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

# /mg/ - Math general

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

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

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.

**veekyforums.com**

Depends on the gauge group [math]G[/math] as well as the manifold [math]M[/math] (obviously). In general the local tangent space [math]T_\alpha \mathcal{A}[/math] 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 [math]M \times_G G[/math] 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.

My bad, the homotopy quotient is [math]M \times_G EG[/math] where [math]EG\rightarrow BG[/math] is the classifying [math]G[/math]-bundle.

**ncatlab.org**

What are the prerequisites necessary to understand this article

No, undrestand the difference between combinations and permutations though.

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.

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.

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).

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

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

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

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.

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.

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).

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).

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.

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).

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.

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)

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

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

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

p-please.

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

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?

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.

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.

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

A literal retard spotted.

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

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

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.

Is anime your secret?

It's mainly not visiting websites such as "reddit.com", "facebook.com" and the likes.

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

Oh sorry I forgot my HILARIOUD animr pic and my cliche snarky remark

mfw physicits don't even know delta-epsilon

2hu

animr

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

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

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.

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

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

Advanced Applied Numerical Methods

Stochastic Simulation

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

Why do you think that your question is appropriate for this thread? Ask in the engineering threads.

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.

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

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

I'm asking about mathematics courses

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

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.

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.

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.

Wew.

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

[math]\frac{1}{2}cr[/math]

[math]\pi r^2[/math] makes no intuitive sense at all.

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

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

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.

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

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

proof and concept

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

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

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.

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?

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.

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).

Leray spectral sequence

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

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

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.

legandre transform, geometric interpretation and applications

Didn't even read your post. Ask in the physics threads over at /toy/ and Veeky Forumscatalog#s=phg%2F.

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

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 [math]G[/math]. 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.

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.

We don't speak your language around here. Return to /v/ with your filthy dialect.

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

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.

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.

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.

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.

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

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.

you don't "really" understand real functions until you've done with analysis

Jesus christ america.

apply to real world phenomenon

Ask in some other thread and read the thread name before posting.

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.

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.

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

But you can fuck off to some other thread if you want to discuss that.

Do you need to swear?

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?

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.

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this is a christian board, please refrain from insults or cursewords. thank you

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.

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

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

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.

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.)

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.

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

[math]

$(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)$

[/math]

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

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.

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

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

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

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

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

please gz

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.

OR is called the disjunction and is defined that way, like an axiom

x,y or both but not neither

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

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.

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.

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 [math]\mathscr{P}(\prec)[/math] but that doesn't really make sense if you think about it.

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

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?

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.

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

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?

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 .

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.

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.

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.

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

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

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

[citation needed]

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.

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)

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

Watch your profanity.

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.

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?

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.

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

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

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

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

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

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.

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).

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

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.

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?

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

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?

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.

He didn't say he was going to engineer grad school.

Engineering isn't required for doing "pure math" (also known as "math").

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.

Would mathematical statistics be more useful?

For your kind? Sure. Just post about that in the physics threads at /toy/ and Veeky Forumscatalog#s=phg%2F instead of here.

the class seems kind of silly upon first inspection

It is indeed silly if your goal is to study anything besides engineering.

Would mathematical statistics be more useful?

For your kind? Sure. Just post about that in the physics threads at /toy/ and Veeky Forumscatalog#s=phg%2F instead of here.

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.

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".

I recommend trying to cheat so you don't have to infect your brain with such "knowledge".

Mathematicians use "we", not "I".

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?

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

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

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

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.

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 [math]H^{1,1}(X,\mathbb{R})[/math], where [math]X[/math] 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 [math]X[/math]. 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.

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

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

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 [math]x_{m}^2-x_{1}^2-\ldots-x_{m}^2[/math]. Here, [math]m=\mathrm{dim}\ H^{1,1}(X,\mathbb{R})=h^{1,1}[/math] and [math]X[/math] 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.

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.

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

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.

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.

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

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.

New:**veekyforums.com****veekyforums.com****veekyforums.com**

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

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

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.

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.

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.

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

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.