/mg/ maths general: châu edition

[Anonymous No.9953706]

http://www.math.uchicago.edu/~ngo/nbc-homepage.html
https://en.wikipedia.org/wiki/Ng%C3%B4_B%E1%BA%A3o_Ch%C3%A2u
https://en.wikipedia.org/wiki/Fundamental_lemma_(Langlands_program)

formerly >>9933606

[Anonymous No.9953757]

>>9953706
first for visualizing unit balls in infinite dimensional hilbert spaces

[Anonymous No.9953783]

I don't know if this is the best way to master math, but fuck it. I'm gonna post this every thread because I'm tired of seeing people keep asking for advice on this matter. Hope you guys don't mind.

>how to go full math monk
http://4chan-science.wikia.com/wiki/Mathematics
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
https://pastebin.com/V8WNshHV

>where to download it
http://libgen.io/

[Anonymous No.9953891]

If Linear Algebra exists, then how come there’s no such thing as Nonlinear Algebra?

[Anonymous No.9953903]

>>9953891
Every time you solve a quadratic equation you're doing nonlinear algebra

[Anonymous No.9953932]

>>9953903
But why isn't there a math branch dedicated exclusively to studying nonlinear algebra like linear algebra?

[Anonymous No.9953939]

>>9953932
Isn't that just multivariable calculus?

[Anonymous No.9953954]

>>9953932
yeah, it's called abstract algebra
algebraic number theory deals especially with the algebra over the integers/rationals
algebraic geometry deals with the geometry that arises from their study

[Anonymous No.9953962]

>>9953932
There's lots of different branches of algebra that are non-linear. The reason it's so widespread is that it arises naturally in a lot of real world problems and it is really easy to work with. Lots of nonlinear problems simply don't have good (easy to fins) solutions in the same way linear ones do. If they do, they sometimes come from approximating them as or reducing them to linear algebra problems.

[Anonymous No.9953999]

>tfw no pure math this semester
>tfw only stochastic processes II in the spring as a math course

[Anonymous No.9954065]

In math, Number Theory is all that matters. Nothing else is important.

[Anonymous No.9954163]

Best math blogs?

John Baez's is my favorite.

[Anonymous No.9954187]

>>9953932
Because categorizing shit into linear and non linear, is like categorizing the objects in the world as either banana, ir non banana. Non linear means everything else and it's not really defined by an overall structure.

[Anonymous No.9954189]

>>9954187
>is like categorizing the objects in the world as either banana, or non banana
I'm going to start doing this

[Anonymous No.9954191]

>>9954187
what about plaintains
do you consider them 0 banana or some nonzero banana measure

[Anonymous No.9954195]

>>9954187
I feel an extreme tendency to make some pun on banach spaces but I can't think of any

[Anonymous No.9954216]

>>9953783
qt

[Anonymous No.9954240]

>>9954163
Woit, mathbabe, terrytao, piper's, etc... There's lots of good ones.

[Anonymous No.9954563]

>August is almost over
>Mochizuki and Scholze still haven't published anything

[Anonymous No.9954856]

lads, am i tweaking?

1 doesn't give an upper bound for the price of cars > 10,000, so the mean has no upper limit,

2 should be read as 3÷1÷9 = 1/3?

[Anonymous No.9954883]

>>9954856
it says median
it should be read 3/(1/(3^2))
3/(1/9)
3*9
3*3^2
3^3

[Anonymous No.9954942]

>>9954883
Why don't you square the 3 first? Order of operations has exponents before division. And the parentheses you put in aren't in the expression.

[Anonymous No.9954966]

>>9953783
>http://4chan-science.wikia.com/wiki/Mathematics
not a good list

>https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
outdated

>https://pastebin.com/V8WNshHV
useless

Here, try this instead.

High School:
• Euclidean geometry, complex numbers, scalar multiplication, Cauchy-Bunyakovskii inequality. Introduction to quantum mechanics (Kostrikin-Manin). Groups of transformations of a plane and space. Derivation of trigonometric identities. Geometry on the upper half-plane (Lobachevsky). Properties of inversion. The action of fractional-linear transformations.
• Rings, fields. Linear algebra, finite groups, Galois theory. Proof of Abel's theorem. Basis, rank, determinants, classical Lie groups. Dedekind cuts. Construction of real and complex numbers. Definition of the tensor product of vector spaces.
• Set theory. Zorn's lemma. Completely ordered sets. Cauchy-Hamel basis. Cantor-Bernstein theorem.
• Metric spaces. Set-theoretic topology (definition of continuous mappings, compactness, proper mappings). Definition of compactness in terms of convergent sequences for spaces with a countable base. Homotopy, fundamental group, homotopy equivalence.
• p-adic numbers, Ostrovsky's theorem, multiplication and division of p-adic numbers by hand.
• Differentiation, integration, Newton-Leibniz formula. Delta-epsilon formalism.

[Anonymous No.9954968]

>>9954966
Freshman:
• Analysis in R^n. Differential of a mapping. Contraction mapping lemma. Implicit function theorem. The Riemann-Lebesgue integral. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Hilbert spaces, Banach spaces (definition). The existence of a basis in a Hilbert space. Continuous and discontinuous linear operators. Continuity criteria. Examples of compact operators. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Smooth manifolds, submersions, immersions, Sard's theorem. The partition of unity. Differential topology (Milnor-Wallace). Transversality. Degree of mapping as a topological invariant.
• Differential forms, the de Rham operator, the Stokes theorem, the Maxwell equation of the electromagnetic field. The Gauss-Ostrogradsky theorem as a particular example.
• Complex analysis of one variable (according to the book of Henri Cartan or the first volume of Shabat). Contour integrals, Cauchy's formula, Riemann's theorem on mappings from any simply-connected subset C to a circle, the extension theorem, Little Picard Theorem. Multivalued functions (for example, the logarithm).
• The theory of categories, definition, functors, equivalences, adjoint functors (Mac Lane, Categories for the working mathematician, Gelfand-Manin, first chapter).
• Groups and Lie algebras. Lie groups. Lie algebras as their linearizations. Universal enveloping algebra, Poincaré-Birkhoff-Witt theorem. Free Lie algebras. The Campbell-Hausdorff series and the construction of a Lie group by its algebra (yellow Serre, first half).

[Anonymous No.9954971]

>>9954968
Sophomore:
• Algebraic topology (Fuchs-Fomenko). Cohomology (simplicial, singular, de Rham), their equivalence, Poincaré duality, homotopy groups. Dimension. Fibrations (in the sense of Serre), spectral sequences (Mishchenko, "Vector bundles ...").
• Computation of the cohomology of classical Lie groups and projective spaces.
• Vector bundles, connectivity, Gauss-Bonnet formula, Euler, Chern, Pontryagin, Stiefel-Whitney classes. Multiplicativity of Chern characteristic. Classifying spaces ("Characteristic Classes", Milnor and Stasheff).
• Differential geometry. The Levi-Civita connection, curvature, algebraic and differential identities of Bianchi. Killing fields. Gaussian curvature of a two-dimensional Riemannian manifold. Cellular decomposition of loop space in terms of geodesics. The Morse theory on loop space (Milnor's Morse Theory and Arthur Besse's Einstein Manifolds). Principal bundles and connections on them.
• Commutative algebra (Atiyah-MacDonald). Noetherian rings, Krull dimension, Nakayama lemma, adic completion, integrally closed, discrete valuation rings. Flat modules, local criterion of flatness.
• The Beginning of Algebraic Geometry. (The first chapter of Hartshorne or Shafarevich or green Mumford). Affine varieties, projective varieties, projective morphisms, the image of a projective variety is projective (via resultants). Sheaves. Zariski topology. Algebraic manifold as a ringed space. Hilbert's Nullstellensatz. Spectrum of a ring.
• Introduction to homological algebra. Ext, Tor groups for modules over a ring, resolvents, projective and injective modules (Atiyah-MacDonald). Construction of injective modules. Grothendieck Duality (from the book Springer Lecture Notes in Math, Grothendieck Duality, numbers 21 and 40).
• Number theory; Local and global fields, discriminant, norm, group of ideal classes (blue book of Cassels and Frohlich).

[Anonymous No.9954973]

>>9954971
Sophomore (cont):
• Reductive groups, root systems, representations of semisimple groups, weights, Killing form. Groups generated by reflections, their classification. Cohomology of Lie algebras. Computing cohomology in terms of invariant forms. Singular cohomology of a compact Lie group and the cohomology of its algebra. Invariants of classical Lie groups. (Yellow Serre, the second half, Hermann Weyl, "The Classical Groups: Their Invariants and Representations"). Constructions of special Lie groups. Hopf algebras. Quantum groups (definition).

Junior:
• K-theory as a cohomology functor, Bott periodicity, Clifford algebras. Spinors (Atiyah's book "K-Theory" or AS Mishchenko "Vector bundles and their applications"). Spectra. Eilenberg-MacLane Spaces. Infinite loop spaces (according to the book of Switzer or the yellow book of Adams or Adams "Lectures on generalized cohomology", 1972).
• Differential operators, pseudodifferential operators, symbol, elliptic operators. Properties of the Laplace operator. Self-adjoint operators with discrete spectrum. The Green's operator and applications to the Hodge theory on Riemannian manifolds. Quantum mechanics. (R. Wells's book on analysis or Mishchenko "Vector bundles and their application").
• The index formula (Atiyah-Bott-Patodi, Mishchenko), the Riemann-Roch formula. The zeta function of an operator with a discrete spectrum and its asymptotics.
• Homological algebra (Gel'fand-Manin, all chapters except the last chapter). Cohomology of sheaves, derived categories, triangulated categories, derived functor, spectral sequence of a double complex. The composition of triangulated functors and the corresponding spectral sequence. Verdier's duality. The formalism of the six functors and the perverse sheaves.

[Anonymous No.9954976]

>>9954973
Junior (cont):
• Algebraic geometry of schemes, schemes over a ring, projective spectra, derivatives of a function, Serre duality, coherent sheaves, base change. Proper and separable schemes, a valuation criterion for properness and separability (Hartshorne). Functors, representability, moduli spaces. Direct and inverse images of sheaves, higher direct images. With proper mapping, higher direct images are coherent.
• Cohomological methods in algebraic geometry, semicontinuity of cohomology, Zariski's connectedness theorem, Stein factorization.
• Kähler manifolds, Lefschetz's theorem, Hodge theory, Kodaira's relations, properties of the Laplace operator (chapter zero of Griffiths-Harris, is clearly presented in the book by André Weil, "Kähler manifolds"). Hermitian bundles. Line bundles and their curvature. Line bundles with positive curvature. Kodaira-Nakano's theorem on the vanishing of cohomology (Griffiths-Harris).
• Holonomy, the Ambrose-Singer theorem, special holonomies, the classification of holonomies, Calabi-Yau manifolds, Hyperkähler manifolds, the Calabi-Yau theorem.
• Spinors on manifolds, Dirac operator, Ricci curvature, Weizenbeck-Lichnerovich formula, Bochner's theorem. Bogomolov's theorem on the decomposition of manifolds with zero canonical class (Arthur Besse, "Einstein varieties").
• Tate cohomology and class field theory (Cassels-Fröhlich, blue book). Calculation of the quotient group of a Galois group of a number field by the commutator. The Brauer Group and its applications.
• Ergodic theory. Ergodicity of billiards.
• Complex curves, pseudoconformal mappings, Teichmüller spaces, Ahlfors-Bers theory (according to Ahlfors's thin book).

[Anonymous No.9954985]

>>9954976
Senior:
• Rational and profinite homotopy type. The nerve of the etale covering of the cellular space is homotopically equivalent to its profinite type. Topological definition of etale cohomology. Action of the Galois group on the profinite homotopy type (Sullivan, "Geometric topology").
• Etale cohomology in algebraic geometry, comparison functor, Henselian rings, geometric points. Base change. Any smooth manifold over a field locally in the etale topology is isomorphic to A^n. The etale fundamental group (Milne, Danilov's review from VINITI and SGA 4 1/2, Deligne's first article).
• Elliptic curves, j-invariant, automorphic forms, Taniyama-Weil conjecture and its applications to number theory (Fermat's theorem).
• Rational homotopies (according to the last chapter of Gel'fand-Manin's book or Griffiths-Morgan-Long-Sullivan's article). Massey operations and rational homotopy type. Vanishing Massey operations on a Kahler manifold.
• Chevalley groups, their generators and relations (according to Steinberg's book). Calculation of the group K_2 from the field (Milnor, Algebraic K-Theory).
• Quillen's algebraic K-theory, BGL^+ and Q-construction (Suslin's review in the 25th volume of VINITI, Quillen's lectures - Lecture Notes in Math. 341).
• Complex analytic manifolds, coherent sheaves, Oka's coherence theorem, Hilbert's nullstellensatz for ideals in a sheaf of holomorphic functions. Noetherian ring of germs of holomorphic functions, Weierstrass's theorem on division, Weierstrass's preparation theorem. The Branched Cover Theorem. The Grauert-Remmert theorem (the image of a compact analytic space under a holomorphic morphism is analytic). Hartogs' theorem on the extension of an analytic function. The multidimensional Cauchy formula and its applications (the uniform limit of holomorphic functions is holomorphic).

[Anonymous No.9954987]

>>9954985
Specialist: (Fifth year of College):
• The Kodaira-Spencer theory. Deformations of the manifold and solutions of the Maurer-Cartan equation. Maurer-Cartan solvability and Massey operations on the DG-Lie algebra of the cohomology of vector fields. The moduli spaces and their finite dimensionality (see Kontsevich's lectures, or Kodaira's collected works). Bogomolov-Tian-Todorov theorem on deformations of Calabi-Yau.
• Symplectic reduction. The momentum map. The Kempf-Ness theorem.
• Deformations of coherent sheaves and fiber bundles in algebraic geometry. Geometric theory of invariants. The moduli space of bundles on a curve. Stability. The compactifications of Uhlenbeck, Gieseker and Maruyama. The geometric theory of invariants is symplectic reduction (the third edition of Mumford's Geometric Invariant Theory, applications of Francis Kirwan).
• Instantons in four-dimensional geometry. Donaldson's theory. Donaldson's Invariants. Instantons on Kähler surfaces.
• Geometry of complex surfaces. Classification of Kodaira, Kähler and non-Kähler surfaces, Hilbert scheme of points on a surface. The criterion of Castelnuovo-Enriques, the Riemann-Roch formula, the Bogomolov-Miyaoka-Yau inequality. Relations between the numerical invariants of the surface. Elliptic surfaces, Kummer surface, surfaces of type K3 and Enriques.
• Elements of the Mori program: the Kawamata-Viehweg vanishing theorem, theorems on base point freeness, Mori's Cone Theorem (Clemens-Kollar-Mori, "Higher dimensional complex geometry" plus the not translated Kollar-Mori and Kawamata-Matsuki-Masuda).
• Stable bundles as instantons. Yang-Mills equation on a Kahler manifold. The Donaldson-Uhlenbeck-Yau theorem on Yang-Mills metrics on a stable bundle. Its interpretation in terms of symplectic reduction. Stable bundles and instantons on hyper-Kähler manifolds; An explicit solution of the Maurer-Cartan equation in terms of the Green operator.

[Anonymous No.9954988]

>>9954966
>>9954968
>>9954971
>>9954973
>>9954976
Nice meme Russianon.

[Anonymous No.9954989]

>>9954987
Specialist (cont):
• Pseudoholomorphic curves on a symplectic manifold. Gromov-Witten invariants. Quantum cohomology. Mirror hypothesis and its interpretation. The structure of the symplectomorphism group (according to the article of Kontsevich-Manin, Polterovich's book "Symplectic geometry", the green book on pseudoholomorphic curves and lecture notes by McDuff and Salamon)
• Complex spinors, the Seiberg-Witten equation, Seiberg-Witten invariants. Why the Seiberg-Witten invariants are equal to the Gromov-Witten invariants.
• Hyperkähler reduction. Flat bundles and the Yang-Mills equation. Hyperkähler structure on the moduli space of flat bundles (Hitchin-Simpson).
• Mixed Hodge structures. Mixed Hodge structures on the cohomology of an algebraic variety. Mixed Hodge structures on the Maltsev completion of the fundamental group. Variations of mixed Hodge structures. The nilpotent orbit theorem. The SL(2)-orbit theorem. Closed and vanishing cycles. The exact sequence of Clemens-Schmid (Griffiths red book "Transcendental methods in algebraic geometry").
• Non-Abelian Hodge theory. Variations of Hodge structures as fixed points of C^*-actions on the moduli space of Higgs bundles (Simpson's thesis).
• Weil conjectures and their proof. l-adic sheaves, perverse sheaves, Frobenius automorphism, weights, the purity theorem (Beilinson, Bernstein, Deligne, plus Deligne, Weil conjectures II)
• The quantitative algebraic topology of Gromov, (Gromov "Metric structures for Riemannian and non-Riemannian spaces"). Gromov-Hausdorff metric, the precompactness of a set of metric spaces, hyperbolic manifolds and hyperbolic groups, harmonic mappings into hyperbolic spaces, the proof of Mostow's rigidity theorem (two compact Kählerian manifolds covered by the same symmetric space X of negative curvature are isometric if their fundamental groups are isomorphic, and dim X> 1).
• Varieties of general type, Kobayashi and Bergman metrics, analytic rigidity (Siu)

[Anonymous No.9955014]

>>9954989
>dim X> 1
Shouldn't it be dim(X) > 2? Hyperbolic surfaces are not rigid.

[Anonymous No.9955040]

That was a very nice meme list, my man. How are you doing through it yourself?

[Anonymous No.9955069]

>>9954966
done
>>9954968
done
>>9954971
done
>>9954973
done
>>9954976
done except the last 3 points
>>9954985
done except algebraic k-theory stuff
>>9954987
done about half of these
>>9954989
done a couple of these

ez list

[Anonymous No.9955157]

>>9955069
If I may ask, is it a good list?

[Anonymous No.9955164]

>>9955157
>If I may ask, is it a good list?
Obviously.

[Anonymous No.9955168]

>>9955157
It is extremely bias towards one field of research, with a few unrelated things thrown in.

[Anonymous No.9955178]

Has anyone computed the Lurie cohomology of the category of axioms?

[Anonymous No.9955253]

>>9955178

I computed the cunt cohomology of your mother's morphism

[Anonymous No.9955261]

>>9955157
no its a meme

[Anonymous No.9955285]

>>9954883

>>9954942
>it says median
HOLY FUCK MY STUPID ASS

also this \/
>>9954883
why should it be read with parentheses that aren't there?

Here's a similar example, this time very slightly more reasonable considering the placement of the plus signs, but even this case is bullshit because the geometric position of arithmetic signs has literally never been assumed to determine order of operations.

[Anonymous No.9955287]

>>9955285
no wait, that's fucking bullshit, my answer was literally identical to the question.

[Anonymous No.9955336]

>>9953932
There are tons of math and physics departments that study nonlinear stuff

[Anonymous No.9955338]

>>9954065
Why did the thread continue after this comment?

[Anonymous No.9955415]

>>9953706
Might as well ask this question here, I really wnated to get into applied math (which is the closest thing to a pure math coruse 100 miles form where I live), but my parents despised it because it wasn't "practical" and I wouldn't get a "job".

tldr;

My question is, Will studying electronic engineering (my current major) allow me to study pure math later? It's a good course in it's own right, but does it have enough maths?

[Anonymous No.9955447]

>>9954065
Can you convince me of this? Quite frankly, as an abstract harmonic analyst, it seems the least interesting.

[Anonymous No.9955468]

>>9955157
No. The list doesn't even mention measure theory and then mentions Ergodic theory, something you can't make sense of without measure theory. That, and the fact it's tailored towards understanding some very specific things in geometry.

[Anonymous No.9955472]

>>9955415
Sorry m8, you'll see absolutely nothing resembling pure math in any engineering whatsoever. Doesn't make it inherently bad, nor does it mean it lacks mathematics, it's just there's a very distinct school of thought between pure and applied math.

[Anonymous No.9955536]

Question to you all, have you ever looked much into philosophy? Aside from brief glances at math related topics (like mathematical platonism) I've always got the impression that philosophy is a bit of a meme, but occasionally I do feel like studying it seriously.

Have any of you guys studied philosophy? Did it impress you? What topics did you find the most interesting?

[Anonymous No.9955592]

>>9955536
by far the best book on philosophy of mathematics is Synthetic Philosophy of
Contemporary Mathematics by Fernando Zalamea.

[Anonymous No.9955624]

>>9955536
I'm double majoring in math and philosophy. The two go together better than physics and math, I think

[Anonymous No.9955716]

Finally I don't have to squint my eyes trying to tell y'' from y' on this site

Thanks Paul

[Anonymous No.9955734]

>>9955536
Ah, you're one of those calculator types that treat math like a game.
That's kinda sad...

[Anonymous No.9955738]

>>9955624
This.

[Anonymous No.9955857]

>>9953783
>tfw 30 year old boomer hs dropout about to go full math monk mode
Last thing I ever remember doing was algebra.

[Anonymous No.9955859]

>>9953706
Is a mathematician isomorphic to a large pizza? Is a mathematician elementary equivalent to a large pizza?

[Anonymous No.9955866]

>>9955859
define mathematician
define pizza
define what constitutes a """large""" pizza

[Anonymous No.9956026]

What is the fundamental group of a bump?

[Anonymous No.9956044]

My complex analysis teacher has a hateboner for homotopy. Why is this?

[Anonymous No.9956458]

>>9953783
Keep up the good work desu

[Anonymous No.9956472]

>>9956044
Why don't you ask him and find out?

[Anonymous No.9956683]

How useful is Linear Programming?

I expected multilinear/tensor algebra after linear alg course but LP is all they got

[Anonymous No.9956695]

>>9956683
It has a lot of practical applications, and can be generalized further with different types of functions (quadratic ones, for example).

[Anonymous No.9956696]

>>9956683
As useful as it is boring: very.

[Anonymous No.9956769]

How to keep up with modern math? I'd like to know what's going on, but I don't know any sources other than Arxiv.

[Anonymous No.9956773]

>>9953932
That's algebraic geometry.

[Anonymous No.9956808]

>>9956769
Find some blogs to follow. Lots of mathematicians have them.

[Anonymous No.9956811]

>>9956808
How can I find relevant mathematicians? I only know Scholze, Mochizuki, Baez and Schwede by name.

[Anonymous No.9956826]

>>9956811
http://lmgtfy.com/?q=math+blogs

[Anonymous No.9956827]

>>9956826
Fuck off.

[Anonymous No.9956870]

>>9956811
see >>9954240

[Anonymous No.9956873]

>>9956870
They all seem shitty.

[Anonymous No.9956880]

>>9956827
>Fuck off.
Do you need to swear?

[Anonymous No.9956882]

>>9956472
>Why don't you ask him and find out?
She's not a "him".

[Anonymous No.9956884]

>>9956880
Yes after a useless reply. I asked for relevant mathematicians, not how to find some math blogs.

[Anonymous No.9956906]

>>9956044
Homotopy sucks ass and we don't fully understand it plus it's super hard to compute, on the other hand, we have "tamed" homology and its super easy to compute

[Anonymous No.9956923]

>>9956906
>we don't fully understand it plus it's super hard to compute
Speak for yourself.

[Anonymous No.9957073]

Any1 got any math bookcharts? Especially interested in the fundamentals but not necessary

[Anonymous No.9957083]

How do anons learn math on their own? Do you just read and take notes/do problems? What if a book has no exercises? Any tips?

[Anonymous No.9957310]

>>9953932
That's logic.

[Anonymous No.9957316]

>>9956906
It also contains way more information than homology. Of course it's hard to compute.

[Anonymous No.9957566]

What is /mg/'s favorite way to do tomography? Radon transform? Conjugate gradient descent? Compressed sensing? Explain your reasoning.

[Anonymous No.9957603]

>>9954966
>>9954968
>>9954971
>>9954973
>>9954976
>>9954985
>>9954987
>>9954989
Sorry for the stupid question, but what are these? Those aren’t books, right? How can I get access to these materials?

[Anonymous No.9957618]

>>9955536

I like philosophy because it's fun to see if and to what extent I can model problems in philosophy mathematically. Thinking about ethics from a mathematical perspective is fun, for example. Can you think of a way of modeling problems in ethics mathematically?

[Anonymous No.9957624]

>>9957566
I'm not sure what this has to do with math. I can't think of any time a math person would do this unless they got tricked into slaving away for some science pleb.

[Anonymous No.9957660]

>>9957624
>t. pure math virgin

[Anonymous No.9957667]

>>9957660
Nice try sciencelet, why don't you try handling your own shit like an adult for once. We have better things to do like troll each other with subtle Wildberger references and shitpost about Scholze vs Mochizuki.

[Anonymous No.9957676]

>>9957667
>when you realize that calculus, the finite element method, modern formulations of the laplace transform, and basically everything important in analysis was created by applied mathematicians
>when you realize that pure math autists can't even solve simple PDEs because the solutions aren't closed form

[Anonymous No.9957680]

>>9957676
>babby math

[Anonymous No.9957681]

>>9957680
Go ahead and solve babby Navier Stokes then. I'll sit here and wait lmao

[Anonymous No.9957696]

>>9955536
I find that philosophy has a lot of different perspectives across its many fields and a lot of time is wasted ib pretentious nonsense and/or arguing about whether famous superstar philosophers actually believed this or that. Beyond the scope of formal logic stuff, the most interesting and compelling papers I've read in philosophy are almost all written by analytic/exact philosophers.
I've read some stuff on the philosophy of beauty but nothing I've really agreed with. Though I think the topic is of fundamental importance to mathematical writing and programming.

>>9957618
In my undergrad I took an ethics course by a logic prof who meticulously structured the course using axiomatic systems and proofs. Unfortunately we used no textbook and he didn't produce lecture notes so I can't offer you any resources, but in principle it's doable.
Personally I thought it was an interesting exploration but ultimately I don't agree with the usefulness of normative ethical theories. I think creating ethical systems where one tries to model how people 'should act' instead of how they actually do act ultimately does more harm than good.

[Anonymous No.9957700]

>>9957681
Refer to >>9957667
>Nice try sciencelet, why don't you try handling your own shit like an adult for once. We have better things to do like troll each other with subtle Wildberger references and shitpost about Scholze vs Mochizuki.

[Anonymous No.9957705]

>>9957603
>>>9954966
libgen(d0t)io, but don't even bother with that list it is a fucking meme

[Anonymous No.9957707]

>>9957316
Yes, actually there are some pretty new results persistent homology and topological data analysis that are making people develop a shit ton of techniques for homological algebra and at this point I don't that it's worth it trying to develop mechanisms for homotopy grups

[Anonymous No.9957712]

Cryptanalysis is apart of math, right? Come on, you must be a faggot if you think deciphering secret military codes aren’t cool.

[Anonymous No.9957716]

>>9957705
I know about libgen, but libgen are for ebooks only. I just wondering how he got those kind of materials, because those are certainly not titles from books.

[Anonymous No.9957808]

>>9956882
>She's not a "him".
Mathematicians use "we".

[Anonymous No.9957828]

>>9956811
Terrence Tao links a shit ton in the sidebar of his blog: https://terrytao.wordpress.com/

[Anonymous No.9957840]

>>9953706
>Ng%C3%B4_B%E1%BA%A3o_Ch%C3%A2u
What an extraordinary name for such a generic looking chinaman.

[Anonymous No.9957852]

>>9954240
Piper? That tumblrina meme queen?

[Anonymous No.9957860]

>>9957716
Those are topics, and any time he refers to a reference in bracket it's a book. It's still a meme shit-list though.

[Anonymous No.9957879]

>>9956769
Math is huge, it's kind of silly to expect to keep up with it the same way people keep up with the sciences.
Instead, find a field you're interested in and have background knowledge of. Then see if there are online communities or blogs dedicated to that field (sometimes finding conferences and reading up on the organizers can be helpful).

>>9957852
>unironically saying tumblrina
I bet this is the type of undergrad who brags about 4chan in public and openly says shit like "kek" and "reee".

[Anonymous No.9957968]

>>9957828
Maybe I could check his links then. Thanks.

>>9957879
I know the basics of CT and AT, but I don't know what they are like nowadays. Maybe I can find something conference-related. Thanks for the tip.

[Anonymous No.9958004]

>>9957968
There's a lot of category theory stuff out there. The n-category cafe is the obvious place to look but you're probably already familiar with it, still people there often link to other resources. That said, I'm not sure what you mean by 'basics', if you're still learning the material then there are places like
https://www.math3ma.com/
or OPLSS that focus on more beginner level concepts.

[Anonymous No.9958021]

>>9958004
Thanks for the link. What I mean by the basics is that I have a master's degree with a lot of studies on those things.

[Anonymous No.9958125]

>>9957860
>It's still a meme shit-list though.
What do you mean?

[Anonymous No.9958259]

>>9957712
Nope, it's applied and therefore inferior.

[Anonymous No.9958338]

I wish I was autistic enough to lose interest towards a math branch if it’s practical in the real world

[Anonymous No.9958451]

Some good people here told me that exercise is necessary if you want to continually study math. How many times should I do per week and how many hours per exercise?

[Anonymous No.9958521]

>>9955536
I used to love philosophy, specially existentialism and post-structuralism stuff. Then I started to feel that philosophy consists mainly of useless circlejerking, and that moved me more towards studying arts.

[Anonymous No.9958528]

>>9958521
>philosophy consists mainly of useless circlejerking
The same goes for many areas of math.

[Anonymous No.9958535]

>>9958521
>>9958528
delete these posts

[Anonymous No.9958538]

>>9958528
There are nothing in this world more useless and meaningless than philosophy. Kindly fuck off to your philosophy boa... Oh wait, you assholes don’t have a board. Sad.

[Anonymous No.9958541]

>>9958535
Why?

>>9958538
Why should I do that? I'm a mathematician.

[Anonymous No.9958542]

>>9957073
Tell us what you want, instead of using meme-tier bookcharts.

>>9957083
Using a single book may be a common error. I study using different books, youtube videos, taking my own notes and talking about the subject with people, since intuition around definitions/theorems may vary but that only makes it better.

>What if a book has no exercises
what kind of math "book" would that be
btw, there are aimless books that just list a bunch of exercises with no direction whatsoever. Herstein's Topics in Algebra is a great book in the sense that the exercises are put not just because, but with a didactic intention behind.

>>9957618
>thinking about ethics mathematically
Holy shit what kind of drugs you're taking man

[Anonymous No.9958551]

>>9958541
>Why should I do that? I'm a mathematician.
Mathematicians use "we", not "I".

[Anonymous No.9958552]

>>9958528
No problem. Mathematicians often recognize themselves as premium circlejerkers, and most of the time don't waste energy in finding applications of the theory they develop.

Philosophers on the other hand tend to take an ethical/purposeful stand.

>>9958538
>there is nothing more meaningless than philosophy

Some philosophers would agree tho

[Anonymous No.9958556]

>>9958538
>There are nothing in this world more useless and meaningless than philosophy.
And nothing more useful or meaningful either.

[Anonymous No.9958557]

>>9958551
Make the world a better place for all of us and kill yourself.

[Anonymous No.9958653]

>>9958557
Better.

[Anonymous No.9958672]

>tfw The Lord got banned
My loneliness... is KUHILLING ME

[Anonymous No.9958701]

>>995854
Hardys Number Theory has no exercises. It's just lecture.

[Anonymous No.9958719]

>>9958672
Good riddance. He was so obnoxious.

[Anonymous No.9958722]

>>9958672
Really? Finally, one of the few autists on this board that got my blood boiling from his arrogance and stupidity

[Anonymous No.9958734]

>>9958672
Who's that?

[Anonymous No.9958779]

>>9958719
That was my first thought as well but now I kinda miss arguing with the guy.

[Anonymous No.9958803]

Dependency graphs are comfy af. Where can I find more of these (preferably for algebra)?

[Anonymous No.9958814]

>>9958803
What an absolutely autistic graph.

[Anonymous No.9958999]

made a video on directed acyclic graphs (and more generally graph theory concepts). Excuse my accent.

https://youtu.be/5hg8Ahp3d58

[Anonymous No.9959011]

>>9958999
>Hello boys and girls
That's quite cisnormative on your part, and we refuse to get lectured by a shitlord of your caliber.

[Anonymous No.9959173]

>>9958542
I want books about the fundamentals to calculus and maybe a little beyond that

[Anonymous No.9959338]

>>9959173
Honestly speaking, calculus is not a subject that needs a lot of math background to be understood. Assuming you're aiming towards a more abstract and rigorous treatment to calculus (without getting to much into analysis), Spivak should be your pick, maybe with Halmös' Naive Set Theory to really grasp the set-theoretic-related intuitions in calculus.

My main conflict with Spivak's is that the treatment on sequences is at the end, while it could perfectly be a good starting point. Results related to sequences are pretty simple but help to develop a more proof-oriented math perspective.

Now if you're looking for standard undergrad introductory math, A Transition to Advanced Mathematics by Smith, Eggen and St. Andre is the best for that.

(btw it does not hurt at all to get immediately into analysis if you're already comfortable with proofs and abstract thinking, get bartle & sherbert's intro to real analysis!!)

[Anonymous No.9959381]

>>9958451
Smolov routine

[Anonymous No.9959549]

>>9958803
Cool graph.

>>9958814
Fuck off, retard.

>>9958999
Emma Stone? I wasn't aware you were still around. What's the deal with all the blockchain stuff you're doing lately?

>>9959173
What are you looking for exactly and what is your interest in studying calculus?

[Anonymous No.9959564]

>>9954966
>>9954968
>>9954971
>>9954973
>>9954976
>>9954985
>>9954987
The fuck is this essay niglet? You think anyone's going to read through your shit?
Just read Rudin's trilogy together with Spivak's Calculus on Manifolds and you're done with analysis. Pick up Herstein/Artin and Lang and you're done with algebra. Give Spanier a spin and you're done with algebraic topology. Can't think of something for n theory off the top of my head for now but 2-3 books and you're done with that too. Then pick an area of graduate specialization and you'll find max 3-4 books clearing the shelf with it, and then you're exclusively looking at research papers.
Moral of the story: yap less faggot

[Anonymous No.9959597]

Is math in Brazil a meme or is it worth trying?

[Anonymous No.9959610]

>>9959564
>Just read Rudin's
Rudin is a meme.

[Anonymous No.9959664]

>>9959597
Math outside the US and Europe is a meme.

[Anonymous No.9959677]

>>9959610
>he thinks his opinion matters
He goes over all the essential theorems and main results, so it is not lacking in content. As for style, a Bourbaki approach is unironically the way to go - no one has time to read useless spergtext.
All in all, it is one of the most succinct and formal takes on analysis.

[Anonymous No.9959680]

>>9959677
How long do you think it would take for a physics grad to read through all of rudin's books? Do you recommend doing all the problems?

[Anonymous No.9959698]

Russian are pretty good at math.

[Anonymous No.9959701]

To master algebra, first you need to read of Euler’s works.

[Anonymous No.9959729]

What maths should I pick for an elective as an EE major?

[Anonymous No.9959740]

>>9959680
Do you have any exposure to analysis? What has been your experience with previous pure math courses?
I'm not going to jump to conclusions, but I have dealt with enough physicists to note that they have a rather boorish idea of "proof" and mathematical objectives in general. I will tell you that it is nothing like performing circus algebraic manipulations; there is no interest in spinning equations and re-writing them in fancy ways.
For a beginner, I would say the first book should take about a month, the second two to three, and the third about four, assuming you spend a couple of hours studying everyday. I expect a student to be able to emulate or devise proofs to all theorems presented and do every exercise in the texts after perusal for the stated period.

[Anonymous No.9959742]

>>9959729
What math courses are requirements for you? What have you already taken?

[Anonymous No.9959839]

>>9959664
+Japan, they also have a pretty good mathematics school/tradition. But yeah, as a Brazilian if you want to do math try the USA or Europe (especially France).

[Anonymous No.9959888]

>>9959742
I’ve finished Calc 1-3 and differential equations.

[Anonymous No.9959892]

>>9959888
Take more applied math courses. Also definitely focus on PDEs and FEM.

[Anonymous No.9959916]

Periodic maps in p-adic geometry (Scholze): https://www.youtube.com/watch?v=7xD_JIJj22Y

[Anonymous No.9959918]

>>9959916
period*

[Anonymous No.9959941]

>>9959338
Thanks, tho I meant from fundamentals in math to calculus. And I know that calculus isnt that special but I just want to really understand what i am doing while i do calculus, proofs and math in general, I want to know the philosophy behind it per say so im not just doing math without knowing what i really do if you know what i mean, it's hard to explain

[Anonymous No.9960084]

>>9959916

[Anonymous No.9960098]

>>9954989

this meme has been reposted at least 1000x times on this forum alone, this is from a russian school of math curriculum and no way in fucking hell any1 here understands any of this to even teach someone

this is a physics biased list for quantum field theory research

[Anonymous No.9960159]

https://arxiv.org/pdf/hep-th/0609022.pdf

>>9953932
>>9953939 >>9953954 >>9953962 >>9954187 >>9955336 >>9956773 >>9957310

[Anonymous No.9960322]

>>9960159
Thanks

[Anonymous No.9960431]

>>9960159
>Concise introduction to a relatively new subject of non-linear algebra
>relatively new
Huh, I’m surprised that mathematicians didn’t fiddle their around with the subject earlier, considering there are more nonlinear systems than linear ones.

[Anonymous No.9960434]

>>9960431
*their dicks
Forgot the most important part of my post

[Anonymous No.9960983]

What kind of math is best for trying to keep depression and nasty voices away? Algebra?

[Anonymous No.9960998]

>>9960983
Number theory.

[Anonymous No.9961008]

>>9960998
I'd rather have the demons screech inside my head.

[Anonymous No.9961018]

>>9961008
Hyperbolic geometry.

[Anonymous No.9961023]

>>9961018
That's a decent field.

[Anonymous No.9961051]

>>9961023
Yeah. I got into it because I liked the models of hyperbolic space and how they work, and was pleasantly surprised when I discovered it's quite an expansive field.

[Anonymous No.9961063]

>>9961051
Yes. You'd easily just assume it's like Euclidean geometry which is quite narrow in the end.

[Anonymous No.9961070]

>>9961063
It's not narrow, it just have been developed since antiquity and it intuitively aligns with our daily notions of the structure of space. Hyperbolic hasn't have nearly the same time, and it's applications are not that big.

[Anonymous No.9961091]

Going to start self learning this bad boi, I've had a analysis 1 and 2 (It's kinda calc an analysis in one in my college) and linear algebra.

What's awaiting me? Could I get through it? Tips (should I make summaries?)

[Anonymous No.9961142]

>>9961091
>Could I get through it?
Why don't you try it and find out?

[Anonymous No.9961172]

>>9961091
>Shlomo Sternberg
>"Advanced Calculus"
You don't belong here.

[Anonymous No.9961188]

>>9961091
Nice book, but it's a just a wee bit outdated. It's pretty easy to read, imo.
If your courses were any good a decent chunk of material in the first couple hundred pages (up until it starts talking about manifolds) is going to be review for you so don't be afraid to skim it.

[Anonymous No.9961529]

>taking calc 2
>first day of lecture
>10min in and prof makes a mistake doing a problem on the board
>spend remaining class time trying to find fix it but can't
>"ok guys do some problems from 6.2, see you next week"
>6.2: find the area of rotated region

what the fuck did I sign up for? help

[Anonymous No.9961558]

>>9961529
(You)

[Anonymous No.9961599]

>>9960159
>Russian
I love Russians. They contributed so much to mathematics.

[Anonymous No.9961706]

>>9960159
10/10 post

[Anonymous No.9961957]

>>9960159
That's neat.

[Anonymous No.9961960]

>>9953706
Elongated muskrat

[Anonymous No.9962014]

>>9960431
i think its because non linear systems are much much harder to work with than linear ones, so they didnt even bother.

[Anonymous No.9962036]

>>9962014
That's not it. It's because you can use linear approximations for a whole lot of shit.

[Anonymous No.9962077]

>>9961172
Oy vey!

[Anonymous No.9962176]

I can feel my mathematical power coming back to me.

[Anonymous No.9962214]

>>9962176
too old

[Anonymous No.9962259]

>>9957879
So you actually find her shit worthwhile. Why? What about her blog do you find interesting?

[Anonymous No.9962267]

>>9962259
I didn't say her shit was worthwhile. Believing that anon is cancer and that she is shit are not mutually exclusive.

[Anonymous No.9962300]

Im taking "linear algebra and differential equations"

What am i in for?

[Anonymous No.9962796]

>>9962176
>I can feel my mathematical power coming back to me.

[Anonymous No.9964040]

Is there such a thing as math audiobook?

[Anonymous No.9964120]

>>9964040
Learn to read faggot. Or if you're a pontrjagin type, get a sugar mommy to read for you.

[Anonymous No.9964201]

>>9964120
Bitch, I want to listen to math related stuff while I’m jogging or driving my fucking car.

[Anonymous No.9964208]

>>9962300
pretty pics like this

[Anonymous No.9964338]

>>9964040
>>9964201
>he thinks he can learn math by just listening to someone talking about it
You're either a genius with incredible working memory or a full blown retard.

[Anonymous No.9964367]

>>9964338
You could listen to something like history of math

[Anonymous No.9964372]

Another day, another affirmative action award given to in the name of diversity, and then used as a reference to "prove" the supposed value of diversity.

[Anonymous No.9964409]

>>9964372
What is this nazi talking about, my fellow sissy bois?
>>9964120
I'd like to hear more of this "sugar mommy reading maths to you" system Pontrjagin (Pontryagin?) developed.

[Anonymous No.9964428]

>>9964409
>my fellow sissy bois
Speak for yourself. I am a complete chad and an absolute unit.

[Anonymous No.9964438]

>>9964428
>mathematics student
>Chad
>on /mg/

[Anonymous No.9964463]

>>9964438
>hasn't learned how to just be himself
Sad!

[Anonymous No.9964493]

Good short text about tensors? Popped up in my fluid mechanics course and I know nothing about them.

[Anonymous No.9964496]

Is a real analysis course worth doing if I want to be an engineer?

[Anonymous No.9965093]

some memes if you please
>inb4 Lang

[Anonymous No.9965167]

>>9964493
If you want to read about tensors, look up "multi-linear algebra." In the way that Linear algebra is the study of vectors and linear maps (represented by matrices) Multi-linear algebra is the study of vectors and multi-linear maps, represented by tensors.
The best I've read on tensors is probably Numerical Tensor Analysis by Hackbush. It isn't short though. In my readings, tensors are usually a chapter in a book which uses them, but not their own book. There might be a dover book on tensors.

(To others reading this, I am aware that is an overly simplistic explanation.)

[Anonymous No.9965175]

>>9964493
"The analysis of linear partial differential operators I-IV" by Hormander is a great place to start

[Anonymous No.9965178]

>>9965167
>(To others reading this, I am aware that is an overly simplistic explanation.)
The disclaimer is unwarranted, you insecure brainlet.

[Anonymous No.9965193]

>>9965178
>attempt to help a poster learn where to find a book
>acknowledge that a quick explanation is not exhaustive
>somebody complains anyway
classic /mg/ pedantry

[Anonymous No.9965243]

cheers lads, brainlet here.

How do i generate a curve that looks rather like a negative parabola, but curved on the edges more like an exponential curve (just like the shape of a normal curve)? I just need one that returns small values close to 0 and 25, and large values near 12.5. I know a parabola does what i'm suggesting, but i want the output curve to be more bell-shaped. Sorry i only took maths to calc 2 so I'm not too bright.

[Anonymous No.9965252]

>>9965243
I believe that you are looking for the first equation in the introduction:
https://en.wikipedia.org/wiki/Normal_distribution

[Anonymous No.9965379]

>>9965252
sure, I didn't read the fine print but it looks pretty simple. I thought there might be a simpler way to imitate the curve but that's reasonably straightforward.

[Anonymous No.9965487]

You know a proof is good when it contains the phrase "by general nonsense"

[Anonymous No.9965491]

>>9965243
Try the derivative of the sigmoid function:

https://math.stackexchange.com/questions/78575/derivative-of-sigmoid-function-sigma-x-frac11e-x

[Anonymous No.9965625]

>>9964493
"Tensors" are just multilinear maps. What you want to learn is differential geometry, differential forms and PDEs.

[Anonymous No.9965643]

>>9965487
Post

[Anonymous No.9965691]

>>9965625
>an analyst fails to understand the meaning of a tensor

[Anonymous No.9965696]

>>9965691
What? Theres no modern geometer who uses" tensors" as in any tensor calculus book. Its literally juts differential geometry.

[Anonymous No.9965950]

>>9964496
yes, so you can weed yourself out

[Anonymous No.9965952]

>>9965643
literally any book that uses homological algebra

[Anonymous No.9966067]

>>9964496
If you're interested in something like control theory then yes