# /mg/ - Math general

TalkBomber

What kind of math are you studying, /mg/?

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Evil_kitten

tfw want to finally understand Stokes' theorem but the prerequisites are high-level topology and I have no idea where to learn all that since all proofs online are either dumbed down physishit trash or doesn't prove important lemmas

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Snarelure

If you really want to understand it, you pick a book up and start reading.

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Evilember

Which book, you dumb fucking supid weeb? The Veeky Forums sticky is a laughable meme as always.

TurtleCat

Find out what you don't know but need to know, then google stuff like
good textbook [subject name here]
and also try to behave. You made me cry.

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ZeroReborn

good textbook [subject name here]
L M F A O

BinaryMan

L M F A O
cringe

FastChef

PurpleCharger

Don't talk to me, you meanie.

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cum2soon

Techpill

Depends on the gauge group $G$ as well as the manifold $M$ (obviously). In general the local tangent space $T_\alpha \mathcal{A}$ can always be constructed, but the difficulty comes when you try to patch together the locally-defined measures, and this requires compactification of the moduli space (unless you don't care about convergence).
The main point is that if your homotopy quotient $M \times_G G$ is nice enough (i.e. vanishing odd-degree cohomology or a stabilizing Leray spectral sequence), then you the path integration becomes just the equivariant fibre integration, and the stationary phase approximation works via Deligne-Verne. In some cases if the Thom class is trivial you can even identify the path integral with the Euler characterisitc.

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Emberburn

My bad, the homotopy quotient is $M \times_G EG$ where $EG\rightarrow BG$ is the classifying $G$-bundle.

Booteefool

ncatlab.org/nlab/show/(infinity,1)-topos

Evil_kitten

Is it worth memorizing n choose k values?

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haveahappyday

No, undrestand the difference between combinations and permutations though.

SomethingNew

Basic Mathematics by Serge Lang, along with G Chrystal's Algebra texts. Glad to be part of this intellectual general. I just got to surds.

iluvmen

Sure, I've already got that down.

I just think it might comfy to be able to expand powers of binomials quickly and without having to draw one of those meme triangles.

idontknow

Why?

Crazy_Nice

where do y'all go when you want to look at futanari porn?

w8t4u

Doing group theory, on quotient groups atm. It's ok. When does the really cool stuff start though?

Are there any professors in /mg/. My linear algebra professor from last semester seems like the kind of guy that would post here (he had a Ph.D. in math and an anime girl desktop background on his laptop).

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Playboyize

cringe
cringe

Methnerd

Not a prof but I feel like most people in math are on Veeky Forums, we're a fucked up breed.

Playboyize

hello there

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ZeroReborn

Starting this book. I've heard good things about it (from other physics shitters)

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LuckyDusty

It's good if you want good visual examples from differential geometry, but unecesarry for full blow diff geo in manifolds. Do it if you have the time, but don't lose a lot of time if your goal is riemannian geometry

CouchChiller

Nice find on Chrystal.

DeathDog

Serge Lang
intellectual

RavySnake

This is a common question but if I want to learn math from the beginning (not counting or arithmetic) do I read the books assigned in the sticky or can I do Khan Academy instead? And to what level, most people recommend Khan Academy up until precalc then read a proofs book and understand mathematical logic, then jump into single variable calculus, linear algebra and then multivariate calculus.

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BinaryMan

This is a common question but if I want to learn math from the beginning (not counting or arithmetic) do I read the books assigned in the sticky or can I do Khan Academy 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.

AwesomeTucker

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).

JunkTop

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).

PurpleCharger

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.

CodeBuns

If you're serious, how long would this take?

BunnyJinx

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).

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).

Fuzzy_Logic

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.

New_Cliche

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)

Ignoramus

Stop posting that garbage analcyst curriculum

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Spazyfool

I haven't read a math book for almost 1 month /mg/. Please suggest a mathematical way to kill myself. Thanks.

Stark_Naked

Garbage Can Lid

That would indeed be a cruel way to die

hairygrape

How can I work out pic related? I've got the normal vector field, but what else do I need for GC?

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TreeEater

This.
This.
This.

Lunatick

you know that it's international give mercy to a brainlet day, right?

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King_Martha

quotient objects are the coolest things breh

SomethingNew

This is amazing senpai, but where is combinatorial set theory?

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Bidwell

Finishing calc 2 so improper integrals, trig substitution and simple fraccion separation.

SniperGod

abelprisen.no/seksjon/vis.html?tid=73018

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StonedTime

Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate;
which will be non-degenerate
why?

BunnyJinx

What are degenerate conics? For example a single point is one, but that can't happen because you have five distinct points (due to non-colinearity). Similarly, you could have a line which is also degenerate as a conic, but then you would have five (and thus any three) points be colinear. Think of the other degenerate cases through.

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idontknow

this shit get's posted everytime someone asks for academic advice and it's unreasonable and frankly unnecessary. Going through this rigorous of an outline for years straight at such an early age will kill someone. Assuming the freshman - senior correspond to undergraduate standings, no one is learning such a clusterfuck of topics when they're 18.

Poker_Star

When you take a second course.

Emberfire

What is a quotient group to you?

Soft_member

Formally,

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SomethingNew

Going through this rigorous of an outline for years straight at such an early age will kill someone.
A literal retard spotted.

Methnerd

Sometimes you explain a concept inuitevly, or give an idea and then you give a more mathematical definition, you fucking autist.

StrangeWizard

Never seen such a thing. Any good definition is already "intuitive" and self-explanatory. Assuming you aren't brain-dead, of course.

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Nude_Bikergirl

Wow you are so smart and cool. Is anime your secret?

SomethingNew

you are so smart
If you think that someone who is merely not retarded qualifies as being smart, then I have bad news for you. I don't think it's impressive. It would be sad if it was.
and cool
Thank you.
It's mainly not visiting websites such as "reddit.com", "facebook.com" and the likes.

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cum2soon

Oh, so it's the autism.

Who ENS here?

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idontknow

What the fuck is your problem? Your kind is not wanted here, you fucking simpleton.

TreeEater

Oh sorry I forgot my HILARIOUD animr pic and my cliche snarky remark
mfw physicits don't even know delta-epsilon

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Emberburn

2hu
animr
You reek of /r/catalog#s=eddit%2F and /v/. We don't like your kind around here.

Firespawn

mfw physicits don't even know delta-epsilon
Who are you quoting?

TalkBomber

Is this a new meme?

WebTool

Or maybe you should fuck off to /jp/ for falling in such retarded bait.

CouchChiller

Pretending to be retarded is just being retarded. You are not welcome anywhere outside of /v/.

ZeroReborn

Refer to

CodeBuns

Sounds like an IQ problem, sorry.

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Ignoramus

I'm studying algebra one, course I have adhd and never learned math when I was in school.

The componentd if the first fundamental form. Find a parametric representation of your tangent plane at every point if the surface and plug and chug.

TreeEater

I memorized the definition of a manifold, but I still have no clue what it is. I can't envision the difference between a manifold and a non-manifold

PackManBrainlure

Just signed up for a minor in Computational Mathematics. I've already taken diff eq, just gotta take:
Linear Algebra
Applied Numerical Methods
And I get to choose two of:
Intro to Finite Element Method
Numerical Linear Algebra
Stochastic Simulation

What electives do you nerds recommend I take? (I am in mechanical engineering)

Skullbone

TurtleCat

Well I'm 3/4 through the chapter, will fully flesh out the stuff about defining the coset operation by choosing a normal subgroup today. My understanding is a quotient group is just a group we get by defining an operation between the fibres of some homomorphism between groups.

Fried_Sushi

Gee, I dunno, I'm asking about mathematics courses. This seems like a pretty good place for that.

Crazy_Nice

None of the things on your list is even remotely related to mathematics.

Switch major to Math then take Real Analysis, Topology, and Probability in the same semester

Boy_vs_Girl

Can you point me to the so-called "mathematics courses" in your post? I don't see any.

Spamalot

Real Analysis
Probability
Those are engineer courses, why would he need to switch majors to take them?
Topology
I'm assuming you mean point-set garbage. That's also an engineering course.

Soft_member

welcome to /mg/. it's not math if it's not arrows.

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farquit

everything is engineering

cum2soon

Everything which is engineering is engineering. Correct.

Inmate

Everything is arrows, even engineering.

SniperGod

Thumbing through pic related atm.

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ZeroReborn

So it was a buttmad physishit, who would've thought.

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Inmate

My economist sister aced her probability exam. It seems my superior intellect radiates itself onto people around me. What I touch turns to gold, where I walk flowers start growing through the snow layer. I am divine.

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WebTool

To be fair, you don't have to be very intelligent to ace exams in subjects such as "probability" where you can simply make shit up as you go along.

What should I read to start understanding this?

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Poker_Star

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Techpill

mathematics courses
No such thing.

King_Martha

But she's not intelligent.

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Methshot

Wew.

Just realised, the area of a circle makes complete intuitive sense when it's described as:

$\frac{1}{2}cr$

$\pi r^2$ makes no intuitive sense at all.

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Sharpcharm

Thinking it makes any difference what you call certain constants is what makes you an actual brainlet.

Emberfire

Smart people see beauty in tau and ugliness in pi.

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FastChef

does it take long to learn latex? is it difficult?

Truly smart people see ugliness in any number.

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Ignoramus

Amen.

$\neg\text{yes} \land \neg\text{yes}$

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Stupidasole

Not that long. Condom companies seem to be good at it, so it's probably not too difficult.

Supergrass

reddit tier joke

Need_TLC

It's not a joke, it's an answer to an off-topic question about latex. Tiers as in video games? I don't play those.

Crazy_Nice

algebraic number theory, basic complex geometry, basic intersection theory
Then again, not sure why you would want to if you don't even understand what it's about

Boy_vs_Girl

I chuckled regardless.

CouchChiller

computational tasks should always be done via computer. save the space in your head for proof and concept.

JunkTop

proof and concept
Clearly such things don't matter to someone who would even consider asking such a question.

Gigastrength

maybe its just some undergrad with no experience. i try to give idiot questions the benefit of the doubt

LuckyDusty

What's a fun book to read for an undergrad? I've kinda stopped reading books and I'd like to read something fun that may help me on the future. Any recommendations? Been thinking on Abott's Understanding Analysis.

nah man. it's pretty intuitive honestly. Want to write a fraction? there's \frac{}{}. Want to make a cute little triangle ABC? you do \triangle ABC. P implies Q you mean? Fucking P \implies Q.

The structure is kinda weird to understand though. Just steal templates on internet.

Fried_Sushi

So if we are constructing tangent spaces, this implies the moduli space is more than just a topological space right?

It has some type of analytic or algebraic structure?

hairygrape

They don't like set theory here because the post is more about math that sounds hard.
I'm missing finite-dimensional algebras and quantum groups.

Carnalpleasure

Wow rude. You guys are mean. I'm going back to /pol/.

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StonedTime

Just imagine a space that looks locally (but not necessarily globally) like the familiar n-space and that is not too large (second countability). Like a surface, an open ball, or an n-sphere.
These are the topological objects that still look "geometrical" (vaguely spoken).

FastChef

Correction - just found the quantum groups.

StrangeWizard

what kind
transfinite analysis mostly

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Gigastrength

Leray spectral sequence
Do you mean Leray spectrum? That's what we deep mathematical physisicts use.

massdebater

Just think of a paracompact space with countable basis that is locally like R^n

Playboyize

Pinter's Abstract algebra

Firespawn

Any good PDFs on the legandre transform, geometric interpretation and applications? Basically I just don't understand how do you get a symplectic structure from it.
hurr durr physics faggot gtfo
I'm interested in a pure mathematics perspective.

Evilember

legandre transform, geometric interpretation and applications

RavySnake

ahahahaahh im a stupid algebwaist feed me eqwuals signs
Fuck off, kid

BunnyJinx

Boohoo ż'œş math is exact and not just a chain of inequality signs between integers!

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Epic my dude.

Fuzzy_Logic

integers
Integrals*, silly me~<3

Inmate

So if we are constructing tangent spaces, this implies the moduli space is more than just a topological space right?
Yes. It's an infinite-dimensional vector bundle. Regarding what I said before about Euler characteristics, in certain cases the Yang-Mills path integral is a generalization of the Euler characteristics to infinite-dimensions via Mathai-Quillen.
It has some type of analytic or algebraic structure?
Mostly algebraic, from the structure group $G$. But if you want to look at matter fields coupled with the gauge fields then you'd need a lot more analytic structure (Swieca regularity, say) for a well-defined QFT.

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Firespawn

eqwuals signs
We don't use those in mathematics, we use $\cong$.

SniperGod

mathematics
This is not well-defined.

PurpleCharger

This is not well-defined.
This is not well-defined.

StrangeWizard

sharelatex.com has a built in compiler, an amazing tutorial and every resource you need.
Its simple af, just learned yesterday in 10 mins and already submitted a paper using it.

Spazyfool

Epic
my dude
We don't accept refugees from /v/ here.

Raving_Cute

Shillax my men, I'm just busting his balls a bit. Don't be so square.

Crazy_Nice

girlDog

Bruuuuh, your gettin all mad for nothing, we all friends here :)

Evil_kitten

We
Speak for yourself.

Snarelure

is there research being done into new analytical DE methods?

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TalkBomber

Try asking in the physics threads maybe? Why did you decide to post this here?

BunnyJinx

HAHAHAHA XD

Flameblow

You might be mentally challenged.

RumChicken

You might be a meme loving faggot

FastChef

faggot
Why the homophobia?

Booteefool

Abstract algebra

DeathDog

Hi anons, i'm taking a precalc class and I was wondering if someone here could provide me some insight. Most of the class is just trig and the unit circle. I know how to solve the problems fine enough, but unlike Algebra 1-2, I wouldn't say I have gained any deeper understanding or insights of the subjects. How do you gain an intuitive understanding of mathematical principles? At what point in your education would you say you began to "get" things. I have occasional "aha" moments but I feel like largely i'm jut memorizing the identities and the rules to get a solution arbitrarily, with only a fuzzy and vague understanding of why I make each step.
The usual answer I receive is to go over an intro to proofs book, but the one's i've seen all say you should have familiarity and experience with up to "Calculus I" first, and i've never taken a Calculus course before.
Here's the textbook we use for the course If anyone has interest I can probably upload a PDF, i'd appreciate if someone can tell me whether it look quality or not, and also if anyone has any textbooks they do recommend.

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eGremlin

What's there to "get" about trig and algebra?

BunnyJinx

I don't understand what the goal of solving such problems are. I guess what i'm failing to grasp is exactly how these equations apply to real world phenomenon.

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Dreamworx

They don't apply "defacto", it's just to make you comfortable manipulating that, the same way you practice how to solve for x. Personally, if you know the geometric defintion and maybe some basic identities, everything else is just a waste of time, but some old professors think that you need to suffer like they did because you couldn't look up some tedious identity and so you need it to memorize it by heart, but do understand how to apply it to geometrical problems, and if you are asked to learn it for a test, suck it up.

Stark_Naked

Are you retarted? Your brain has more than enough space to store 2.5 petabytes of info, that's 2500000 gb. Remembering 100 values of n choose k would maybe effectively take a mb.

Need_TLC

It's still retarded.

MPmaster

How?

Evil_kitten

Elementary algebra is really just about becoming competent with basic manipulations and applying common rules that apply to various functions. It's sort of an introduction to real functions, but you don't gain much insight at that level. e^x usually doesn't make much sense until you see it in a calculus course for instance.
With trig, you should be able to prove all the identities you could ever want just by manipulating a relatively short list of basic ones, all of which can be derived from euler's formula. But euler's formula doesn't really make sense until you're comfortable with power series functions and their properties, which you usually cover in calculus.
And then you don't "really" understand real functions until you've done real analysis anyway

farquit

Memorizing n choose k values? What on earth would anyone do that besided pur autism? No, even autistic people memorize much more interesting and applicable shit, and yes that includes minecraft shit names.

haveahappyday

you don't "really" understand real functions until you've done with analysis
Jesus christ america.

iluvmen

apply to real world phenomenon

idontknow

Why? Well firstly, because we can. Secondly, because it's making working equs out much more fluenter. Imagine not remembering trig identities or basic algabraic tricks. Sometimes the best insites come due to the fact that you rely on your memory and good number instincts.

kizzmybutt

because it's making working equs out much more fluenter.
And why would one need to do so?
Sometimes the best insites come due to the fact that you rely on your memory and good number instincts.
Perhaps in physics or engineering. But you can fuck off to some other thread if you want to discuss that.

hairygrape

Yea, but n choose k values?

Not math

Techpill

Not specifically them but the more the merrier. It's not that you're wasting storage space.

Methnerd

Who are you quoting?

PackManBrainlure

But you can fuck off to some other thread if you want to discuss that.
Do you need to swear?

Carnalpleasure

You are retarded.

Burnblaze

quoting
Not well defined

Firespawn

Forcing memes is funny, amirrite reddit?

TalkBomber

And why would one need to do so?

Because math is expressed in equs in most cases, and a good mathematician knows how to handle and manipulate them.

Perhaps in physics or engineering. But you can fuck off to some other thread if you want to discuss that.

So insites in math are not number related?

StonedTime

How did you conclude that you fucking monkey?

BunnyJinx

StrangeWizard

amirrite reddit
Your kind isn't welcome here. Refer to /v/.

Ignoramus

Because math is expressed in equs in most cases
This is not the case beyond the premises of your high school.
So insites in math are not number related?
No, since numbers usually don't have anything to do with math.

Raving_Cute

@9607878 (You)
@9607881 (You)
@9607876 (You)
@9607863 (You)
@9607852 (You)
@9607848 (You)
@9607844 (You)
@9607843 (You)
@9607841 (Y(ou)
@9607839 (You)
@9607838 (You)
@9607833 (You)
@9607828 (You)
this is a christian board, please refrain from insults or cursewords. thank you

Lunatick

math
This is not well-defined.

Boy_vs_Girl

Refrain from existing kid ;)

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King_Martha

This is not the case beyond the premises of your high school.
Have you ever seen any of Euler's proofs for infinite series'? Or almost any graph theory related proof? They do have numbers. Math uses abrstactions to skin off the unnecessary parts of an object and mostly we end up with numbers. If you are referring to the fact that most equs have letters instead of numbers in them than go to /h/.

Maybe math does not talk about numbers but one of the ways that it talks about those things is through numbers.

girlDog

I can say the same.

god i wish I could. Unfortunately matter can't not be created nor or destroyed :/

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SomethingNew

I'm currently studying the advanced intellectual lectures presented by Dr Micheal Vsauce.

cum2soon

Have you ever seen any of Euler's proofs for infinite series'? Or almost any graph theory related proof?
I'm not an engineer, no.
They do have numbers.
Yeah, engineers tend to use numbers. What point are you trying to make here?
Math uses abrstactions to skin off the unnecessary parts of an object
Correct. And thus numbers get skinned off and exiled to the physics departments.

w8t4u

It can

it can
wrong

Bidwell

Refer to /v/ if you want to post reddit frogs.

massdebater

wrong
Right

hairygrape

thanks me as well
don't ever reply to me or my son again, r*dditor

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Poker_Star

I'm not an engineer, no.
These are math subjects -_-

Yeah, engineers tend to use numbers. What point are you trying to make here?

THESE ARE MATH SUBJECTS

Correct. And thus numbers get skinned off and exiled to the physics departments.

The objects are not numbers to begin with, so you don't abstract more than numbers. Also, say I'm skinning off a number, what am I left with?(By numbers I'm aldo referring to letters expressing numbers in equs btw.)

Snarelure

Antimatter, Einstein's e=mc^2, the sum of mass of the particles making up an atom is greater than the actual mass of the atom impliying that some of the mass is stored in the energy binding the atom together. These are 3 examples where you are wrong.

How do I find the vertices of the smallest enclosing right simplex for an n-dimensional rectangular prism?

Time is of the essence.

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Emberburn

math
This is not well-defined.

RumChicken

I have physics for some reason as part of my Computet Engineer degree. That’s okay, but I’ve totally forgotten how to solve some trigonometric equations which is part of one task
It’s like this
$(0.500 kg)(4.00 m/s) = (0.500 kg)(2.00 m/s)(cos \alpha) + (0.300 kg)(4.47 m/s)(cos \beta) \\\\ 0=(0.500 kg)(2.00 m/s)(sin \alpha) - (0.300 kg)(4.47 m/s)(sin \beta)$

I know I should isolate cos b and sin b and that cos^2b+sin^2 b=1 but no idea what to do otherwise or get one of the a trig functions isolated after adding up to solve a

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Stark_Naked

What do I read now I'm almost finished with Spivak's Calculus

King_Martha

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cum2soon

no

WebTool

What does a "family of subsets of a n-set" mean? A set with n elements or a set where each element has n elements? Google's not helping much.

LuckyDusty

homework has a question that's supposed to be done via proof by exhaustion for brainlets
I autistically spent hours trying to prove the statement for all natural numbers

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Lord_Tryzalot

what do you wanna learn, more calculus/analysis or algebra? Maybe even topology would be nice

depends on the context. I've never heard n-set but it sounds suspiciously like a multiset

kizzmybutt

It's being used in the context of combinatorics here (choice function specifically)

Playboyize

I hate this general.

Methshot

o-ok...

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RavySnake

It's definitely sounds like multiset then, but the notation is incredibly ambiguous

RumChicken

Folks, I just received a fully funded (tuition+maintenance grant) PhD offer at a top university in algebraic number theory and algebraic geometry!!!

Fuck you.

Ignoramus

I hate you.

Gz $^\frown \smile ^\frown$

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MPmaster

Hey guys, brainlet here:

So I'm taking my proofs/ logic/ sets class this semester. I think - brainlet although I may be - I may have stumbled upon an entirely overlooked quirk of logic that may prove to destroy the very foundations of mathematics (and quite possibly reality).

So recall x ≥ y ≡ (x > y) v (x = y)
... and by """definition,""" that's the 'inclusive or,' mind you. So essentially the statement above reads "x is greater than or equal to y is identical to saying x is greater than y, x is equal to y, or both x is greater than y and equal to y." Which is obviously false. A number cannot be greater than AND equal to another number. The logical notation should be the 'xor' symbol, but I suppose """mathematicians""" allow greater flexibility for their useless masteurbation by ignoring this obvious quirk and using the 'inclusive or.' How/ why is this overlooked?

pic-related is related because it's mfw the entire universe of mathematics destroys itself today because I shitposted this proverbial ton of dynamite onto the mathematics section of this obscure Norwegian kite-flying forum

See you faggots in hell.

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girlDog

It's the best I've got :(

w8t4u

OR is called the disjunction and is defined that way, like an axiom
x,y or both but not neither

idontknow

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Gigastrength

I hate you more.

Burnblaze

I hate this general.
Why?

DeathDog

I hate you more.
cringe

JunkTop

am I a brainlet if I didn't understand a word of what those people said

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Raving_Cute

those people
It's just one guy samefagging.

Nude_Bikergirl

guy

Booteefool

die

MPmaster

Do you have to be a prodigy to succeed in mathematics?

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King_Martha

Sup Veeky Forums, anyone doing complex analysis at the moment? Shit's fun as fuck

Spamalot

Nah man, you just gotta work at it pretty much every day.

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takes2long

I mark complex analysis hw ama

Anyone good enough at Statistics to help?

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iluvmen

How hard is it compared to other fields? I'm taking it this term and I'm a second year undergraduate.

It's not particularly hard. If you've done real analysis before, it's relatively easier (if not, idk what you're doing taking this class. It involves more abstract thinking, in the sense that complex functions require 4D to think about, evaluating integrals don't always require computing the integral, and classically bounded functions like sin, cos are unbounded. You get a lot of surprising results which makes it quite fun (residue theorem, once differentiable implies infinitely differentiable, bounded differentiable implies constant), and also on top of that, you have to start thinking more topologically. The best part is it's applications, like using the residue theorem to compute real integrals, or using winding numbers to prove the fundamental theorem of algebra.

Fuzzy_Logic

I've taken two courses on real analysis so I've got a decent grasp on that. Got a midterm on Friday about complex involving open sets, metric spaces, line integrals etc.

Sharpcharm

The real fun begins with meromorphic functions

Snarelure

Seems to be exactly what I'm looking for. I'll look at it. Thanks.

Pls respond

DeathDog

If you make and equivalence relation out of a strict partial order is there a name/notation for "lifting" said partial order to the quotient set?

I've just been calling it $\mathscr{P}(\prec)$ but that doesn't really make sense if you think about it.

BinaryMan

What's a good foreign language to learn? I am a native English speaker.

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JunkTop

Do you mean project to the quotient set with the equivalence relation that two objects are in the same class if they belong to the same chain? Pretty sure that's not well defined

CodeBuns

French for algebraic geometry

StrangeWizard

Somali

Nojokur

Sup /mg/ I'm an engineer, I work on cars and fighter jets and shit, and just the other day a category theorist came up to me to tell me how do my job. So they tells me that I should learn category theory because it will solve all the problems I'm having. They also said that they're not like the old category theorists(they got banned from getting NSF funding?).

So they showed me a couple of toy examples and messes of diagrams that looked like what happens when I toddler play around with simulink, but they didn't really seem to do much. All they seemed to be doing is spending a lot of time expressing completely obvious shit we already know in a mathematical formalism. Oh wow so you made a mathematical formalism to represent air traffic control all under the same tent in only 8 months and if anything changes you have to remake it if any assumptions change. So what? How the fuck does this help me as an engineer? I can already draw boxes with arrows between them and shit.

Just how the fuck am I supposed to use category theory as an engineer? Is this category theorist just yanking my chain?

Nude_Bikergirl

What's a good foreign language to learn?
Chinese, it's the future

Boy_vs_Girl

I'm assuming this is a troll, but in case it's not the benefit in formulating your problem as an abstraction lies in applying other theorems from related pure math abstractions that might aid your own problem.

If your problem doesn't have smooth or polynomial structure there is essentially no reason to this.

Physicists tend to fall into the trap of simplifying their theories so that they can work in variations of linear and smooth spaces which fits into abstractions that are richly developed in mathematics. Even many quantum field theories are simplified to allow for analysis using group theory methods. This is not realistic when you're working with real world problems that are highly non-linear and discontinuous.

Gigastrength

it's not a troll. They want to 'solve' this one engineering field using category theory.
If your problem doesn't have smooth or polynomial structure there is essentially no reason to this.
explain. This is urgent. It is very rare for problems in my field to be smooth. Phenomena such as friction and contact are not smooth.
physicists
no this was a category theorist who wants to go from pure to applied

TreeEater

I mean [eqn]p \sim q :\Leftrightarrow \lnot(p \prec q) \land \lnot (q \prec p)[/eqn] followed by [eqn][p]_\sim \prec_\oplus [q]_\sim :\Leftrightarrow \forall p' \in [p]_\sim : \forall q' \in [q]_\sim : p' \prec q'[/eqn] Does this make sense?

Flameblow

multivariable m8

CouchChiller

I'm going to unironically go with this one.

TechHater

Japanese, we're on Veeky Forums after all.

PurpleCharger

I have so many reasons to learn Japanese (mainly in the form of untranslated games and manga) and yet no motivation whatsoever to learn it . I think I need an academic / career related reason to motivate me .

Need_TLC

They want to 'solve' this one engineering field using category theory.
Just tell them you're working with Navier-Stokes equations they might realize they're retarded.

If you're not using N-S you're definitely using coupled non-linear equations (by coupled I mean some variables or parameters appear as a non-linear term in more than one equation that needs to be solved or simulated simultaneously). Something which is even more unsolved than N-S smoothness and continuity.

But most of all don't waste time with mouth breathing autists who are probably unpublished.

explain
While category theory purports to try and find a unification of all abstract mathematical concepts and structures. Its success has been largely limited to finding morphisms between structures in algebraic topology. Topology is fundamentally the study of properties preserved under continuous transformations. We know a lot about smooth spaces from algebraic topology, just like we know a lot about polynomial equations for algebraic geometry.

Note that there are various subfields based on discrete topologies etc, but these fields are not nearly as developed as the smooth (including Hausdorff space) topologies. Many geometries in engineering are not even manifold.

Basically once you have highly complex non-linear behaviour (such as chaotic systems), discontinuities (such as variables or parameters where no solution exists) or coupled non-linear systems then you really know fuckall about the system. If this was not true then chaos theory (within which most developments have been largely numerical simulations) would be a solved problem already. As would the millennium prize for the navier-stokes conjectures.

Virtually all problems in engineering fall into these "categories". Solved problems in smooth spaces are not really worked on by research engineers. Only applied in industry.

Garbage Can Lid

no this was a category theorist who wants to go from pure to applied
This usually happens when a mathematician fails to break into academia and then realize he's otherwise unemployable. It's his own fault for not studying outside his field. Tell him to apply to the undergraduate engineering course. Anyway I was just trolling any mathematical physicists that might have been reading my posts.

Booteefool

Nevermind that first part doesn't work.

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linguistic entropy

Inmate

Idk man start easy and work your way up. Don't make it a chore or you'll quit.
OR make it your one goal in life and grind until you got it then break.
OR something moderate but painful.

BinaryMan

Try adding the equations and using the harmonic identities

New_Cliche

I think I've had enough of Calculus, am I ready for Analysis like Rudin/Tao? Not sure I can do Topology yet.

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Ignoramus

Still in high school but this took me aback:

"What value of x would set the divisor to 0"

Why the fuck would we do that? So many memes about dividing by 0, now we're evaluating f(X) with values of x that render a null divisor. WHAT THE FUCK

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Stark_Naked

Well, some of the best algebraists read his basic algebra book as a minor.

Lunatick

some of the best algebraists read his basic algebra book as a minor
[citation needed]

Garbage Can Lid

so you know where the undefined values of X are obviously

farquit

But this is for the factor theorem, so every time its going to do that. What would it actually tell you about the graph? Man, I'm dumb, sorry.

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likme

it'd tell you where the asymptotes are on the graph and also give you lots of information about applying the function.

please calm down with the meme spamming it's really an eyesore to the thread

Yeah, to put this outline in perspective, I alone at my school undergraduate level (junior currently) have the potential to finish a outline like this (not the one above, I follow something more algebraic), with the last successful such person graduating in 2012. And I go to a top 10 university. There are many other great students; it is that they specialize earlier, a pathway I would strongly discourage (though one should specialize midway through the second year if they want a shot at top schools)

PackManBrainlure

He's underage he can't help it.

Carnalpleasure

Sanskrit, Tuvan or Livonian.

Why do you think you aren't ready for topology? All you need is basic set theory to get started.

FUCK

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SniperGod

It took me a week to pick up the ropes, and about two months to gain complete fluency. I recommend reading the wiki through and through, and to use LaTeX.

TurtleCat

Currently working though pic related, but I am also looking to for a decent book on spectral theory.

My only background in it is in the chapter in this book, the 3 chapters in Kreyszig's functional analysis book and obviously the baby version in linear algebra.

Does anyone here have any recommendations?

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StonedTime

I think I've had enough of Calculus, am I ready for Analysis like Rudin/Tao?
Calculus IS analysis. DESU i find algebra to be more fun, but whatever floats your boat. Maybe you should try Tao, Rudin is a meme.

Need_TLC

Kind of hard to cite as I heard it from them personally.

Nude_Bikergirl

German duh. Don't you wanna be Gauss??

massdebater

Linear algebra and diff. Equ.

Emberfire

calculus 1,2,3

Flameblow

Homology (no Homo) and Real Anal.

WebTool

what does "space" mean? like fock space, probability space, etc

is it always a vector space? or is that another type of space?

yes im brainlet

Ignoramus

what does "space" mean?
Nothing.

is it always a vector space?
No.

Raving_Cute

there's a wikipedia article that is literally the answer to your question

Lunatick

A space is a set or Cartesian product of sets together with a distance function.

For example the Euclidean space of dimension n is $\mathcal{R}^n$ with associated distance function $d(x, y) = \sqrt{x^2 + y^2}$.

Lord_Tryzalot

and yes, you're a brainlet. not because you don't know what a space is, but because you would rather ask people to solve your problems than google for fucking two minutes

TurtleCat

2nd year linear algebra exam in 4 days and I can only do RREF

What's the quickest way to learn about it within extremely limited time

BlogWobbles

it takes 5 minutes, no it's not difficult

StonedTime

i've mostly done things in the realm of category theory/logic because that's been most useful to my research, but recently been getting into alg geo and diff geo.

not coming from analytic background, diff geo was hard for me at first, but I have been really liking pic related after trying a bunch of books including . The best paced and most well-organized so far in terms of giving you solid things to compute but also very conceptual. Written in a way such that if yk cat theory many of the proofs and constructions will be obvious.

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whereismyname

It can be a whole lot of things. The majority of the time it is a set with additional structure.

i.e. -Measurable space has a sigma algebra
-Topological space has a topology
-Vector space has linear structure
-Manifolds, Varieties, Schemes have a topology and a sheaf of rings

But sometimes they are not even sets.

ex. We often want to consider "Moduli Spaces", which are spaces whose points correspond to some type of equivalence classes of some type of geometric object. Such spaces are often best structured as a Stack, which has either a fibered category or a pseudofunctor underlying it (not a set).

takes2long

Understand the formula and it will be easy.

Methshot

get a trip

Flameblow

You are a brainlet for posting reddit trash.

Nojokur

Since we're talking about mathematics, usually it means "topological space" (i.e. CW complex) or "algebraic space".

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Illusionz

How can CW complexes be real if Euclidean spaces aren't real?

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Inmate

I learned to latex in a couple of minutes. You know how to pronounce it?

RavySnake

Trying to learn about sheaves on sites and forcing to finally be able to read Plato's works on the deep sexual ontology of meta-philosophy. I'm an applied philosophy major.

TurtleCat

Is it well defined to have a sum with uncountably many zeroes? For example, I have a partition of unity subordinate to a (possibly uncountably infinite) cover. The functions of the partitions can be non-zero only finitely many times. So is it well-defined to some over uncountably many functions, when only finitely many are non-zero?

StonedTime

yes

CouchChiller

no

eGremlin

well defined
What do you mean?

Nevermind, it is well defined, if you define the sum to just take the value over the finite non-zero values

StrangeWizard

anime posters need to die

Fuzzy_Logic

anime posters need to die
>>>/reddit/

Stupidasole

This general is the worst place on Veeky Forums.

whereismyname

Transferring from cc to university next semester (I'm not a brainlet and my iq is pretty decent, I just had interesting life circumstances, let's put it that way) for pure math (possibly with a physics double major), is an undergrad PDEs course a meme or useful?

Working through baby rudin on my own. Undergrad PDEs seems kind of memey, just more fourier transforms with some green's functions and whatnot. But I wanted the opinion of someone more experienced.

Would mathematical statistics be more useful?

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Nojokur

This general is the worst place on Veeky Forums.
Then leave

Illusionz

I would wait and take a grad PDEs course.

Spazyfool

Yeah do PDEs even if you do pure math.

Supergrass

Undergrad PDEs is literally a meme

Fried_Sushi

maybe

Stark_Naked

Undergrad PDEs is literally a meme
Only if you go to a school for brainlets

Need_TLC

is an undergrad PDEs course a meme or useful?
Would mathematical statistics be more useful?
possibly with a physics double major
I'm not a brainlet and my iq is pretty decent
I doubt it with the retarded questions you're asking.

Lunatick

retarded
Why the ableism?

Crazy_Nice

He didn't say he was going to engineer grad school.
Engineering isn't required for doing "pure math" (also known as "math").

Booteefool

that's what I assumed, thanks, think I'm going to wait until I have upper-division analysis done then do the PDE sequence that comes after that

They're legitimate questions because the class seems kind of silly upon first inspection. That's why I asked.

Harmless_Venom

math
This is not well-defined.

MPmaster

Would mathematical statistics be more useful?
the class seems kind of silly upon first inspection
It is indeed silly if your goal is to study anything besides engineering.

girlDog

Would mathematical statistics be more useful?
I'm interested in pure math above all though. Statistics is a graduation requirement at the university in question for the math BS so it is something I'd have to take regardless.

w8t4u

I'm interested in pure math above all though.
There is no such thing as "pure" or "impure" math.
Statistics is a graduation requirement at the university in question for the math BS
Your "university" is literal garbage in that case. Adding economics or electrical engineering graduation requirements would be about as relevant for mathematics. I recommend trying to cheat so you don't have to infect your brain with such "knowledge".

Bidwell

I recommend trying to cheat so you don't have to infect your brain with such "knowledge".
Mathematicians use "we", not "I".

massdebater

Mathematicians
see

kizzmybutt

Does anyone know of a program where I can change the Center Radius angle on this picture and get calculations of each segment for a defined radius?

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Techpill

Try asking in the appropriate place for such questions. That place being the /g/catalog#s=hetto%2F or Veeky Forumscatalog#s=sqt%2F.

StonedTime

Is this always well-defined?

Lord_Tryzalot

Is anyone an expert regarding the weil petersson metric on manifolds that are not Riemann surfaces?

WebTool

Yeah. I'm actually the one who defined them.

RumChicken

Why am I such a brainlette that I have trouble with simple linear algebra proofs?

Stupidasole

Don't you funny me user. Specifically, I'm interested in complex 3-dim. Kahler mfs., I want to understand how to explicitely calculate the WP metric for such manifolds.

Need_TLC

I want to understand how to explicitely calculate the WP metric for such manifolds
What for?

They are nice invariants of (compact) CY 3-folds which have not been studied too extensively yet. Basically I know how they look like, i.e. you take the negative Hessian of the 3-fold cup product in $H^{1,1}(X,\mathbb{R})$, where $X$ is your CY 3-fold, and then restrict it (viewed as a Lorentz type bilinear form) to level sets of the 3-fold cup product in the Kahler cone of $X$. The 3-fold cup product is a cubic homogeneous polynomial with some automatically fulfilled properties, like having a hyperbolic point. But I do not understand how to calculate said polynomial when given a specific compact 3-dim. CY. Sources for that problem are rare, as it is more analysis flavoured and thus usually avoided by algebros.

Boy_vs_Girl

How am I supposed to study for a proof based exam?

Evil_kitten

The kind that is actually Mechanical Engineering :^)

Maybe your book is shit. Maybe your class is shit. Maybe you don't know how to deal with abstraction yet.

idontknow

Has anyone ever been able to explicitly write out a metric for any calabi-yau 3-fold?

SniperGod

I haven't found a single example that starts with a coordinate-description, or a specific homogeneous CY 3-fold. In dimension 2, that is for Riemann surfaces, you know how the WP metric looks like locally around every point, simply because there exists up to linear transformations precisely one hyperbolic quadratic polynomial, namely $x_{m}^2-x_{1}^2-\ldots-x_{m}^2$. Here, $m=\mathrm{dim}\ H^{1,1}(X,\mathbb{R})=h^{1,1}$ and $X$ is your Riemann surface. But for higher dim Kahler manifolds like CY 3-folds the moduli space of hyperbolic homogeneous polys in more than 3 variables is very complicated.

A good start for my problem would be to understand how to determine the Kahler cone of some explicitely given CY 3-fold, that alone is nasty.

WebTool

Memorize all the definitions and major theorems.

Train yourself to be able to recall all of them and apply the basic techniques behind them on command.

If someone gives you a problem, you should immediately have an idea of what you need to do and what results you need to solve it.

TurtleCat

Ah fuck latex and fuck me, meant to write $x_m^2-x_1^2-\ldots-x_{m-1}^2$.

StrangeWizard

We're using Linear Algebra Done Right, which seems well regarded, and the class is an honors course taught by a professor who is supposed to be among the best.

I guess I just need to get used to the abstraction, then.

Garbage Can Lid

Yeah that should be a good course. The legit linear algebra course at my school uses that book too. Linear algebra is usually the first introduction to abstraction so it makes sense that you're in the process of learning it. Keep in mind real math is all about generalization and mathematical thinking takes time to develop, at least it did in my case.

Crazy_Nice

at least it did in my case
As it usually does in the case of brainlets.

Boy_vs_Girl

I've already accepted that I'm slightly above average at best. There's no need to be so condescending about it.

Spamalot

are you a girl? then that's why.

girlDog

I'm slightly above average at best
Perhaps in the company of brainlets. Anyone who writes "real math is all about generalization" is clearly below average.

Evil_kitten

Congrats on popping out the womb reading Rudin.

I'm not interested in engineering so I don't read such books.

takes2long

iluvmen

Anyone who writes "math is all about specific examples " is clearly retarded, so it all checks out.

kizzmybutt

I mean do you not understand that was sarcasm? That's a bit sad.

Gigastrength

The truly sad thing here is that you think those two positions are somehow "opposite" and that one of them is somehow "correct".

TalkBomber

Well from your characteristic use of quotes I know you're the anime posting girl of /mg/ and you definitely know more about math than me. I was just trying to give some advice to someone in a similar position to me some time ago and what helped me back then was thinking more abstractly. I do think math is taught in either one of the two camps, you have computational example ridden math lite course and more general courses that focus on developing concepts.

Garbage Can Lid

the anime posting girl of /mg/
This doesn't uniquely determine anyone. We're all anime posting girls here.
thinking more abstractly
I don't understand what you mean by this.
I do think math is taught in either one of the two camps
These camps don't exist as stated. There is math and then there is stuff which can't be considered math by any stretch of the imagination (e.g.,"computations with matrices").
more general courses that focus on developing concepts
The very nature of the subject forces every math course to be focused on developing the understanding of certain concepts.

takes2long

Well my first exposure was what you rightly consider to not even be math. So I guess thinking more abstractly was just actually understanding what was going on instead of looking for the "trick" to solve whatever was in front of me.

eGremlin

I'm trying to solve $\hat{f}(\omega)=e^{ic\omega}$ but all I get is $\int_{-\infty}^\infty e^{\omega(ic-ix)}d\omega$, which is unbounded. What am I doing wrong?

AwesomeTucker

Dammit.

math
This is not well-defined.

iluvmen

This but unironically

Methshot

Does it matter where you get your undergrad degree? I go a decent public Uni and I am thinking of transferring to a more rigorous private school or an IV league.

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