/mg/

[Anonymous No.11491787]

math alks
formlly >>11482035

bootstraps edition

[Anonymous No.11491798]

>>11491787

[Anonymous No.11491801]

>>11491798
what if you made a living organism like a klein bottle by rippin a hole into it and putting its anus at its mouth? how would it work out?

why do ppl say klein bottles are from 4d if they look like 3d? and why do these things feel paradoxical even if theyre totally logical. something about lacking a normal trait through fliptricks.

[Anonymous No.11491846]

>>11491801
>why do ppl say klein bottles are from 4d if they look like 3d?
nobody says "klein bottle is from 4D". it's a 2D object which cannot be embedded in a 3D space, but can be embedded in a 4D space. it's not from anywhere, it exists on its own.
>and why do these things feel paradoxical even if theyre totally logical
what's paradoxical or illogical about a Klein bottle?

[Anonymous No.11491847]

>>11491798
It's odd, I've seen a resurgence of videos about the Klein bottle...
But if I'm not ill-informed, I always thought the "Klein bottle" comes from the translation of the German "Kleinsche Flasche", which was a translation of the original "Kleinsche Fläche", which means "Klein surface".

[Anonymous No.11491852]

>>11491847
oh, yeah I see the Engl. Wikipedia article says this too. Maybe I even picked it up from there some time ago..

[Anonymous No.11491860]

>>11491846
what do you mean by embedded? i see it in 3d isnt it embedded there?

its not paradoxical, it just feels paradoxical because it loses a trait of normal things by doing a weird switch flop

[Anonymous No.11491870]

>>11491860
The 3D glass object you see people represent the bottle with is not the object as mathematically defined. The Klein bottle is defined as a manifold and as such has a tangent plane at each point. Wheres the glass object has this intersection where, for points at the intersection, you can't define what exactly the tangent space is (it's not unique). That is to say, the Klein bottle doesn't wouldn't have any self-intersection in any embedding. (The embedding can't be in R^3, because there we can proof that we can only represent it with that intersection.)

[Anonymous No.11491877]

>>11491860
The 3D glass object you see people represent the Klein bottle with is not the object as mathematically defined.

The Klein bottle is defined as a manifold and as such has a tangent plane at each point.
Wheres the glass object you see has an ringlike self-intersection where, for all points of this intersection, you cannot define what exactly the tangent space should (it's not unique, there's two tangent planes). That is to say, the mathematical Klein bottle doesn't have any self-intersection in any embedding and wouldn't have a self-intersection in a faithful representation. As can be proven, the embedding can't be in R^3, we can proof that we can only coursely represent it (but not really) with that intersection.

[Anonymous No.11491882]

>>11491860
>>11491877
maybe I should add this for differentiation (no pun intended)

https://en.wikipedia.org/wiki/Immersion_(mathematics)

[Anonymous No.11491901]

>>11491860
>what do you mean by embedded?
realized as a subspace. first you need to acknowledge that objects do not a priori live in some ambient larger space. this may be against intuition for some because of how human imagination works. you cannot picture "just a point" or "just a sphere". you can only picture a point or a sphere living in a portion of a 3D space. this is simply how brain works.
take for example a circle. you probably think of a circle as a subset of the plane. but you can also realize it as a subset of R^3, for example as the set of points having the same distance from the origin and having the z-coordinate equal to zero. it can be also realized as a subset of some cylinder, subset of a sphere etc. this is to say that a circle, as an abstract entity, can be embedded into a plane, a 3D space, a cylinder, and a sphere. there are other mathematical models of the circle, for example you can take the interval [0,1] and identify the end points, so that passing through 1 moves you back to 0 (clearly this is like walking in circles). this is topologically also a circle, but it's an abstract circle - it's not defined as a subset of some bigger ambient space.

[Anonymous No.11491914]

Is it worthy reading the 900 pages of Tannenbaum's Ordinary Differential Equations considering that I want to specialize in Complex Geometry or Algebraic Geometry?

[Anonymous No.11491920]

>>11491914
My response to "is it worth reading X" is always yes. I mean we spend so much time doing shit, reading one more book is always good.
Besides, you won't read it straight through anyway. Reading math books is a quest through time.

[Anonymous No.11491921]

Is it worthy reading the 900 pages of Tannenbaum's Ordinary Differential Equations considering that I want to specialize in Complex Geometry or Algebraic Geometry?

[Anonymous No.11491924]

>>11491877
>>11491882
so saying its immmersible is just like a weaker embedding, where it fits in 3d and is injective but maybe not all of the properties remain (such as smoothness of wiki), and in kleins case the having 2 tangent planes.

btw is this singular tangent plane thing for klein and vector for mobius , is this what they call the non orientability?

and i think thats what i mean by the paradox, its still so weird to me. you can remove orientability, or as ive seen elsewhere, the notion of inside/outside, yet still have it be closed and loop back to itself, without any notions of projective space points at infinity.
i guess this specifically matters because, why should inside/outside have anything to do with paradox, its not a necessity of reality well - i think containment and boundaries of things are very valuable philosophically, they represent void within and non void without, separating void. but if you skip past this you have a self stable, or rather, closed structure, that also doesnt cut void.
i gues what im trying to say closedness without boundary is so weird
even the word closed and bound are linguistically wired in our brains to feel similar. the fact that they're differnet., of course its not a paradox. but, it shows subtle ripples from the origins of logic and structure, its so beautiful i wanna cry

[Anonymous No.11491925]

>>11491920
It's 900 pages though, I don't even know how important ODEs are in complex/algebraic geometry

[Anonymous No.11491944]

>>11491924
embedding must be injective while immersion is not necessarily injective. however immersions are precisely "locally embeddings" - if you restrict the map to a small enough open set, you always get an embedding. I've made a picture to show what I mean. it's a map which takes a circle and maps it into the plane as a figure eight. this is not an embedding because of the self intersection (and it's true that circle and figure eight are simply different spaces, they have distinct topological properties). however if you restrict to a small portion of the circle and forget about the rest, it's always an embedding, in this case of an interval into a plane.

[Anonymous No.11491946]

>>11491921
Nah.
>>11491925
>I don't even know how important ODEs are in complex/algebraic geometry
They aren't particularly important.
There's
>muh proof of the Calabi conjecture using PDEs
m etc, but overall I don't think I've ever seen ODEs in complex or algebraic geometry.

[Anonymous No.11491947]

>>11491901
i see, so i guess anon was saying it can be realized in 4d space butnot fully realized in 3d so not embeddable there, under certain realization methods at least.

by your definition of circle though, doesnt circle mean something different depending on what space youre in, since spheres and 4-spheres are equidistant from orig in different spaces?

[Anonymous No.11491948]

Threadly reminder that tohou poster is the most intelligent poster here

[Anonymous No.11491952]

>>11491944
okay okay, this makes sense. what is non orientability btw? i guess this is different than what you meant by two tangent planes because its one per each intersection, not negative vs positive confusion.

but yeah can u explain non orientability? also, ur the guy who made the drawing helping me with stokes theoreom! thank you, it helped me understand it and get a better intuition for parametrics in general

[Anonymous No.11491953]

>>11491946
Thought so, which undergraduate subjects should I focus then?

[Anonymous No.11491956]

>>11491947
I'm that anon.
there are topological properties and there are geometrical properties. a topological space without extra structure doesn't posses any geometry - it's meaningless to speak of lengths, volumes etc. circle embedded in a plane (let's say) inherits it's geometry from the ambient space. it has a definite volume (in this case volume = circumference) and you can measure lengths of its tangent vectors for example. circles of diameter 1 and 2 respectively are distinct from geometry point of view, but they're the same from the topology point of view.
the [0,1] with points identified circle is just a topological circle. it doesn't have any length or diameter.

[Anonymous No.11491965]

>>11491953
Complex analysis, algebra, topology and differential geometry are the main things, in my experience. Also functional analysis.
>inb4 dude Kugelsatz results from complex analysis don't work on SVC, which you'll actually need for complex geometry
Kinda sorta yes, but it's still pretty useful and brings in a lot of intuition.

[Anonymous No.11491977]

>>11491965
Thanks, you're awesome. What CA and DG books you recommend, my man?

Also, when you say topology, does it include Algebraic Topology as well?

[Anonymous No.11491983]

>>11491956
hmm... i feel like rigor is needed to thresh the meanings out. but one thing, for circle of r = 1 and 2, couldnt that be the equidistant topology with a definition for r added on? and for the [0,1], its like walking ina loop but it could be any closed loop not just circle. and the last thing is, wjat if you define a space with vector elements containing every <a,b> that has a norm of 1, but no other points in the space. then havent u defined a geometric circle without a space? if u were to ever draw it you need a space otherwise its floating poonts but it holds the algebra of a geometry and u could get the space separately from the circle space and just plussem up, altho its kinda cheating and addition is equivalence but definitions bleh

[Anonymous No.11491986]

>>11491977
>CA
Eisenbud.
>DG
Tu.
>Also, when you say topology, does it include Algebraic Topology as well?
Yeah. Read Fuchs-Fomenko.

[Anonymous No.11492005]

>>11491986
>Eisenbud
But he doesn't have one...
>Tu
It's graduate level though, I'm still undergrad

[Anonymous No.11492011]

>>11492005
>It's graduate level though, I'm still undergrad
what's the difference?

[Anonymous No.11492014]

>>11492005
Oh, CA was complex analysis and not commutative algebra.
I like Kodaira. It should also get you quite some experience with Riemann Surfaces, which is ultimately one of the things you want to study.
>Tu is graduate
I don't really have undergrad recommendations for differential geometry, my bad.

[Anonymous No.11492021]

>>11491952
my posts are >>11491846 >>11491901 >>11491944 >>11491956

>but yeah can u explain non orientability?
okay, so let's take GL(n), the group of all invertible linear transformations. this has two connected components - one is maps with positive determinant and the other is maps with negative determinant. in linear algebra, a map with negative determinant changes orientation of the vector space, I hope this is intuitively clear.
so what does it mean when a space is non orientable. pick a point in the space and pick some basis B1 of the tangent space. now consider a loop in the space starting (and ending) in your point. I'll skip technicalities, but you can continuously transport your basis along the loop and you will end in your point but with a different basis B2. the bases B1 and B2 differ by some invertible linear map, namely an element of GL(n). if the map has negative determinant, that means that the space is non orientable - there exists a loop which "changes orientation".

related notion is one- or two-sidedness, which can be defined similarly using loops. consider a manifold of dimension n embedded in R^(n+1). at each point you can consider a unit normal vector and clearly there are two choices. similarly you can transport this unit normal along any loop on the manifold. two surface is one-sided if there exists a loop along which the unit normal gets transported to its opposite - intuitively if you stand on the surface you can walk around the loop to get to the other side (check this for mobius strip in R^3).

the difference is that orientability is an intrinsic property, it doesn't need any embedding. sidedness requires an embedding into a space one dimension higher. when the ambient space is R^(n+1), non-orientability and one-sidedness are equivalent. but IIRC these notions may not be equivalent when the ambient space is something else.

[Anonymous No.11492022]

>>11492014
Thanks my man. God bless you.

[Anonymous No.11492024]

>>11491952
also if this stuff is interesting to you, read the book The Shape of Space by Weeks. I cannot recommend this enough, this should be a mandatory bed time read for anyone interested in topology.

[Anonymous No.11492042]

>>11492005
Lee for undergrad dg

[Anonymous No.11492045]

>>11492021
>when the ambient space is R^(n+1), non-orientability and one-sidedness are equivalent.
so non orientability, which means traverse allows flip, means sides can flip flop,negating boundary. figures and its an embedded hack past bounds by simply mixing them with the twist..ok

>pick some basis B1 of the tangent space
autistic question but it feels important, why does it have to be a basis of the tangent space? for mobius my visualization shows it would work for any vector emanating from the chosen point, aside from the horizontal ones

>if the map has negative determinant, that means that the space is non orientable - there exists a loop which "changes orientation".
why does having an orientation changing loop mean an orientation cant be statically chosen? i could start from some orientation, traverse and move back and its flipped so my orientation doesnt hold under movement, but couldnt it hold if i say it doesnt move, or perhaps classify it as something like, positive orientation under even loops, negative under odd # of loops

[Anonymous No.11492048]

>>11492024
wowow! i am excited, ive been itching to start reading new stuff. i will check it out. i am also looking to work with algebraic and geometric proofs since less abstract and more intricate/partful proofs are my weak spot, someone recommended me conics by apollonius, tho i havent read euclid

[Anonymous No.11492059]

>>11492024
just from the preview of that
>he compared flatland to a circle, finite area no boundary
just realized any closed loop even has some paradoxical feeling traits to it that get deleted by hacks, and twists are related concepts to loops! spirals bridge pockets of void and light

[Anonymous No.11492083]

>>11491965
>>11491986
>>11492014
>>11492042
All right, this is what my next 2 years will be like:

Year 1
>Topology
Undergrad: Munkres
Grad: Fuchs-Fomenko
>Complex Analysis
Undergrad: Kodaira
Grad: Ahlfors, Conway
>Algebra
Undergrad: Dummit and Foote
Grad: Aluffi
>Differential Geometry
Undergrad: Lee, do Carmo
Grad: Tu

Year 2
>Commutative Algebra
Eisenbud
>Algebraic Geometry
Undergrad: Ueno, Shafarevich
Grad: Hartshorne
>Complex Geometry
Still don't know any books on this subject, I accept recommendations

Rate my plan lads.

[Anonymous No.11492085]

>>11492083
how the fuck do you read books so fast? it take me like 6 months to read a math book

[Anonymous No.11492093]

>>11492045
>autistic question but it feels important, why does it have to be a basis of the tangent space?
because one vector you can translate to itself or to its opposite always. it doesn't tell you anything. however. look at the first loop. you can try completing the red vector to a basis and translate also the second vector. you will see that as the red vector rotates, the second vector will need to rotate also (so that they form basis at each point!!). as a result, when the red vector ends flipped, the second vector will also end flipped. therefore the linear map relating B1 and B2 will be something like

-1 0
0 -1

which has positive determinant.

[Anonymous No.11492097]

>>11492083
>Still don't know any books on this subject, I accept recommendations
Basically, if Gratzer wrote it, it's gold.

[Anonymous No.11492102]

>>11492097
>Gratzer
*Grauert.

[Anonymous No.11492108]

>>11492045
>>11492093
pic is what happens on mobius strip. if red is first vector and green is second, the difference between B1 and B2 is something like

-1 0
0 1

which has negative determinant.

[Anonymous No.11492115]

>>11492102
Awesome. Do you work on that area?

[Anonymous No.11492119]

>>11492083
>Undergrad: Lee, do Carmo
>Grad: Tu
my take is that Tu is definitely an easier and less detailed read than Lee

[Anonymous No.11492120]

>>11492115
No, I work in applied maths and study that stuff on the side.
Mostly complex geometry, tho.

[Anonymous No.11492122]

>>11492093
wait. now im confused from a new angle. so in loop 2 youre basically showing a vector in the ambient space right? i was thinking, what if it were forced to remain on the surface. such a stipulation, that remains on the surface, mimics the intuition of the choosing a basis of the tangent space and moving it.

the question is, how does one formally define "sticking" to the surface along the path, and that stickiness jiving with flipping? based on what you mentioned about forming a basis at each point and a group of linear transformations in the prior post, would it be that the initial tangent space from point A gets transformed with each successive point on the loop, thus rotating the basis? i think that makes sense.

then the next question is, how are these transformations defined? is it done analytically from the ambient space or can it be intrinsic or could it be done in a synthetic geometry kind of method?

lastly, do they really use linear algebra like this formally in higher differential math and manifolds? its so cool!

[Anonymous No.11492130]

>>11492108
is that mobius topology on a strip in r2 with the loop occuring at the "abstract glue" of the two ends?

also generally unrelated, what are the formal definitions of R^N? in lin alg the definition used is simply number of basis vectors. ive noticed but i dont think ive formally proved it, that there needs to be at least N slots in the vector space for R^N to occur. is higher dimensional space solely defined with vectors containing slots (i guess slotted arrays are the definition of vectors..) or are there other ways (assuming we stay within reals and dont use complex or quaternions etc).topologically, how is dimension defined? reminds me more of synthetic geometry with perpendicular lines rather than bases and making multiple groupings of R, one in each slot

[Anonymous No.11492143]

>>11492119
But the guy there said it was for undergrads...

[Anonymous No.11492154]

Guys, I need a book or set of lecture notes that deal with multivariable differentiation and in particular Taylor's Theorem for functions
[math]f:\mathbb{R}^n \to \mathbb{R}^m[/math], through the use of tensors.

I don't know if it is because I suck at searching but I cannot find a good book that does this. Most multivariable books only deal with up to 3-dimentions and most treatments of Taylor do the typical Jacobian+Hessian approximation but nothing more.

[Anonymous No.11492162]

>>11492122
think of the first picture as a portion of some 2D surface. or you can think of it as a plane for simplicity. surely the red vector never "sticks out of the plane". it does stick out of the loop though, but this is of course allowed (otherwise translating a basis wouldn't make any sense since all vectors would need to be multiples of the curve's tangent).

sticking out of the surface may happen only if the surface lives in some ambient space. otherwise there's nowhere to go.

well, I've said that I won't go into technical details about what does the translation of a basis along a loop actually mean rigorously. we would necessarily get to the question of how do we even define tangent vectors when we're not in R^n. and that itself is more complicated that one would expect.

yes, in manifold stuff linear algebra is everywhere. everywhere.

>>11492130
this is a rectangle with left and right side glued but with a twist (which is what the opposite arrows indicate). it's a model of mobius strip similar to the circle as [0,1]/~.

formal definition of R^n is the set of n-tuples of real numbers. that's literally it.

a manifold is a space which is locally homeomorphic to a portion of some R^n. in this case, this "n" is the dimension. so for manifolds the dimension is sort of a part of the definition. for a general topological space it's a bit tricky and I don't know much about it. you can google Hausdorff dimension.

[Anonymous No.11492179]

>Routine is a necessity for success in all fields.
Is this ever false?

[Anonymous No.11492194]

using the shutdown to finally learn calculus, any thing to keep in mind? I'll be using Peter Lax's Calc book

[Anonymous No.11492196]

>>11492162
>formal definition of R^n is the set of n-tuples of real numbers
what about a vector space where every vector is of the form <a,b,c,2c>? For every 3rd slot, 4th slot is constrained to be based on it, forming a line. so you have one line for the last two slots, the basis <0,0,1,2> per se, and then two other free slots which can associate with <1,000> and <0,1,0,0> normal bases. So its a 4 tuple, but is R^3. like the higher dimensional version of a plane with some z traits, a space with some hyperspace in it but not filling hyperspace

[Anonymous No.11492201]

>>11492179
You're getting banned.

[Anonymous No.11492211]

>>11492143
Lee's smooth manifolds can definitely be understood by undergrads. the things is that the book is an absolute tome in which every little detail is formed as a rigorously proved theorem AND with walls of text of explanations. it's an incredible book, but as a cover to cover reading it's "can't see the forest for the trees", there's just so much material. I'd suggest reading Tu to stay grounded and skimming through Lee, actually working through a section only when you feel like it.

[Anonymous No.11492223]

>>11492211
I see, so you think it's a better idea to use Do Carmo in undergrad and then proceed to Tu in grad while using Lee as a reference? Or should I just go straight to Tu as an undergrad?

[Anonymous No.11492228]

>>11492201
mhm, why do people get banned for posting topless progress pics of guys while posting 30 pics of anime children per thread goes through?

[Anonymous No.11492236]

>>11492223
do Carmo is a book on classical differential geometry (curves and surfaces in R^3), while Tu is modern differential geometry (manifolds stuff). it's not necessary to know the classical stuff, but it's good for motivation and general knowledge. I would say something like read both with giving do Carmo a head start, but I don't know man, math isn't learned 100% linearly. it just doesn't work like "now I read a book on complex analysis cover to cover and then I will know complex analysis". I had a course on classical differential geometry in undergrad, but I was a slacker back then so all I got from it was just some impression. after several years I learned about manifolds and then I came back to the classical stuff and it all made sense.

[Anonymous No.11492246]

>>11492228
They'll get banned as well if they post semi-naked anime girls. There's no defending your post, dude.

[Anonymous No.11492257]

recommend math movies for quarantine please

[Anonymous No.11492259]

>>11492228
Yukari is 1200 years old
https://en.touhouwiki.net/wiki/Yukari_Yakumo

Remilia is 500 years old
https://en.touhouwiki.net/wiki/Remilia_Scarlet

Mokou is ageless, she's literally immortal
https://en.touhouwiki.net/wiki/Fujiwara_no_Mokou


What other anime 'children' are posted here? Go on, so I can refute you again.

[Anonymous No.11492260]

jannies are trannies, except jannies are worse because trannies are alright

actually janny defenders are even worse. and that guy was pretty hot (not a fag)

[Anonymous No.11492266]

>>11492259
>yukari is a gap youkai
immediately felt empathy cause my jap name i gave myself was -kai from yokai and i relate to mercury, got of bounds gaps and lovecraftian twisties

[Anonymous No.11492275]

>>11492236
Oh, I see, that makes sense, thank you very much. What do you think of my 2 year study plan? Is it doable?

[Anonymous No.11492368]

>>11492257
there's a mathematician in eyes wide shut

[Anonymous No.11492449]

>>11492257
There is not a single movie that accurately portrays mathematicians, because the people who know enough to make it are too busy doing mathematics.

[Anonymous No.11492495]

>>11491787
>bootstraps edition
https://arxiv.org/abs/1902.05969

[Anonymous No.11492497]

>>11492368
really? who?

[Anonymous No.11492500]

>>11492495
Representation Theory is one of the most boring fields in Algebra

[Anonymous No.11492503]

>>11492495
Is that a female mario that peach is hugging?

[Anonymous No.11492504]

>>11492503
Lmao yes

[Anonymous No.11492537]

>>11492495
>We apply numerical conformal bootstrap techniques
im sorry but pulling yourself up by your bootstraps does not conform to reality

[Anonymous No.11492704]

>>11492154
Analysis 2 by T. Tao

[Anonymous No.11492788]

>>11492083
At what level do you plan on learning each subject? Because deeply learning a particular subject usually requires a ton of time and experience with it, and unless you're planning on pulling 12 hour sessions of learning math, I'm not totally sure this is doable, this coming from someone who tried something similar and having it not pan out. To be fair, most of that was due to poor planning, poor time management, and having a job, but there are few things to make this a lot better. For the most part, being consistent with your studying is key. If you read and understand about ten pages a day, you can finish dummit and foote in a few months. Hell, given how much of it is more or less fluff, you can probably do it less time.

First thing, how much experience do you have with proofs? If you have none, then this plan is completely and totally unrealistic. Furthermore, how "mathematically mature" do you think you are? That is to say, if you were given only the most basic core concepts required to prove a theorem, could you successfully fill in all the gaps without too much trouble? Are you able to read proofs with a critical eye in order to spot possible leaps in logic, a common one is where students don't even question whether a map is well defined (always make sure it is!). That being said, let's look over your plan itself. There's a lot of overlap in the books you're looking at, so maybe you only want to read some of each or cut some out entirely. For example, for complex analysis, you really could just start out with Conway or Ahlfors, considering both build things up from the very definition of complex numbers. Furthermore, given where you want to go and the overlap of both books, I'd say just skim a few chapters of each and pick one and stay with it. Both cover most of the essential material from complex analysis necessary to move forward.

Also, not sure what you want to get from Aluffi that you won't get from dummit and foote.

[Anonymous No.11492789]

>>11491798
> "hi, im mr klein bottle"
> "THIS IS A KLEIN BOTTLE!"
> he lift up something
> its a klein bottle
> "I HAVE 5 GORILLION OF THESE IN MY GARAGE"
> He shows us his cellar
> there are 50 levels below ground.
> ALL OF THEM are filled with klein bottles
> He built a machine to sort the klein bottles
> "I actually have a very specific fetish"
> Shows us his klein bottle magazine
> Starts masturbating furiously
> Comes on klein bottle
> Brady flees

[Anonymous No.11492793]

>>11492788
Either or is fine, and D&Fs length is mostly due to the amount of examples and exercises, if you take those out it isn't nearly as long. Again, look around and see which you find most appealing. As for topology, while munkres is fine I do think there are better options, for example, lee's topological manifolds book is quite nice, though I suppose munkres is a bit more leisurely, I prefer the former. It really only requires maybe the first four chapters of rudin as background and a little algebra, but all of this is covered in the appendix. It'll cover some of the material is fomenko as well, though I'm not sure you'll really need most of fomenko for what you want to do, so you might want to drop that one (though it is a good book, though worth mentioning a lot of books develop spectral sequences over again so it might be okay not to focus on it here).

As for differential geometry, your choices are a touch confusing. General theory of smooth manifolds, Tu is great as an intro, lee is also fantastic for basically presenting everything step by step with tons of examples. I would also say the latter is great at presenting not only the theorems, but the kinds of techniques you would typically use to attack those kinds of results, really learning you ABC's (when confronting embedded manifolds, Always Be using slice Charts). Though de Carmo is also great for your purposes, I would definitely supplement one with the other.

As for AG, the nice thing about CAG is that you can sort of skip over learning regular AG and just sort of dive in. Certainly, Harris or Voisin or Demailly don't assume you know what a sheaf is. Also, Miranda's book on algebraic curves builds things Riemann surfaces and fleshes out some really beautiful mathematics.

Finally, when it comes to actual study habits, again, consistency is the key. Furthermore, make sure to carefully work through every result, don't just read the statement of the theorem and move on, try proving it yourself.

[Anonymous No.11492795]

>>11492789
>Comes on klein bottle
In*

[Anonymous No.11492820]

>>11492795
wrong

[Anonymous No.11492842]

>>11492789
my klein cum jar

[Anonymous No.11492858]

>>11492788
>>11492793
Hello, I am the guy you were replying to. Let me answer some of the questions you made throughout your post.

I do have some experience with proofs and right now I'm going through Real Analysis (not Rudin though, I'm working through Tao and eventually reading Pugh). I certainly think I need to get better though and I'll use those quarantine days to work through a lot proof-based problems in analysis and algebra (I heard Dummit and Foote has fairly friendly exercises).

I thought Conway and Ahlfors were too high level, didn't know they started from scratch, so I should start with one of them already after finishing Real Analysis?

Well, to be honest, when I first got into Algebra I tried reading several books, but they all seemed weak to me, but when I read Aluffi I fell in love with his books (at least the first two chapters were god tier), but he uses categories a lot and I thought ir would be better reading Aluffi after Dummit and Foote which is a more traditional and gentle approach.

As for Topology, DG and Algebraic Geometry I don't know much about the books and all, so I was just following what was recommended.

I wasn't expecting a post like yours, very fantastic reply my man, thanks very much for taking your time to correct my study plan. My main objective is to be able to work on Complex Geometry after I graduate, so I wanted to focus on the subjects that are most important during undergrad and grad.

[Anonymous No.11492878]

>>11492858
>I thought Conway and Ahlfors were too high level, didn't know they started from scratch, so I should start with one of them already after finishing Real Analysis?
No, you should read Kodaira and then Conway, or read Conway and then read a book about Riemann surfaces (Donaldson is good), or read Kodaira and then Donaldson (which I'd actually recommend).

[Anonymous No.11492909]

>>11491948
Refrain from posting my wife.

>>11491787
How hard would it be to go into a Physics/CS path or MechE/CS path also taking Real Analysis and Set Theory?
I really like math but I do not want to pursue it as a career for various reasons. I have shitty self-study habits so I figured I'd take the courses I want in college, but I'm worried about the difficulty?
Is it feasible?

[Anonymous No.11492942]

>>11492858
No prob anon. Also, you don't need to stick to one schedule throughout, I'd recommend finding a prof you want to work with or who at least works in complex geometry and just chatting with them. If you love Aluffi, just stick with it anon, you don't need to read dummit and foote. Hell, if anything, it'll probably serve you a bit better given categories are the natural language of schemes. The important thing is to master the material.
>>11492878
Maybe you're right, I never tried Kodaira, instead I dived into Ahlfors and didn't have any problems. To be fair, I took complex analysis a bit later than most and was in a better position to handle the subject than someone just starting out. I'll second Donaldson and maybe also suggest checking out Donald Marshall's book.

[Anonymous No.11492961]

>>11492858
Also, to add to what I left out here >>11492942 a somewhat common thing people do is just to read Lang or Aluffi or Rotman, and then just doing the exercises in DF and not really reading the material itself. Also, once you want to dive into more advanced material, Complex Algebraic Geometry by Kollár should serve you well, it even includes an intro to the kind of AG you'll need, so I guess this one is better to read in batches, the beginning can be read fairly early on, and then you come to the later chapters after more experience.

[Anonymous No.11492995]

>>11492858
>Well, to be honest, when I first got into Algebra I tried reading several books, but they all seemed weak to me, but when I read Aluffi I fell in love with his books (at least the first two chapters were god tier), but he uses categories a lot and I thought ir would be better reading Aluffi after Dummit and Foote which is a more traditional and gentle approach.
I second that if you like Aluffi, then read Aluffi. once you finish DF, you will already know all the material. and while Aluffi does provide a different perspective, again, I can't imagine you reading it from cover to cover at this point. maybe try reading both, or read one while skimming through the other, I don't know man. as I've said math isn't really learned linearly. you'll need to figure out what works best for you. just don't expect you'll be reading book after book, cover to cover.

[Anonymous No.11493178]

>Hey when should I give up on a problem from an exercise set in the textbook? What about time n?
>Math Professors everywhere: time n is too short
>What about n+1
>Math Professors everywhere: time n+1 is too short
....
That said its been 2 months and I'm still stuck on the 5th problem of exercise set 1 in a fucking analysis textbook and my autism won't let me move forward.

[Anonymous No.11493188]

>>11492858
>but when I read Aluffi I fell in love with his books (at least the first two chapters were god tier), but he uses categories a lot
I can't blame Aluffi's book entirely for the rise of undergrad category theorists but jesus christ he sure made it a hell of a lot worse

[Anonymous No.11493191]

>>11493178
>its been 2 months and I'm still stuck on the 5th problem of exercise set 1
bruh
skip it and come back

[Anonymous No.11493204]

>>11493191
Can't do that man, sorry. Since I have no upper bound on a time limit and since I can't find any documentation on minimum time limits per problem, it's literally gatekeeping me from the rest of the text.

[Anonymous No.11493214]

>>11493178
Just ask your professors or post it on /sqt/, Jesus Christ.

[Anonymous No.11493219]

I just want to know if its ok to use R or C to prove stuff about N or other subclasses

[Anonymous No.11493270]

>>11493204
If a problem takes you more than a week, skip it and come back. If longer than 2-3 months, just skip it entirely. Sometimes seeing the later material helps you gain intuition on the earlier stuff

[Anonymous No.11493315]

Interval scheduling problem
There are N jobs w_i (i = 1,2, ... N).
The start time of each task w_i is s_i and the end time is t_i.
You must choose to participate or not for each job. If you take part in a job, you have to participate in it from start to finish. That is, they must not overlap in time with other work to participate. It is not permissible for only the start and end moments to overlap.
Find the maximum number of jobs you can participate in.

[Anonymous No.11493466]

>>11493188
Why's it bad that people are learning category theory ealier again?

[Anonymous No.11493483]

>>11493214
>Jesus Christ.
Religion is not allowed on this board

[Anonymous No.11493510]

frens, i'm trying to get back into Math after taking an extended gap year (about 2 years). i'm thinking of going back to grad school, what would be a good way to get back into the math mindset?

in undergrad i took undergrad/grad courses in algebra, analysis, complex analysis and point set topology/homotopy theory. my smooth topology and PDE are a bit weak since i haven't taken many courses on it. what would be the best way to review and which would be some good references? i want to be ready for the prelims and not have to retake the introductory graduate sequence again. i have Dummit and Foote, Lee (Smooth Manifolds) and Folland. would this be enough or what other books would you guys recommend?

[Anonymous No.11493515]

>>11493178
hav you considered that you're just stoopid anon and perhaps have no talent for mathematics, and suffer from a genetically predetermined deficiency in quantitative reasoning?

[Anonymous No.11493523]

>>11493510
It's over my man, two years is too much timd, now the gap between you and someone who kept studying during those 2 years will never be closed. Just try to find happiness in a job somewhere.

[Anonymous No.11493524]

Advanced Calculus of Several Variables, CH Edwards; Advanced Calculus, Lynn Loomis and Shlomo Sternberg; Analysis on Manifolds, Munkres; Calculus on Manifolds, Spivak.

You will no more about the topics than most posters on /mg/ if you can do L&S. Don't read multi books they're written for Enginiggers and physicists

[Anonymous No.11493526]

>>11493524
forgot Mathematical Analysis I (last two chapters I believe), and Mathematical Analysis II (first few chapters), Vladimir Zorich.

[Anonymous No.11493527]

>>11493524
Loomis and Sternberg is used by freshmen in math 55 and you brainlets here talk as if it's grsduate-level, kek.

[Anonymous No.11493529]

>>11493527
>durr hurr durrrrrrrrrrrrrrrr
kys nigger

[Anonymous No.11493532]

>>11493529
Gud gud, who's a big boy who's a big boy?

[Anonymous No.11493539]

>>11493532
have you ever been punched in the jaw before anon?

[Anonymous No.11493543]

>>11493539
By a manchild who thinks undergraduate books are grsduate-level? Never, why?

[Anonymous No.11493544]

>>11493529
>nigger
Why the racism?

[Anonymous No.11493550]

>>11493544
Because he's still a child, he likes to be edgy.

[Anonymous No.11493555]

>>11493550
because it makes you uncomfortable

[Anonymous No.11493570]

>>11493555
I'm a black man that's more successful in math than you probably will ever be though, so that's fine by me.

[Anonymous No.11493602]

>>11493510
D&F should cover most of the algebra you need, so working through it will likely get you up to snuff, though you may want to supplement it with some lie theory, the later chapters of fulton harris go through the representation theory of lie groups/algebras. Same with Lee, though I imagine just smooth manifolds won't be enough, his book on topological manifolds has a good amount of point set topology and basic homotopy theory. I'm not a big fan of Folland, I'm honestly on the Simon analysis hype train. You can find a ton of past prelims online, like form (harvard, berkley, and so on), and if you find that you're able to get a passing score in the allotted time that's a good indication that you're ready.

[Anonymous No.11493606]

>>11493466
Not him but the issue isn't that people are learning category theory, rather it's the undergrads. It's not like I and others don't see the value in category theory in some circumstances, like in algebra, but that hardly justifies the autism of the undergraduate category theorist. See, those of such ilk tend to try phrasing everything in terms of categories, even to the point where it no longer becomes useful. I remember in of our manifolds classes some undergrad asked the teacher if Seifert-Van Kampen's theorem can be phrased in terms of categories (it can), to which the prof something to the effect of "sure, but it really isn't useful to do so since we use if for computation and phrasing it in terms of categories loses sight of that". And yet this student insisted that this was "the right way of viewing it". Which is an obvious problem since a computational tool should not be rendered computationally useless. It's not formalizing the statement that's wrong, it's the constant attempt to categorify things to the point that all of the interesting or useful material is completely obscured. Undergrads, not even knowing the basic material, then forgo the actual act of learning the material in a way as to properly engage with the subject. They not only lose the ability to dig into things, but they gain this feeling that the only mathematics out there are those that can be categorified, even though that's not really true, nor a useful perspective. There's a reason why there are so few pure category theorists and even then many just stay in a very insulated bubble, it's fragile. And the behavior that not only glorifies it, but attempts to shove it down your throat can be annoying.

[Anonymous No.11493626]

Threadly reminder to work with physicists.

[Anonymous No.11493629]

>>11493626
Threadly reminder to kiss and hold hands with physicists.

[Anonymous No.11493635]

I graduate in the summer and have no jobs in line :(

Should i pursue the possibility of a PhD or Masters? My adviser has suggested maybe doing my research in AI even though i don't see how a mathematician can enter a field like that without a strong engineering/CS background. I have done well in my degree throughout but i'm hoping there are careers other than banking/finance/business analytics. Applied to a bunch of small tech firms as well as large ones and they all wan't engineering experience.

[Anonymous No.11493644]

>>11493629
Lewd.

[Anonymous No.11493676]

>>11493466
Because what happens is they learn an extremely minimal amount of category theory early on (e.g. Aluffi doesn't even define a functor until almost 500 pages in, because Aluffi's "categorical" approach to algebra is completely trivial and literally just means explicitly labeling things as universal objects instead of only showing you they are), well before they've even heard of any of the structures it's supposed to be generalizing, and then they get obnoxious about it and say ridiculous pretentious shit like "I fell in love with his book after reading the introductory chapter on sets because of how CATEGORIES it is"

[Anonymous No.11493679]

>>11493635
If you plan on going into industry, then go for a masters. You may need some cs, but it honestly isn't all that much, learn some c++ and you'll be good. The reason people suggest AI is because it is a hot field, and, in some cases like neural networks, the mathematics is actually way easier to handle than you might expect. Really anon, if you just learn a programming language and get a little experience, plus a masters with maybe a couple of computational/applied maths courses thrown in, you'll get any job you want (in the space of jobs attainable by you skill set) 300 k starting (plus or minus 300 k)

[Anonymous No.11493704]

cat

[Anonymous No.11493747]

>>11493704
If you're gonna post animals, post cuter ones than that.

[Anonymous No.11493776]

>>11493602
thanks fren. other than simon's Analysis book, what do you think would be another good reference? would big Rudin suffice? i'm kind of fond of Folland since i used it for my courses but wouldn't mind brushing up my Analysis from another book. for ps topology/homotopy theory do you think Munkres/Hatcher is a good substitute or should I use Lee's text instead?

again, thanks fren. that's some great advice. a final question, do you have any advice on discipline/adhering to a schedule? i was pretty lazy during my undergrad and did really well but found out i can't do the same kind of improvisation for grad courses.

[Anonymous No.11493793]

>>11493676
Damn, that's a really stupid post.

[Anonymous No.11493805]

>>11493747
cat

[Anonymous No.11493808]

>suppose

[Anonymous No.11493812]

>>11493793
hit a nerve there?

[Anonymous No.11493860]

>>11493812
But you were the one who got triggered because someone posted they liked Aluffi's book.

[Anonymous No.11494020]

>>11493776
While I also like Rudin, at the end of the day you should choose the textbook that works best for you. If you like Folland, then stick with it, in terms of material it should suffice. You may also like Stein And Shakarchi. Munkres and Hatcher would certainly work as well, I just have my own preference for Lee. At the end of the day the material is the same.

As for studying habits, I subscribe to the idea of "swallowing the frog for breakfast". That is to say, wake up early in the morning, possibly taking a cold shower to keep myself up, eat a solid breakfast and then study. Frankly, I find it much harder to study later on in the day, since I just want to relax and shitpost online (like right now), so instead I try to do as much studying as I can the in morning when I'm feeling energized and sharp. I would also say it helps to put yourself in an environment that helps you study, for example, a library. I also had trouble studying in my dorm room during undergrad since I just ended up fucking around since nothing could stop me. There are also environmental keys you can create in order to facilitate studying, basically I have a small table that is dedicated to studying, and so whenever I sit there I reflexive feel in the mood to study. Afterwards I reward myself with some cream soda. Sort of pavolvian really. Conditioning via positive reinforcement is a real thing. Another thing you can do is use negative reinforcement. There are various websites that allow you to put money into a holding account and give primary control to another trusted person, like your parents or friend. You then set a goal and name an organization that you despise, then, if you do not reach your goal, the money will be donated to said organization. If you do meet that goal, the trusted individual will signal that the goal has been met and the money will be returned to you. Or you make a bet directly. I made a bet my mom and sister I could lose the most weight, and I did, 10 lbs

[Anonymous No.11494044]

>>11493776
>>11494020
Building on my previous post, there are tons of articles about this technique or that method or blah blah blah, but I do find some of the things people say to be useful. I do think that taking breaks at 45-50 minute intervals is useful. I also think being able to effectively break up tasks into manageable chunks it better, that is to say, instead of saying to yourself "I am gonna read this whole book" say, "I am gonna read this chapter" and then iterate that n times, where n=#of chapters in book. I also like keeping some physical representation of my progress, since that gives me a further impetus to be consistent, and consistency is the most important thing. For me, I have a calendar in which I draw a big green check everyday that I meet my daily goals, and a big red X everyday that I don't meet said goals. The fact that it is right in my face makes it hard to ignore. Also, I downloaded some software called "rescuetime" that basically allows me to set certain activities as "productive" and "distracting" and tracks the time on my computer that I spend on each activity. That helps me quantify my productivity and see where I am spending the most time doing bullshit. Because of this, I can make a conscious effort to reduce going to those websites. I remember, the first day that I installed the software, it showed that I spent nearly 11 hours on 4chan that day, not good. So that helps. I have reduced my time spent here to about 1-2 hours.

[Anonymous No.11494050]

>>11494020
fair point.

that anecdote is certainly hilarious, and i'll try out positive/negative reinforcement for my study routines. thanks a lot fren. i assume that you're a grad student or in academia, what is your area of research?

[Anonymous No.11494057]

More revisions to IUT II & III, so Mochi's still safe from coronavirus

http://www.kurims.kyoto-u.ac.jp/~motizuki/2020-03-22-iu-teich-revisions.txt

>Inter-universal Teichmuller Theory II
>-------------------------------------
>Corrected a misprint involving parentheses in the text preceding the second to last display of Remark 1.4.1, (ii)

>Inter-universal Teichmuller Theory III
>--------------------------------------
>Corrected a misprint involving parentheses in the text following the first display of Remark 1.1.2, (i)

[Anonymous No.11494059]

>>11494050
No prob anon, I'm a math grad student, though I haven't settled on a research area. There's just so much interesting stuff out there that I have trouble fully committing to one thing. Right now I am taking a few reading courses with potential advisors to narrow things down. Basically down to geometric measure theory, algebraic combinatorics, and optimal transport.

[Anonymous No.11494130]

Hevapin sethera, four five six: Lay down your magic fiddlesticks.

[Anonymous No.11494191]

>>75171242

[Anonymous No.11494329]

>>11494059
yeah i get what you mean, i'm sure it'll work out in the end. those sound like really cool areas of research anon. one final question, how do you deal with frustration and getting stuck when doing problems/getting through hard proofs? i find myself frustrated at not being able to see some problems quick enough, which in turn leaves me staring at a blank piece of paper for hours on end. this happened sometimes to me as well in exams. is it just a matter of doing hundreds of exercises 24/7 to get a feel for the material? in my undergrad i mostly improvised and did the bare minimum to get a good grade, but i'm not sure if this is adequate for grad school courses though.

[Anonymous No.11494502]

>>11493570
you’ll always be a nigger a mathfag, and a brain dead elitist insect.

[Anonymous No.11494510]

[Anonymous No.11494530]

Roman fathers were wont to name their fifth sons Quintus, for some reason no-one has been able to figure out. Discuss all normal towers of the symmetric group on five letters, and thus show that fathers of five or more sons were not in general solvent

[Anonymous No.11494655]

redpill me on Jacob Lurie

[Anonymous No.11494679]

>>11492257
Gifted (2017) https://www.imdb.com/title/tt4481414/
>>11492449
>There is not a single movie that accurately portrays mathematicians
That is what I believed until I saw this movie last week, expecting to hate it. It's actually really fucking comfy, and it's as good a "math film" as you're gonna get.

[Anonymous No.11494714]

>>11493606
>I remember in of our manifolds classes some undergrad asked the teacher if Seifert-Van Kampen's theorem can be phrased in terms of categories (it can), to which the prof something to the effect of "sure, but it really isn't useful to do so since we use if for computation and phrasing it in terms of categories loses sight of that". And yet this student insisted that this was "the right way of viewing it".
fuck I can actually feel the cringe

[Anonymous No.11494782]

Honestly, every math PhD student should be able to easily solve all the IMO (and Putnam) problems, perhaps after some reflection, but best instantly. If you're a math student, you should learn the stupid tricks, they are at the high school level. If you can't solve them, you probably are going to have a hard time solving a hard unsolved problem anyway, so you should learn to do these things first, otherwise, frankly, you are not going to be a very competent student.

[Anonymous No.11494798]

>>11494782
Obvious bait

[Anonymous No.11494811]

>>11494798
>t. no future in mathetmatics

[Anonymous No.11494912]

>>11494782
>If you can't solve them, you probably are going to have a hard time solving a hard unsolved problem anyway
unironically this

[Anonymous No.11494941]

[Anonymous No.11494947]

Why does knowing how [math]n[/math] is a product of two primes [math]p[/math] and [math]q[/math] make it easy to compute the square roots of some number modulo [math]n[/math]?

I literally have no idea how this helps. does it split it up into [math]x \equiv a (mod p)[/math] and [math]x \equiv b (mod q)[/math], or something to that effect?

[Anonymous No.11494955]

>>11494947
Yes, just take square roots mod p and mod q and use chinese remainder theorem back and forth..
Taking square roots mod p can be done fast, see tonellli-shanks algorithm.

[Anonymous No.11494977]

>>11493527
t. brainlet

[Anonymous No.11495107]

>>11494811
>>11494912
In the 1% chance you're not actually baiting and is actually that idiot:

https://link.springer.com/chapter/10.1007/978-3-642-19533-4_5

https://www.quora.com/How-is-solving-Olympiad-problems-different-from-doing-mathematical-research

[Anonymous No.11495127]

>>11495107
Ok, but you get the general idea instantly, then it's piddling around for 5-10 minutes when you solve it. It's not so rewarding once you understand the principles, I agree. But one should understand the principles and move on.

[Anonymous No.11495289]

I want to verify that I understand this notation correctly.

In the first equation the summand is an n-dimensional vector multiplied by the r scalars [math]v^j_{i_k}[/math]. Is this correct?

[Anonymous No.11495315]

>>11495107
putnam problems are literally basic undergrad knowledge + playing around with the problem and basic algebraic manipulations
if you can't score, let's say, 30 at putnam, I simply think you are not very talented as a mathematician

[Anonymous No.11495362]

>>11495315
Oh no, not this, STOP THE PRESSES EVERYONE. What must we do now that 'Anonymous' thinks someone is not talented enough? This might represent a whole revolution in the academia, I propose banning all of those who scored below 30 on the Putnam from all STEM Courses, this will teach them to take 'Anonymous' seriously, heh.

I wonder sometimes how many 15 year olds are posting here.

[Anonymous No.11495367]

>>11495362
Let's find out.
https://www.strawpoll.me/19600304

[Anonymous No.11495380]

>>11495289
>Is this correct?
No

[Anonymous No.11495404]

>>11495380
Yes it is, brainlet.

[Anonymous No.11495408]

>>11495404
>[math]\partial_x f[/math] is a vector
No. Wrong. Bad, go back to the engineering thread.

[Anonymous No.11495422]

>>11495408
Retard.

[Anonymous No.11495457]

>>11495362
i simply voiced my opinion and you already shat yourself, you must be quite insecure
reminder that academics are overly polite, no professor will tell you that you're an idiot even if he thinks so

[Anonymous No.11495508]

Are cellular automata /mg/ related, especially if it generates phase transitions at exact roots of an equation, which are coincidentally trigonometric values?

[Anonymous No.11495525]

>>11495289
>In the first equation the summand is an n-dimensional vector multiplied by the r scalars vjikvikj. Is this correct?
yes
>>11495380
>>11495408
retarded brainlet uninstall math pls

[Anonymous No.11495552]

Effort beats talent. Prove me wrong if you disagree.

Examples of effort beating talent:
>Naruto vs Neji
>Ryu vs Ken
>Goku vs Vegeta
>Yusuke vs Togaru

[Anonymous No.11495569]

>>11495552
Well Vegeta later trained much harder than goku and goku fucked him up. Naruto has the 9 tails meme.

[Anonymous No.11495577]

>>11495552
Both are eventually necessary if you plan on doing a PhD and research-level maths. Effort + talent > effort with no talent, and likewise talent + effort > talent with no effort:
>(...) even if one dismisses the notion of genius, it is still the case that at any given point in time, some mathematicians are faster, more experienced, more knowledgeable, more efficient, more careful, or more creative than others. This does not imply, though, that only the “best” mathematicians should do mathematics (...)
>In some cases, an abundance of raw talent may end up (somewhat perversely) to actually be harmful for one’s long-term mathematical development; if solutions to problems come too easily, for instance, one may not put as much energy into working hard, asking dumb questions, or increasing one’s range, and thus may eventually cause one’s skills to stagnate.
https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

[Anonymous No.11495582]

>>11495577
>Terence tao
>IMO gold medal when he was still a child
What the hell would he know about the suffering and struggles of average people?

[Anonymous No.11495594]

>>11495552
>effort beats talent
>all the examples are imaginary characters

>>11495577
see here >>11495457
>reminder that academics are overly polite, no professor will tell you that you're an idiot even if he thinks so

[Anonymous No.11495613]

>>11495582
Well considering he nearly failed his preliminary exam and basically only passed because he got lucky and the profs took pity on him, a little, yeah. the whole
> if solutions to problems come too easily, for instance, one may not put as much energy into working hard, asking dumb questions, or increasing one’s range, and thus may eventually cause one’s skills to stagnate.
This is actually true in Tao's case, since he basically coasted on raw talent until hitting a massive wall in grad school, to which he started buckling down and working very hard to get better.
>>11495457
>academics are overly polite, no professor will tell you that you're an idiot even if he thinks so
You've gotta be fucking kidding me, I've been at enough conferences to know this is complete bullshit. Sure, they won't say "get lost you fucking moron" but they will indirectly tell you that they think you're an idiot, they do that shit all the time.

[Anonymous No.11495663]

>>11495613
>>11495582
grad school is a different beast.

i knew a guy who had a 4.0 gpa in undergrad, extremely smart, solutions came to him pretty much instantly and helped everyone out in class. once he got to grad school though, he started slacking and couldn't juggle the responsibilities of having to grade/TA/coursework and ended withdrawing from the program. i don't think anyone has heard anything from him ever since but some people have told me he's very depressed and can't find a job. you definitely need both effort and talent, and i'd say that effort is even more important than talent.

[Anonymous No.11495671]

Hey guys, I'm attempting to return to math after a hiatus following my BSc. I'm gonna take a few 4th year courses at a local uni before I apply for MSc. I'm going to review: calculus (differentiation, integration), linear algebra, differential equations, probability/stats, and then real analysis (rudin). The first four should take 2-3 weeks each and real analysis will be a summer thing. I hope to take measure theory and probability. Is this a good study review plan?

[Anonymous No.11495754]

>>11495671
sounds reasonable to me, I mean you can't go wrong with reviewing everything
diff eqs and probability/stats are much less important than the rest (in terms of how much they will come up in other subjects)

[Anonymous No.11495776]

>>11495754
Hoping to go into probability/SDEs, potentially stochastic dynamical systems and SDE modelling, so prob/stats probably the most important.

[Anonymous No.11496006]

>>11495552
Data Set Source: FUCKING FICTION

[Anonymous No.11496021]

>>11495776
>hoping to get into SDEs
Jesus Christ anon, I'd sooner shoot myself.

[Anonymous No.11496037]

Brehs, there is a class offered at my university for the first 5 week summer semester called math 4900, "Special Problems", here is a link because idc if yall know the mediocre state school I attend: http://catalog.unt.edu/preview_course_nopop.php?catoid=20&coid=76514 It is unironically the only elective I can take with a high enough course number to fit my advanced elective requirements for me to graduate this december. There is no course description, no prereqs, and 15 open seats out of 15 seats. I'm pretty sure its just a supervised research class, but idk if I can just sign up for that kind of shit. How do supervised research classes generally work in american unis, can I just place myself in one without consulting a professor?
By the way yes, I know I'm a brainlet.

[Anonymous No.11496049]

>>11496037
oh and I asked a counselor and she said she didn't know what it was either.

[Anonymous No.11496066]

>>11495776
SDEs can have very interesting applications actually.
https://arxiv.org/abs/1610.08468

[Anonymous No.11496075]

>>11496021
>>11496066
The duality of anime posters
>>11496037
>>11496049
Yeah, this is most likely a research class for a student and their mentor to work on problems together. This is something you definitely do with a prof you want to work with.

[Anonymous No.11496112]

>>11496075
alright, noted. Thank you man
So, if I can't take the research class for whatever reason, most likely cause I don't have a mentor, would it be silly to take intro to numerical analysis and diffeq 2(PDEs) in the same 5 week summer semester? I know yall can't get in my brain and see what I can handle, but I will say I have about average intelligence, am almost finished with my math BS at a 3.8 major gpa, and will have 0 other obligations besides math during that summer semester. Have any of yall done 2 advanced math courses for a short semester like that? How did it go?

[Anonymous No.11496137]

>halfway through my math degree
>GPA is 1,24

Is it over for me? Can I still be accepted for a masters in a nice uni? I'm on one of the best unis in the country but I already gave up on building a career here kek

[Anonymous No.11496188]

>>11496137
>Is it over for me? Can I still be accepted for a masters in a nice uni? I'm on one of the best unis in the country but I already gave up on building a career here kek
Unless you somehow get nothing but straight A's for the rest of your courses, your fucked buddy. That being said, another option is to finish your degree, try getting into a decent masters program, get straight A's there, and then transfer to a better program.
>>11496112
Even if they are in 5 weeks, given that you have no other obligations, you should be fine. If you did well in ODEs, you should do well in PDEs as well, since half the time you just use fucking separation of variables or assume some sort of symmetry that reduces the dimension of the problem. Never taken a numerical analysis course, but my friend did and in his experience as long as you had some basic experience with a programing language, or maybe matlab/maple/mathematica, you should be fine. Conceptually nothing is really difficult, it's mostly the implementation and debugging that's a pain.

[Anonymous No.11496219]

>>11496137
I mean you can restart bruv, retake the classes you fucked up on. You can also balls to the wall get A's and beg a professor to let you get in on cool UG research. It's never over until you let it be over. Higher maths is a commitment for a lot of us lad, its not like anything most people have done before in their life.
>>11496188
ty lad, I was a /g/ayboi as a kid so hopefully it helps.

[Anonymous No.11496646]

Can someone explain the logic behind scaling it and why we want to do [math]l = 2\pi[/math]?

[Anonymous No.11496648]

>>11496646
Probably should add context, this is in regards to the proof of the isoperimetric inequality

[Anonymous No.11496654]

>>11496646
Because it's a circle.

[Anonymous No.11496879]

>>11496037
There are a couple good set theorists at UNT. You should try and learn from Steve Jackson or Su Gao.

[Anonymous No.11497016]

>>11494329
I find that very often the methods, techniques, and ways of thinking that are useful in solving problems are those that can be understood and absorbed by reading very carefully the proofs of the key theorems. For example, I mentioned something about embedded submanifolds and slice charts in a previous post. Well, that was design, as in most cases when proving a theorem about embedded submanifolds slice charts are pretty much the go to tool and therefore it makes sense to use them as a tool whenever dealing with slice charts. Similarly, whenever you have some locally defined function that you want to extend to the whole space, a partition of unity is useful. And indeed, pretty much every theorem about the existence of some globally defined object relies on partitions of unity. So I think carefully understanding the proofs of key theorems, which tools were used, why they were used, how they were use, and so on. That'll at the very least give you a tool book that you can throw at a problem once you recognize the kinds of objects you're working with.

As for general frustration, I just take things in stride. I'll never get better if I don't push myself, so I either accept stagnation and decline, or I accept frustration. The latter is vastly more preferable to the former. I guess you could try re framing your frustration at the lack of solving the problem as you challenging yourself. In any case, if you ever find yourself frustrated, taking a long time with a problem and finding out a solution is easy, reflect on that deeply. Why was it easy? What were you missing? What tool/technique/theorem did they use that you were ignorant of/inexperienced with? Make sure that questions "of this type" don't trip you up ever again. Being able to reflect on and improve upon these frustrations is key to getting better. For example, typically students beginning real analysis are unable to prove basic continuity results because they have yet to absorb the "tricks".

[Anonymous No.11497033]

multiplication a*b is a added to itself b times, but how was that definition extended to include other types of numbers like rational and negative numbers? exponents a^b is a multiplied by itself b times, but that explanation falls apart when you want to input anything but non-negative natural numbers. how are binary functions generally extended to include other types of elements?

[Anonymous No.11497038]

Is there an explicit construction of equalisers in the category of small categories? Are there equalisers in the category of abelian categories?

[Anonymous No.11497041]

>>11497033
you deduce some properties for the definition that you have so far and then you ask if you can extend the definition such that these properties still hold. for example for the naive multiplication n*a = a + .. + a you have the distributive law

n*a + m*a = (n+m)*a.

so if you want this to hold you must have

0*a + n*a = (0+n)*a = n*a

which forces 0*a = 0 for all a. similarly you must have

(-n)*a + n*a = (n-n)*a = 0*a = 0

which forces (-n)*a = -n*a.

[Anonymous No.11497398]

>>11497038
>equalisers in cat
if we have two parallel functors F, G with domain C and target D, we can construct the equaliser E as a subcategory of C in the following way: take as objects e the objects in C such that Fe = Ge and as arrows f the arrows in C such that Ff = Gf

[Anonymous No.11497401]

>>11497398
oh and the equaliser arrow is the inclusion from E to C

[Anonymous No.11497414]

>>11497038
for your second question: I think not since the empty category is not an abelian category. so you get problems if your two functors agree nowhere. Well, I mean it of course depends which arrows you use in the category of abelian categories but if you just take arbitrary functors it doesn't work

[Anonymous No.11497419]

>>11497414
nevermind. don't read anything of it. it's nonsense. sowwy

[Anonymous No.11497420]

>we put [math]\mathfrak{U}_1 = rad ~ R[/math], and set [math]I = \{ 1 \} [/math]
>the counterexample is nigger-tier? I don't really give a shit, lmao

[Anonymous No.11497429]

>>11497414
>>11497419
So we have run into the same problem. Thanks for trying, though.

[Anonymous No.11497459]

>>11497419
>>11497429
nevermind my nevermind. I was right that you get problems if two functors agree nowhere. if you take two constant functors (with different values) F and G. Then the diagram F,G:C->D has no cone. because for every arrow H:A->C, we must have F(H(a)) = G(H(a)) for all a in A which cannot be unless A is empty. But the empty category is not an abelian category since it doesn't have a zero object.

[Anonymous No.11497535]

>>11496021
same could be said of most applied maths imho

[Anonymous No.11497709]

>>11497535
I'm not going to defend numerical analysis of PDEs or muh persistent homology for data analysis, but I do like inverse problems.

>the iterative solution method for a well-posed problem
>keep on iterating until you're precise enough, I'll go have some hotpockets in the meantime

>the BVLL iterative method for ill-posed problems
>Steady, steady boy. Nice and easy, just how I like it. Wait, why are you doing an L turn WAIT WAIT STOP FUCK IT'S DIVERGING AGAIN KNEW I SHOULD HAVE PICKED A LARGER [math]\tau [/math] FUCKING STOPPING CRITERIA FUCK I'M PAYING SHANG 5 DOLLARS PER ITERATION ON HIS CLOUD COMPUTING, THE TRIADS ARE GONNA TAKE MY FUCKING KIDNEYS AAAAAAAAAAAAAA

[Anonymous No.11497892]

>>11497709
Wow, I can't believe iterative methods for ill-posed problems cost 5 dollar per iteration, no wonder those inferior applied mathematicians get so much funded, that's the only explanation I'll accept. But this just proves that we should have a mathematician lead oligarchy, ruling over the entirety of planet, that way, no one would ever have to suffer under the tyranny of not being able to run iterations. Now, I saw this knowing that only the subhuman applied mathematicians do such things, but being the noble pure mathematician that I am, I am obligated to care for and help the dull, defenseless, stupid applied mathematicians from the horrid parasites that infect this world (read: non-mathematicians). I believe the corona virus was actually an act from one our many gods, the ideal platonic dodecahedron (the purger), to rid the world of as many non-mathematicians as possible. Our duty is merely to scribe and understand this beautiful work, by letting our slaves (read: statisticians) collect data and build growth models to see the purge in all of its glory. Though, it'll leave the engineers, computer scientists, and physicists alive. After all, we need people to run the factories, update latex, and be our sex slaves.

[Anonymous No.11497903]

Can any math chad advice me here? I am in my late 20s and I have come to realise me being a brainlet when it comes to math is a major reason for my inability to do well in many of the fields I want to get into. So I am re-learning math hopefully master certain topics to a bachelor's degree level.(I am not deluded enough to think I can self teach every topic a math undergrad learns).

With that being said math will to me be a tool to get better at a different field(business/finance or programming) many of which will become far easier to master with a strong math background. So my questions are this.

1) What are some topics that are valuable in other fields like business, finance and CS?

2) Should I re-learn some physics as well? I remember having a conversation with an anon here who said physics phds are sought after from big name consultant companies to even big soccer clubs for sports science.

Sorry if this is vague. Just trying to lay out a path for myself.

[Anonymous No.11497909]

>>11497903
Do you already have a BS?

[Anonymous No.11497920]

>>11497909
Let's just say I ama third world villager with an engineering degree that's basically useless because I just rote memorized through school and college (which I massively regret)

[Anonymous No.11497967]

Say that I have some set [math]X[/math] and some set [math]Y[/math]. If I know that two functions [math]f, g[/math] satisfy

[math]f(x) \leq g(y) \; \forall \; x \in X, y \in Y[/math]

then does it follow that

[math]\mathrm{sup}_{x \in X} f(x) \leq \mathrm{inf}_{y \in Y} g(y)[/math] ?

If so, why?

[Anonymous No.11498025]

>>11497967
yes. for each fixed x, f(x) is a lower bound for { g(y) }. therefore f(x) is lesser or equal than inf { g(y) } since that's the largest lower bound. this holds for every x, this means that inf{ g(y) } is an upper bound for { f(x) } and therefore is bigger than sup{ f(x) } since that's the least upper bound.

[Anonymous No.11498044]

>>11497967
yea. for fixed x, we have that [math]f(x) \leq g(y) [/math] for all y. so f(x) is a lower bound for {g(y)}. therefore [math]f(x) \leq inf g(y) [/math]. Now this is true for all x, so inf g(y) is an upper bound for {f(x)}. Therefore we have what you wanted

[Anonymous No.11498077]

How do you stay concentrated and motivated for math during this times? I'm not used to study at home

[Anonymous No.11498086]

>>11498077
very poorly

[Anonymous No.11498117]

>>11498086
Man i wanna fuck some pussy

[Anonymous No.11498139]

>>11497709
God these are so sexy
http://www.mi-ras.ru/~snovikov/105.pdf
https://arxiv.org/abs/1912.11424

[Anonymous No.11498258]

What are the best books for studying Algebraic Topology?

[Anonymous No.11498274]

>>11498258
Hatcher

[Anonymous No.11498307]

>>11498274
Is Lee's Topological Manifolds an algebraic topology book?

[Anonymous No.11498323]

>>11498077
I have a high iq and am autistic
>>11497920
probability and statistics, numerical analysis, differential equations and linear algebra are all the math that's used in CS and finance

[Anonymous No.11498337]

>>11498323
>probability and statistics, numerical analysis, differential equations and linear algebra are all the math that's used in CS
>I have a high IQ
Yeah, look kid, your mom's been lying to you...

[Anonymous No.11498351]

>>11498337
You should kill yourself faggot.

[Anonymous No.11498605]

[stupid question] I've read once about problem in graph theroy that leads to HUGE numbers. Any clues what could it be?

[Anonymous No.11498656]

>>11498605
Results in Ramsey theory usually have values that end up growing extraordinarily quickly. It is likely a problem in that domain.
>>11498307
More like the first half of a book on algebraic topology.
>>11498077
I masturbate only while reading math books, keeps me focused.

[Anonymous No.11498661]

>>11498656
>More like the first half of a book on algebraic topology.
Is it good?

[Anonymous No.11498701]

>>11498661
it's an amazing reference and should be read by any graduate student for sure. there's plenty of other references which expand on algebraic topology (eg hatcher and others). reading Top/Smooth Manifolds should be a required read for anyone. i would say it's best to master the basics first (first year graduate sequence) and then branch out into the fields which interest you, since it gives you a glimpse into different techniques/areas of math which may be useful later on for solving other problems. good luck fren.

[Anonymous No.11498704]

>>11498605
>Ramesey theory
https://en.wikipedia.org/wiki/Ramsey_theory
>Graham's number
https://en.wikipedia.org/wiki/Graham%27s_number

[Anonymous No.11498708]

>>11498661
I quite it like it, lots of examples and good explanations. I feel like it gives a good introduction into algebraic topology and it serves as a nice segue into something like Bott and Tu or Spanier or Hatcher.

[Anonymous No.11498759]

>>11498708
Thank you.

[Anonymous No.11498781]

Fuck this soul crushing autistic number sudoku
Discrete math really btfod me
I’m thinking about dropping out and becoming a fucking welder

[Anonymous No.11498787]

>>11498759
I mean this is cringy as fuck to say about oneself but that picture is literally me (except the drug-free part, I'll have a beer or a jay from time to time)

[Anonymous No.11498820]

>>11498605
You could be talking about ramsey theory (or a million other things desu)

[Anonymous No.11499079]

Fuck women. I've dexided that from now on my life will be only math and my hobbies, it's the best thing one can do, mathematics is so perfect, it doesn't hurt, it doesn't delude you and then throw yiu away, it's the structure if everything, why would anyone spend time on women when they can do much better? I'm gonna spend all my time doing math and other productive activities from now on. Sorry is this post bothers anyone, but I wanna seal my commitment by writing it all on /mg/, I'm a new man from today on.

[Anonymous No.11499101]

>>11498781
you're a brainlet

[Anonymous No.11499109]

>>11499079
>it doesn't hurt
Topology would like to disagree

[Anonymous No.11499112]

>>11499079
research science is better for a sterile half-life like the one you seek. also women have no control over their propensity to be evil, hating them is a waste of energy

[Anonymous No.11499122]

>>11499112
>also women have no control over their propensity to be evil
Yes, I realize that now, I experienced it once before, but I thought that was an exception, now I tried again and the end result is the same, I'm completely broken, with suicidal feelings, they say they love you one day, then discard you on the next one like nothing, and I don't want anyone saying otherwise because I'm experiencing this evil shit right now, it's terrible, they care not for the pain you feel.

I'll become a full-on math monk from now on, fuck women.

[Anonymous No.11499135]

>>11499122
that's just sexual selection anon, they can't control their behavior any more than you can. there is no malice involved and turning away from life for the sake of avoiding emotional injury is an act of total cowardice

[Anonymous No.11499162]

>>11499135
Whenever a girl breaks up with me I feel an extreme-level depression, like I've never felt before, even if I don't love her all that much, it breaks me completely, last time I barely ate anything for an entire week, this time it hurts all the same, how can I just accept this everytime someone breaks up with me? I don't care if I'm a coward, I just don't wanna have those depressive feelings again, math never betrayed me like that, nor did any of my hobbies, as I grow up I feel like life is all about your hobbies than relationships.

[Anonymous No.11499178]

I took my school's calc series (including vector calc), which was non-rigorous and computation orientated using Stewart's 'Calculus: Concepts and Contexts' book, but have probably forgotten most of it. I've begun to review with Spivak's Calculus and Terry Tao's Analysis I (along with a handful of other supplementary material), but I feel sketchy about learning analysis while possibly forgetting all of calculus.

So, can you recommend a good overview/refresher or series of problem sets to review up to and incluing vector calc? Stewart's book is really big and it's too easy to get bogged down and waste too much time, imo. When I try this, I do suprise myself with how much I've retained, though. Alternatively, is it not even worthwhile to review calc? Should I just plow through with intro analysis?

thanks

[Anonymous No.11499181]

>>11499162
> I just don't wanna have those depressive feelings again
you have no control over this
>math never hurt me
>my hobbies never hurt me
you stake nothing on these activities, the potential loss is so low as to be negligible. can you see why it is that love and friendship can cause you pain but things like academic and personal frivolities cannot?

[Anonymous No.11499186]

>>11499178
No need for that man, you still remember how to solve limits? Remember how to derivate? Chain rule? L'Hôpital? Remember the integration techiniques? If you know those you'll be fine in Analysis, at least I was.

[Anonymous No.11499187]

>>11499178
Spivak isn't analysis, try Courant's two volume set or Apostol's two volume set, otherwise Hubbard and Hubbard, Lax's Calc books which are like a more refined version of what Stewart purports itself to be teaching, and if you have the patience for his atrocious writing, Lang's Calculus books especially his multi book are adequate. You should not try to learn analysis until you have proper foundations in Calculus and can solve the exercise in the first few chapters of Apostol or Spivak. Zorich's mathematical analysis is a true hybrid of Analysis and Calculus but varies in quality, I think his treatment of integral calculus is idiotic but the diff calc and vector calc is top notch

[Anonymous No.11499189]

>>11499181
Well, if that's the case then why should I keep staking on relationships when the end is all pain and unfortune? I should just focus on the things that won't make me hurt at all, am I a coward for not wanting to seek love when all it brings is unhappiness?

[Anonymous No.11499193]

>>11499189
No, you're a coward for asking others to help you protect yourself from living. Do whatever you want.

[Anonymous No.11499198]

>>11499186
Sounds good, I didn't really enjoy Stewart's calculus anyway (compared to Tao or Spivak's expositions) and I like the idea of just speeding right along like a maglev train

>>11499187
Apostol and Courant are both saved as pdfs and I (rarely) refer to them as supplements when Spivak is reaming my ass a little too hard. I'll snag those others though and thanks. I think I'll just proceed learning from Spivak and Tao as they are a good level for my maths maturity and proof writing ability. but if i get hung up on some abstract stuff I may drop back down into some calc review. sound smart? or dumb?

Also, I occassionally see Spivak's text used in intro analysis courses, and chapter 5 is introducing delta epsilon proofs - why is this not considered analysis, or at least intro analysis? I think Munkres has an intro analysis text that is even lighter than spivak's calculus, and spivak says himself in the intro that it should've been titled as an analysis text. genuine question btw no flames

[Anonymous No.11499202]

Is IUT valid or it's a waste of time to try to understand it?

[Anonymous No.11499301]

>>11499202
Mochizuki's "proof" of ABC is a failure.

[Anonymous No.11499305]

>>11499301
Why is it?

[Anonymous No.11499340]

>>11499202
There are debates among the math community my man, no one here or anywhere can say for certain whether or not it's valid, if you're interested in it so much you should read the 4 papers published by mochizuki and read the debates online then form your own opinion.

[Anonymous No.11499341]

>>11499198
you sound dumb, yes. construction of the reals and basic point set topology are absent from the first ~26 chapters of the book. its not real analysis

[Anonymous No.11499352]

>>11499340
>if you're interested in it so much you should read the 4 papers published by mochizuki
While I'm interested, I just fear that I may waste my time, sadly.

[Anonymous No.11499364]

>>11499341
why do i sound dumb? and I didn't say it was a comprehensive real analysis text, but that the author considers it an /intro/ analysis text

[Anonymous No.11499387]

>>11499352
You're already wasting your time here, you already wasted countless time on several other different activities, life itself is just wasting time, just try it already.

[Anonymous No.11499431]

>>11499364
>why do I sound dumb
analyze your own behavior from a position of total detachment and suspicion for a day including every post you've made online in the last 24 hours. you'll find good answers lying in wait for you
>the author said
Spivak isn't a reliable narrator.

[Anonymous No.11499433]

>>11499387
I guess you are right.

[Anonymous No.11499478]

>>11499341
>construction of the reals
imagine giving a shit about this lmao. if you're really curious then read the Wiki article about Dedekind cuts; that's all you'll ever need to know. why waste your or a student's time and brain cells on something that banal

[Anonymous No.11499507]

>>11499478
Welcome to mathematics.

[Anonymous No.11499633]

>>11499431
this post is way more stupid than anything i’ve posted. i was asking for your opinion and observations, not some retarded dribble and advice

also, this is all i’ve posted in the past 24 hours, retard

[Anonymous No.11499657]

>>11494679
good post, thanks, it's a really wholesome movie

[Anonymous No.11499683]

[math]
\text{ }^{\color{#571da2}{\displaystyle\widehat{\infty}}}\text{ }^{^{^{^{\color{#462eb9}{\displaystyle\widehat{\infty}}}}}}\text{ }^{^{^{^{^{^{^{\color{#3f47c8}{\displaystyle\widehat{\infty}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{\color{#3f62cf}{\displaystyle\text{ }}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#437ccc}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#4b90bf}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#56a0ae}{\displaystyle\text{ }}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#62ab99}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#71b484}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#82ba70}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#96bc5f}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#a9bd52}{\displaystyle\text{ }}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#bcbb48}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#ceb541}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#dcab3c}{\displaystyle\text{ }}}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{^{^{^{\color{#e39938}{\displaystyle\widehat{\infty}}}}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{^{^{^{\color{#e68033}{\displaystyle\widehat{\infty}}}}}}}}}}}}\text{ }^{^{^{^{^{^{^{\color{#e3632d}{\displaystyle\widehat{\infty}}}}}}}}}\text{ }^{^{^{^{\color{#de4227}{\displaystyle\widehat{\infty}}}}}}\text{ }^{\color{#da2121}{\displaystyle\widehat{\infty}}}
[/math]

[Anonymous No.11499929]

>>11499683
funny post
i really appreciate this funypost

[Anonymous No.11499933]

>>11499162
>Whenever a girl breaks up with me
>Dated a girl in the first place
Go fuck yourself buddy
>>11499657
Where did you find the movie, kind of want to watch it myself.

[Anonymous No.11499986]

>>11499079
If it doesn't hurt, you aren't pushing your limits.

[Anonymous No.11500001]

>>11491787
Threadly reminder that we're all gonna make it.

[Anonymous No.11500002]

>>11499933
>where did you find the movie
quick piratebay search. magnet link: magnet:?xt=urn:btih:f6f9545e93d91ecae4728964ef5cef54a6f98609&dn=Gifted+%282017%29+%5B1080p%5D+%5BEnglish%5D&tr=udp%3A%2F%2Ftracker.leechers-paradise.org%3A6969&tr=udp%3A%2F%2Fzer0day.ch%3A1337&tr=udp%3A%2F%2Fopen.demonii.com%3A1337&tr=udp%3A%2F%2Ftracker.coppersurfer.tk%3A6969&tr=udp%3A%2F%2Fexodus.desync.com%3A6969

[Anonymous No.11500005]

The theory of statistics (when it isn't about statistical mechanics or pure mathematical measure theoretic things) is usually concerned with the inference problem--- what is the likelyhood of a parameter to be [math] x [/math] when a measured quantity correlated with the parameter is measured to be [math] y_1,y_2,...,y_n [/math] in a sequence of trials.
The complete solution to this problem is given by Bayes's theorem: the probability that the underlying parameter has value [math] x [/math] is given by the probability that this value [math] x [/math] will produce the experimental results [math] y_1,y_2,..,y_n [/math] conditioned by the prior knowledge which gives you some distribution on [math] x [/math] to begin with.
Because Bayes's theorem solves the problem of inference so simply and naturally, the field of statistics is almost entirely built on rejecting it. Most of the field is based on the idea that one should not do Bayesian inference for one cockamamie reason or another, usually based on some silly philosphy which rejects priors or rejects the notion of a fundamental a-priori notion of probability. Because of this, physicists never learn Baysian inference from a class, they have to rediscover it for themselves (I certainly did, and most other people who do inference do too).
This means that if you hire a statistician, they will most often find lousy workarounds for Baysian methods, which will be useless to the experimental physicist. The issue is deeply ingrained--- many famous topics in statistics, like the sufficient statistics or the t-test, are born of the quest for a non-Baysian inference This quest is misguided, and will waste the experimental physicist's time. Within statistics, however, anti-Baysianism is a useful motivation for new results, so the field is dominated by anti-Bayesians.
It is also true in Biology. There, the Baysian method is (with difficulty) replacing statistician's pet inference methodologies.

[Anonymous No.11500007]

>>11500002
Thanks anon, I was being stupid, I'll do better next time.

[Anonymous No.11500015]

>>11498307
>>11498661
there are two main topics in beginner's algebraic topology: homology/cohomology and homotopy theory
Lee's book is first half gentle introduction into general topology, second half is gentle introduction into homotopy theory
I like the book very much and I learned a lot from it. but no way you will "know algebraic topology" after reading it.

[Anonymous No.11500091]

>>11500015
There's a bit of homology in there as well. If you supplement it with his smooth manifolds book as well (basically the chapter going over cohomology), then you have a decent intro to algebraic topology. It gives a good enough basis to attack books like Bott and tu imo.

[Anonymous No.11500098]

brainlet here, how can I git gud at math in 5 months (compsci level)?
Im a neet and have lots of free time lmao

[Anonymous No.11500119]

>>11500098
Just look online for free resources. For example:
https://www.quantstart.com/articles/How-to-Learn-Advanced-Mathematics-Without-Heading-to-University-Part-1/
Just one of many articles. Take it as you will.
But know where to start. One technique is to look up any uni's courses online, and see about what textbooks they use, etc.
You an also take whole free courses in PreCalc, Calc, and other basic things online.
You can buy reference books like Princeton's Companion to Mathematics, to use as you encounter new things you're unfamiliar with.

[Anonymous No.11500231]

Frens, is there hope in this field? Suppose I give my life to it and crush undergrad math with a 4.0 at a decent mid tier school, get enough research chops to finish a reasonable PhD thesis, etc. What's next? Can I reasonably do research math to put food on the table?

I ask because many people opt to be software engineers and researchers solving practical problems in finance and such, likely due to scarce opportunities in pure science. Seems like it would be such a downer to resort to that desu

t. middling software developer considering a second bachelor's in math then math or stats grad school

If I could even be an adjunct prof with some research record that'd be fucking great desu

[Anonymous No.11500233]

>>11500231
I didn't mean to say DESU DESU I wrote t-b-h
That desu shit is fucking annoying lol

[Anonymous No.11500242]

>>11500231
>DASU DASU
lol weeaboo confirmed

[Anonymous No.11500246]

Does icositetrachoron have any stellations? (My spatial imagination upon the very sight of 24-cell said 'fuck off')

[Anonymous No.11500247]

>>11500242
>dasu
Retard confirmed.

[Anonymous No.11500263]

>>11500242
>>11500247
kek

[Anonymous No.11500278]

Fucking corona. I can't even give up on my PhD because getting back to my home country is made practically impossible. I really hate my incompetence in maths.

[Anonymous No.11500313]

post problems
im gonna solve them

[Anonymous No.11500332]

Why is combinatorics so hard? I did everything right and still failed (I got a very low grade). I learned the theory, proofs and all.
The problem is I still had piss poor problem solving skills.
But I did all the problem sets and past exams.

What else could I do to improve my problem solving skills? I guess I must be studying wrong somehow. But not sure what exactly I am doing wrong.

[Anonymous No.11500347]

>>11500001
Thanks, lad. Best of luck.

[Anonymous No.11500359]

>>11500001
Thank you my man

[Anonymous No.11500369]

>>11500332
>Why is combinatorics so hard?
you answered yourself, it requires you to solve problems which don't follow a simple pattern
in other courses there are often just a few typical problems and if you can do those you're guaranteed to pass. Take, for example, linear algebra, an average exam will have questions like
- solve a system of linear equations
- compute eigenvalues and eigenvectors of a matrix

[Anonymous No.11500382]

>>11500369
OK, but how do I do well on such an exam?
Other people did well so obviously there is a way.
I just do not know exactly what I could have done better.
I guess maybe I should have put in more time, and learned the theory earlier, so that I could have done more problems from random textbooks?!
But that is all hindsight. I could not have known that at the start of the class, so I chose to invest my time in other classes.

What else could I have done?

[Anonymous No.11500403]

>>11500382
The challenge of combinatorics isn't the math. It's the language. It's figuring out exactly what the question is asking for and how to solve it.

[Anonymous No.11500413]

why should i learn maths, my life is doomed to do mundaen cooding til i die.
is there any point for a brainlet to learn any advanced maths?

why do you learn or like maths?

[Anonymous No.11500523]

>>11500231
Why would you not just go to grad school for CS instead? That would make much more sense. You can slowly inch your way towards math from there.
But honestly, job prospects wise both in industry and in academia are far worse than for CS and definitely worse than Software Development/Engineering/ICT whatever. If you want to be an adjunct prof, why not in your field of expertise?

[Anonymous No.11500808]

>>11500015
So what algebraic topology book you recommend? Can I use Lee instead of Munkres as a complete beginner to general topology then?

[Anonymous No.11500829]

>>11500808
damn even the doomer meme is easy mode when it's applied to women. "never will know what highschool live is like" lmao hahahaha

[LMC !!6bFXHDKL67m No.11500846]

>>11494679
>>11499657
>>11500002
Holy crap. I've never really enjoyed a feature-length math film before so I had low expectations for this. I think they actually pulled it off, because I kinda ended up loving this film.

[Anonymous No.11500856]

>>11500413
You will find most people will not be able to bullshit you if you have solid math foundations. Specially in coding were people like to use bullshit term for the application of some simple mathematical concepts. The thing is, it will lool useless at first but the you will be able to go into a bunch of topics. That's why since elementary school you are taught 2 basic skills languange and maths, don't skimp on the first to also prevent philosotards from bullshititng you.

[Anonymous No.11500865]

>>11500808
Use Rotman's book on alg topo.

[Anonymous No.11500884]

An infinite number of mathematicians, a polar bear, helium, and a neutrino walk into a bar (ouch). One of the mathematicians then says, "the bar is now empty" and they begin to play hide and seek. The neutrino is then stopped by a police officer. Officer Heisenberg says, "Do you know how fast you were going back there?" The neutrino replies, "I'm positive and a pascal but I don't know where I am." The bar tender then says "You're all idiots, the cows are all black" and pours 10 (in base 2, i mean 10) drinks and there is an extra dollar. The polar bear then dissolves in water while the helium does not react.

[Anonymous No.11500889]

>>11500808
Hatcher is the go to for a lot of people, but it is worth mentioning that a lot of algebraic topology heavily uses category theory and spanier introduces that stuff from the get go and is more in depth. Fomenko-Fuchs is also pretty great. Also, it's not like people typically go through a subject once and never touch it again. Feel free to use multiple books or read part of one and part of another. Lee doesn't cover all the material in Munkres, only most of it. Discussion about separation theorems and whether a space is metrizable are completely left out in the former, simply because they aren't really relevant for the study of topological manifolds. And frankly, I don't think you'll really need them for your purposes, but again, you can just read Lee and then check out the sections in Munkres that leave out some of the general topology.
>>11500382
There are some typical heuristics I always use when attacking a combinatorial problem. A lot of times there are recurrence relations of some kind, and that can help you dramatically simplify the problem. Finding a generating function as well is really useful. For me, I usually mess around with the problem until I get a good feel for the overall structure, and from there it gets a bit easier. Really anon, it goes down to practice. I'd suggest looking up the first chapter of Stanley's ennumerative combinatorics, it goes through a ton of different techniques and combinatorial questions.
>>11500231
I'll second >>11500523, CS theory is math adjacent, and there's a lot of reasonably interesting work there that you can pivot into pure math. Here's a paper written by some cs theory and stats guys that's in the annals
https://annals.math.princeton.edu/wp-content/uploads/annals-v175-n3-p08-p.pdf

[Anonymous No.11500896]

>>11500884
I don't get it, why is the bar empty when there's an infinite amount of mathematicians, a polar bear, helium, a neutrino and a police officer?

[Anonymous No.11500902]

>>11500889
Fuchs-Fomenko is homotopical topology though, so it's the same thing as alg topo?

[Anonymous No.11500914]

>>11500902
Technically speaking, homotopy theory and algebraic topology aren't exactly the same thing, since, say, non-algebraic properties of fibrations and cofibrations aren't really algebraic topology, but there is quite some overlap.
I'd consider homotopy theory to be "the study of homotopy, isotopy and related notions" and algebraic topology to be "the study of functors from Top and Top* to algebraic categories", but it's kinda forced.

[Anonymous No.11500925]

>>11500889
>annals
I'm sorry, totally unrelated to your post, but I've always been curious as to what that word means at all.

[Anonymous No.11500964]

>>11500925
Sort of like the hall of fame, or in this context, more like the place where record the cream of the crop

[Anonymous No.11500972]

>>11500964
So it's like a book where they gather the most relevant scientific papers?

[Anonymous No.11500980]

>>11500889
>>11500902
>Fuchs-Fomenko homotopical topology
Oh Man. Now that's a classic for its illustrations alone. If you've never seen the artwork before, then I insist you go flip through the pdf right fuchsing now. I love to flip through my copy if I ever need to feel deeply inspired. Gives me a righteous wangbone, and a unique feeling that reminds me of the passionate excitement I felt when I was much younger and realizing for the first time that math was a lot cooler than I'd previously believed.

[Anonymous No.11500988]

>>11491787
Anyone know where to read about quadratic equation like Nature of roots, graphs etc not the quadratic formula

[Anonymous No.11500994]

>>11500884
lol

[Anonymous No.11500998]

>>11500972
Basically, the papers that really are ground breaking and will be regarded as classics in the future. Since the annals publishes those papers, it in a sense keeps a record of those classic papers.
>>11500980
His mathematical illustrations book is also amazing, shame it's not online and tracking down a physical copy is difficult. Next best thing, however, is this
http://chronologia.org/art/
Shame the quality is only so so

[Anonymous No.11501064]

Everything in modern mathematics should be written and studied in the lamguage of category theory, we should abandon set theory as a foundation, for although it was once useful, now it has been made completely obsolete with the discoveries of category theory. If we want mathematics to move foward, we must redo it from scratch using only categories alone and keep going with it until a better foundation is discovered, if it ever does.

[Anonymous No.11501073]

>>11501064
do you have any suggestions how to rewrite calculus/basic analysis in terms of category theory ?

[Anonymous No.11501078]

>>11501064
How the fuck do you write local definitions like the derivative and limits in the languange of category theory? You are not always working with a whole class of functions.

[Anonymous No.11501126]

>>11501073
>>11501078
If the efforts of researchers were focused on findings ways to rewrite calculus in terms of categories, I'm sure we would already have opened entire new fields i mathematics, but mathematicians are stagnating, no one challenges the status quo, everyone seems satisfied with the failed foundation of set theory. We must strive for progress, and progress has a name right now: Category Theory. So let's get to work and discover new ways in which we can rewrite classical mathematics in terms of categories.

[Anonymous No.11501136]

>>11501126
>focusing on novel ideas rather than rewriting hundred years old stuff in a different language
>stagnating

[Anonymous No.11501145]

>>11501064
>>11501126
this is hilarious keep up the good work man

[Anonymous No.11501149]

>>11500808
For an introduction there really is no better book than Hatcher

[Anonymous No.11501153]

This has been one of the best /mg/ threads in ages, I don't want it to die.

[Anonymous No.11501171]

>>11501136
By rewriting calculus in terms of categories we could unlock whole new areas of mathematics we didn't even thought existed, everyone is simply ignoring the importance of establishing categories as the main foundation of mathematics, it's not about formality, it's about doing math the right way and if set theory has taught us something it's that it's deeply flawed.

[Anonymous No.11501218]

>>11501171
>unlock
>he says like it's a videogame and the point of maths is unlocking more fields
Fuck, remember when Gauss completed the Theorema Egregium and this allowed Riemann to start the quest that unlocks Riemannian Geometry? Absolute kino. If it weren't for him, Minkowski would have never managed to unlock semi-Riemannian and Einstein wouldn't have been able to use his kill streak bonus from special relativity, photoeletric effect and Brownian motion to succesfully boss rush through General relativity.

[Anonymous No.11501274]

>>11501218
Top kek.

What's riemannian geometry useful for nowadays? What's the best book for studying it? Do carmo's?

[Anonymous No.11501287]

>>11501274
Go for Chavel or Petersen.

[Anonymous No.11501303]

>>11501218
i don't remember because diff geo is gay garbage

[Anonymous No.11501310]

>>11501218
>the point of maths is unlocking more fields
What is it then? The point of math is making progress until we reach and explore all fields possible, we're not even close to that yet and with set theory as our foundation we'll never achieve it, category theory is a shining light at the end of the dark tunnel that set theory has become over the years.

[Anonymous No.11501321]

>>11501310
the point of maths is solving problems
for example, number theory and algebraic geometry is a field created to help in solving problems about polynomials and diophantine equations

[Anonymous No.11501322]

>>11501218

[Anonymous No.11501336]

>>11501153
>This has been one of the best /mg/ threads in ages, I don't want it to die.
>tfw this is the first /mg/ thread in two years that I've posted in.
You're welcome.
>>11501126
>rewrite calculus in terms of categories
>implying it hasn't already
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.297.4139&rep=rep1&type=pdf

[Anonymous No.11501355]

>>11501322
I fucked up the person who unlocked semi-Riemannian geometry, didn't I?

[Anonymous No.11501360]

Why aren't more mathematicians out there committing perfect crimes? Has anyone tried this? I'm gonna try this.

[Anonymous No.11501378]

>>11501360
Think about, when your a prof at a uni you basically sit around all, not doing shit except arcane math that only you and your buddies can actually evaluate the value of, so you spew a bunch of bullshit and people will nod along, then you get funding and grad students to bully. You control the lives of undergrads and they bend to your will. Free donuts or pizza at colloquium talks. Frankly, being a mathematician is already the perfect crime.

[Anonymous No.11501397]

>>11501321
>diophantine equations
no one cares about that ancient crap anymore.

[Anonymous No.11501405]

>>11501171
It honestly just leads to wiring diagram autism
http://math.ucr.edu/home/baez/ACT2017/ACT2017_vagner.pdf

[Anonymous No.11501423]

>>11500889
>Fomenko-Fuchs
Horrible for reading. You will just look at the art.

[Anonymous No.11501460]

>>11501423
Why?

[Anonymous No.11501463]

>>11501397
anon FLT was only like 20 years ago

[Anonymous No.11501489]

>>11501460
Because it is fucking awesome.

[Anonymous No.11501529]

>>11501397
yes, a lot of people don't care
still, there should be some collection of basic problems and basic objects that you care about, and when you develop new definitions and objects, you ask yourself: how is this relevant to <things that I care about>?
otherwise you become an undergrad category theorist who just wants to create more fields of math because he thinks the point of math is creating more definitions

[Anonymous No.11501588]

>>11501463
>that random paper cup in the background.
Holy shit andrew, and I thought my office was messy.

[Anonymous No.11501632]

>>11492257
I've heard good things about The Man Who Knew Infinity, a Ramanujan biopic. Ken Ono and Manjul Bhargava consulted on it.

[Anonymous No.11501639]

>>11501632
It's a terrible movie though. Ramanujan's contributions are heavily overestimated by the NWO who wants to normalize that anyone can be a STEM genius.

[Anonymous No.11501973]

>>11499341
>construction of the reals
>>>/x/

[Anonymous No.11502152]

New thread

>>11502149