about set theory and proofs, I've seen his channel linked in a previous /mg/ but the thread is 404.

>>11016558
Nevermind I found it, it was :

https://www.youtube.com/channel/UCcrSMnEYhIPX_p127jI23qw

Is Calculs from Stewart appropriate as a resource for "computational exercises"? I'm studying Analysis I from Tao but it lacks applications of the theorems and I need to train for things like calculating integrals and limits. Any other recommendations?

>>11016572
Maybe grab some russian text, like Demidovich's Problems in Mathematical Analysis. It's literally filled with thousands of problems to work through. A sample can be seen in the pic.

>>11015712
Studying category theory for itself is a waste of time, constructions in category theory are extremely convenient.

>>11015481
it's constantly shilled here by at most 1 autistic anime poster who is coping for having spent so many hours studying it.

>>11016751
What do you mean by that exactly?

>>11016833
Studying category theory for itself is a waste of time, constructions in category theory are extremely convenient.

>>11016848
Yeah, but what do you mean by that exactly, brainlet?

>>11016870
Studying category theory for itself is a waste of time, constructions in category theory are extremely convenient.

>>11016870
While Grothendieck's technique of abstracting away uneeded parts of the problem to distil it into its basic aspects and facilitate proof is an extremely powerful tool, pursuing abstractions of current concepts with no particular goals is barren.

>>11016833
>>11016870
Ignore him. If you stay in math, you'll come into contact with a lot of people like him, who think that achieving deeper understanding on the tools you use is a waste of time. Just shut up and compute!

>Ignore him

*Ignoring the brainlet who can't into Category Theory*

>>11016572
Calculus Peter Lax

I've just started a maths major. Any recommendations for a book to learn proofs and build maturity?

>>11017796
book of proof by hammack

What is the true power of Linear algebra?

>>11017928
functional analysis

>>11017928
Gaussian Elimination

>>11017796
No such book exists. You need to know rules of inference. Google Fitch style. Also you need to know how to create new definitions and check their well-definedness. Google definitorial expansion. On top of that you write proofs in some language (For example, In English, in some formal language like FOL (First Order Logic), or Mizar language etc).
So Rules of inference, language that you write in and typization form a system. I could give you a system that I'm using. Also there is a logic room at mathstackexchange.com you can ask there.

>>11017875
>>11018074
I didn't mean a book on proofs specifically.
I'm looking for a modern rigorous text in any field that I may read through and learn proofs that way. Sorry for the confusion.

>>11017928
Linear algebra, but over division rings instead of fields.

Struggling with a simple graph theory proof. It seems a little much for /mlg/ or /sqt/ but the folks here will probably be able to prove it

Let a simple graph [math]G=(V,E)[/math] be bipartite,

(i.e., there exists a choice of sets [math]X \subseteq V[/math], and [math]Y /subseteq V[/math] such that for every element of our edge set [math]E[/math], [math]e \in E[/math] is composed of [math]x \in X[/math] and [math]y \in Y[/math])

and that [math]G[/math] is also self-complementary,

(i.e., [math]G \cong G^c[/math], i.e., G is isomorphic to its complement)

Show that G must be such that [math]|X| \leq 2 [/math] AND [math]|Y| \leq 2 [/math]

Essentially, you can't have a bipartite and self-complementary simple graph on more than 4 vertices. Sorry for the long proposition, I'm having fun with latex.

My best approach is trying via contradiction, i.e., assume a G has ALL of the desired properties (simple, bipartite, self-complementary) and that its respective bipartitions have orders of larger than 2. So I list the vertices, i.e., [math]v_1, ... , v_x[/math], and [math]v_x+1, ... , v_y[/math]

But I don't quite see how it leads to a contradiction. Does it have something to do with the fact that self-complementary graphs also need to have vertices in multiples of 4? (something we showed earlier in the assignment)

>>11018534
Would it make more sense to look at the adjacency matrices? matrices being equivalent is trivially obvious and also shows isomorphism, but what characterization is there for bipartite matrices? I suspect dividing it into quadrants and looking at the "northeast" quadrant and the "southwest" quadrants, but I'm not sure

>>11018089
>I didn't mean a book on proofs specifically.

Then you were wrong. And Hammack's book has plenty of examples from things like discrete mathematics, number theory, naïve set theory, etc. etc. What, do you think he just slams a bunch of proof techniques down on the ground and says, get fucked?

I guarantee if you're just starting your math major you probably suck dick at writing proofs and formal mathematical reasoning.

>>11018534
X and Y are disjoint, innit?

>>11018609
yes...

>>11018617
Fuck man, the problem is really stupid, so I feel bad explaining it.
But if G admits a split, then there are no triangles (a, b), (b, c) and (c, a), for obvious reasons. X has all edges in the complement, since it has none of them in G, so if it has more than three sides it has a triangle.

>>11018641
this is correct

>>11018641
>>11018678
I think I see what you're saying, the idea being that once I have 3 or more vertices in either X or Y I will inevitably define a triangle, either in G or its complement - and therefore prevent the graph from being bipartite, or from being self-complementary.

Is that right?

>>11018694
Nah, not quite.
X has no edges to itself in G, so it has all edges to itself in the complement, so if X has more than three vertices, it has a triangle.
But G doesn't have any triangles, so it isn't isomorphic to the complement.

>>11016978
needsmorejpg.jpg

>>11017796
Bourbaki.

>>11017796
Take introduction to set theory by Jech and do the proofs from the beginning by yourself and then check how they compare to the existing ones in the book. If they start to differ and you want to check if your own proof is correct you should learn the things that I mentioned in my previous post.