Why do Amerisharts have to study how to prove things as a separate subject?

[Anonymous No.9824447]

Can't they pick up the patterns from theorems?

[Anonymous No.9824673]

I'm pretty sure it's like that everywhere in the anglosphere aka the civilized world.

We're sorry your 3rd world shithole doesn't do things the proper way.

[Anonymous No.9824694]

>>9824673
>I'm pretty sure it's like that everywhere in the anglosphere aka the civilized world.
It's not.

[Anonymous No.9824698]

>>9824694

I'm from NZ. We have separate classes on proofs.

[Anonymous No.9824700]

>>9824673
Define "proper", kek.

[Anonymous No.9824703]

>>9824694
i'm dutch and we do that

[Anonymous No.9824708]

>>9824447
It's done this way in a lot of places.
Why are you so ignorant and stupid that you couldn't even Google this first?
Also a side note. The book of proof is free.

[Anonymous No.9824709]

>>9824447
Where are you going to learn about DeMorgan's law, inclusive/exclusive OR, power sets, cardinality, Cantor's theorem, Cantor–Schröder–Bernstein's theorem, axiom of choice, continuum hypothesis, LaTeX and good style?

You probably had a watered down analysis, linear, or abstract algebra class that taught them instead of their subject matter.

[Anonymous No.9824722]

>>9824709
You learn about then in a book on Set Theory.
So I assume your course had watered down Set Theory.
What a mong.

[Anonymous No.9824723]

I think it's safe to say OP exposed himself as being from a 3rd world shithole.

[Anonymous No.9824725]

>>9824673
> the civilized world.
That's not how "the lands of the brainlets" is spelled.

[Anonymous No.9824727]

>>9824722
You honestly have a separate course for set theory and don't just pick it up on the go?
jesus christ euros

[Anonymous No.9824730]

>>9824727
Separate courses in "Logic and Set Theory" > courses in "proofs". This is just like how retarded anglos have "calculus" classes, whereas brainiac Euros learn "mathematical analysis".

[Anonymous No.9824732]

>>9824730
>he also needs a separate course on LOGIC
ahahahhahaha holy shit

[Anonymous No.9824734]

>>9824709
>Where are you going to learn about DeMorgan's law, inclusive/exclusive OR,
high school

>power sets, cardinality, Cantor's theorem, Cantor–Schröder–Bernstein's theorem
calculus class

>axiom of choice
linear algebra class

>continuum hypothesis
analysis class

> LaTeX and good style
does not require a class at all

[Anonymous No.9824741]

>>9824734
i'm german and I wish we did this

[Anonymous No.9824746]

>>9824447
>it's another "euros talk up their easy unis after I studied abroad and saw the same exact coursework, maybe slightly harder" episode

Embarrassing. Take note, folks. This is what not having a single uni in the top 10 does to you, save for Cambridge.

[Anonymous No.9824749]

it's probably the biggest red flag I know whenever I see someone on /sci/ post one of those meme proof textbooks or say they took a class just on proofs, I automatically disregard anything they say because they have no taste for quality education

[Anonymous No.9824753]

>>9824749
i guess that's one way to cope with americans being the chads of STEM

[Anonymous No.9824762]

>>9824753
>i guess that's one way to cope with americans being the chads of STEM
I don't concern myself with the STE part, but the French are the chads of maths

[Anonymous No.9824772]

imagine living in such an irrelevant country that you convince yourself that anyone cares even slightly about undergrad, in order to hold off suicide

[Anonymous No.9824793]

>>9824762
>but the French are the chads of maths

What? lol this isn't the 18th century anymore.

The only quantitative skills the French have nowadays are when the women estimate how big an African man's cock is since they love getting stretched out by them.

[Anonymous No.9824804]

for anyone wondering why euro unis are so rigorous, this is why, at least for france

at a very early age, students are given huge gauntlets of IQ tests and placed into their respective castes. if I remember correctly, if you score less than a 140 or so, you are barred, or strongly, STRONGLY discouraged from studying math. those IQ tests will play into uni admissions and if you didn't do stellar, there is literally nothing you can do to go top unis. also, students who have like a sub-110 or so are sent to trade schools and basically forced to work in factories or construction and the like.

[Anonymous No.9824807]

>>9824804
as a result, only people with high IQs go to unis while above average and retards work in manual labour

[Anonymous No.9824808]

>yfw no American has won a Fields medal since 20 years ago

[Anonymous No.9824823]

>>9824804
>there is literally nothing you can do to go top unis.

That's not really saying much since 99% of French unis are garbage lol.

France is a 3rd world shithole. I've seen African cities that look better than Paris.

[Anonymous No.9824849]

>>9824823
>I've seen African cities that look better than Paris.
Shut up mutt-hurt.

[Anonymous No.9824866]

>>9824849
>has literally never been to the US

[Anonymous No.9824916]

>>9824866
Is there a non literal form of that statement?
Why are mutts so stupid?

[Anonymous No.9824934]

>>9824804
>at a very early age, students are given huge gauntlets of IQ tests and placed into their respective castes. if I remember correctly, if you score less than a 140 or so, you are barred, or strongly, STRONGLY discouraged from studying math. those IQ tests will play into uni admissions and if you didn't do stellar, there is literally nothing you can do to go top unis. also, students who have like a sub-110 or so are sent to trade schools and basically forced to work in factories or construction and the like.

[Anonymous No.9824943]

>>9824804
>thinking early age testing is a sufficient gauge for later stage accomplishment abilities
I bet someone who was smart when they were 6 thought of that trash ass logic. At best you're barring only 20-30 percent of smart people from going to university.

>Michael Schumacher will never be a great racing driver: he only finished 4th in 1993.

[Anonymous No.9824971]

>>9824916

Yeah, you could say that statement in a figurative way you dumbie.

[Anonymous No.9824973]

>>9824916
retard

[Anonymous No.9824975]

>>9824943
>>9824934
assmad mutts

[Anonymous No.9824977]

>>9824943
Name one thing wrong with early age testing, specifically starting at 9 or 10, when IQs at those ages correlate vastly with adult IQ.

[Anonymous No.9824987]

>>9824977
>when IQs at those ages correlate vastly with adult IQ.
correlation does not imply causation

[Anonymous No.9824992]

>>9824987
Are you actually fucking retarded
Jesus christ

[Anonymous No.9825002]

>>9824992
>Are you actually fucking retarded
Do you need to swear?

[Anonymous No.9825005]

>>9824741
French model > everything. It's not by accident that the French have been the best mathematicians for the past 400 years.

[Anonymous No.9825006]

>>9824916
yes
>literally does not know what "literally" means
Euros are legitimately braindead.

[Anonymous No.9825009]

>>9825005
>It's not by accident that the French have been the best mathematicians for the past 400 years.

Definitely not after the 19th century. You guys are irrelevant now.

Only thing France is known for is hot French women that love big North African cocks.

[Anonymous No.9825010]

>>9825005
They mostly produce good mathematicians because they segregate the geniuses from the common folk early and condition them to study Maths. Only the smartest go to university in France.

[Anonymous No.9825014]

>>9824804
It's not the meritocratic sorting of students. It's the pedagogy. It's similar in other European countries that follow the French model, even if they don't all sort children by intelligence. Sorting students early might not be a good idea, since IQ isn't stable until adulthood.

[Anonymous No.9825015]

>>9825010
>Only the smartest go to university in France.

Not true. France's smartest people go to other countries to study at universities like Harvard because French universities are trash.

[Anonymous No.9825019]

>>9824977
>Name one thing wrong with early age testing
Children are still developing. Some might develop faster, some slower. Among those that develop faster, some might plateau at a lower level in adulthood. Among those that develop slower, some might peak at a higher level in adulthood.

Many so-called child "prodigies" never achieve much in life simply because they were one of those kids that developed faster mentally, but plateaued bellow their peers in the end, for example.

[Anonymous No.9825021]

>>9825014
IQ is actually pretty stable by age 9, as plenty of giftedness programs here screen at age 7. By age 12 it's set in stone, for the most part

[Anonymous No.9825025]

>>9824977
>IQs at those ages correlate vastly with adult IQ.
The correlation isn't anywhere close to 1, so there is a lot of variance in between, a lot of children that are getting screwed due to an accident of their biology.

[Anonymous No.9825028]

>>9825019
True but every IQ study shows that high IQ children tend to stay at the top of the pack in adulthood.

[Anonymous No.9825030]

>>9825009
>Definitely not after the 19th century.
Not true.

>>9825021
>IQ is actually pretty stable by age 9
Also not true.

[Anonymous No.9825032]

>>9825025
0.83 is pretty close to 1 I'd say

[Anonymous No.9825034]

>>9825030
>Also not true
Wrong.

[Anonymous No.9825037]

>>9824709
what do you study in highschool?

[Anonymous No.9825042]

>>9824694
I can tell this is /sci/'s "why do homophobia" tranny. Kill yourself

[Anonymous No.9825047]

>>9825042
>I can tell this is /sci/'s "why do homophobia" tranny. Kill yourself
I'm not a "tranny".

[Anonymous No.9825058]

>>9825032
>0.83
>pretty close to 1
This system is screwing over a third of the children. That's the relevant point.

[Anonymous No.9825059]

>>9824730
so true. Also some of them have 2 fucking years of this calculus(4 semesters) for retards and then one more semester of "intro to math analysis" where they encounter more rigorous approach. 5 semesters without a single mentioning of a "manifold". I hope these students are smarter than their fucked up curriculum and they self-study sufficient for being able to read 20% of articles in the area of their interest on arxiv after 3 years of undergraduate.

[Anonymous No.9825066]

I don't buy the whole IQ thing to be honest. When I was in high school, I took a stats class where the teacher put all our IQs on the board so that we could analyze them.

Apparently we took IQ tests without knowing it when we were children he found our scores in our files. The funny thing is everyone apparently had a triple digit IQ and about a quarter of the class was above 120.

The problem was that in reality, 95% of the students were complete dumbfucks.

[Anonymous No.9825067]

>>9825058
>over a third
Not him and think the system's dumb, but how do you calculate that?

[Anonymous No.9825069]

>>9825066
You severely underestimate the retardation of 100s and overestimate the intelligence of 120s.

[Anonymous No.9825077]

>>9825067
It falls straight out of the definition for 'correlation'. Basic statistics.

[Anonymous No.9825079]

>>9825042
sounds like you need a break from the computer if you're recognizing anonymous posters

[Anonymous No.9825097]

>>9825047
kill yourself
>>9825079
>le i'm on 4chan but i'm super cool unlike all of you!
kill yourself faggot loser

[Anonymous No.9825129]

>>9825097
>kill yourself
>>9825097
>kill yourself faggot loser
Are you ok? If you need someone to talk to I'm here for you

[Anonymous No.9825142]

>>9824447
they don't *have to*

[Anonymous No.9825146]

Why do Amerisharts have to study humanities as part of their STEM degrees?

[Anonymous No.9825149]

>>9825129
kill yourself

[Anonymous No.9825168]

>>9825146
It's what universities do, institutes don't.

[Anonymous No.9825203]

>>9825168

Wait what? Really?

[Anonymous No.9825242]

>>9825037
The cheerleaders.

[Anonymous No.9825271]

>>9825077
Please elaborate. What is the expectation for miscategorization?

[Anonymous No.9825276]

>>9825010
We don't segregate the geniuses from the rest, no-one is conditioned to study math and plenty of people go to uni

t. frog

[Anonymous No.9825288]

>>9824447
The history of math education in the US is seriously fucked. (See https://www.csun.edu/~vcmth00m/AHistory.html)) You can read A Mathematician's Lament to see how fucked it is to this day.
Anyway, most US colleges have an intro to proof writing course because it is possible to graduate from a US high school without having written a single proof. Proof writing courses serve as an introduction to advanced mathematics. It's an effective and easy solution.

[Anonymous No.9825324]

Imperial does intro to proof and all other intro to meme course first semester as the lecturers know everyone just wants to party

[Anonymous No.9825444]

so if I want to remedy shit amerimutt education what should I study?

[Anonymous No.9825470]

>>9825444
>so if I want to remedy shit amerimutt education what should I study?
High School:
• Euclidean geometry, complex numbers, scalar multiplication, Cauchy-Bunyakovskii inequality. Introduction to quantum mechanics (Kostrikin-Manin). Groups of transformations of a plane and space. Derivation of trigonometric identities. Geometry on the upper half-plane (Lobachevsky). Properties of inversion. The action of fractional-linear transformations.
• Rings, fields. Linear algebra, finite groups, Galois theory. Proof of Abel's theorem. Basis, rank, determinants, classical Lie groups. Dedekind cuts. Construction of real and complex numbers. Definition of the tensor product of vector spaces.
• Set theory. Zorn's lemma. Completely ordered sets. Cauchy-Hamel basis. Cantor-Bernstein theorem.
• Metric spaces. Set-theoretic topology (definition of continuous mappings, compactness, proper mappings). Definition of compactness in terms of convergent sequences for spaces with a countable base. Homotopy, fundamental group, homotopy equivalence.
• p-adic numbers, Ostrovsky's theorem, multiplication and division of p-adic numbers by hand.
• Differentiation, integration, Newton-Leibniz formula. Delta-epsilon formalism.

[Anonymous No.9825474]

>>9825470
Freshman:
• Analysis in R^n. Differential of a mapping. Contraction mapping lemma. Implicit function theorem. The Riemann-Lebesgue integral. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Hilbert spaces, Banach spaces (definition). The existence of a basis in a Hilbert space. Continuous and discontinuous linear operators. Continuity criteria. Examples of compact operators. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Smooth manifolds, submersions, immersions, Sard's theorem. The partition of unity. Differential topology (Milnor-Wallace). Transversality. Degree of mapping as a topological invariant.
• Differential forms, the de Rham operator, the Stokes theorem, the Maxwell equation of the electromagnetic field. The Gauss-Ostrogradsky theorem as a particular example.
• Complex analysis of one variable (according to the book of Henri Cartan or the first volume of Shabat). Contour integrals, Cauchy's formula, Riemann's theorem on mappings from any simply-connected subset C to a circle, the extension theorem, Little Picard Theorem. Multivalued functions (for example, the logarithm).
• The theory of categories, definition, functors, equivalences, adjoint functors (Mac Lane, Categories for the working mathematician, Gelfand-Manin, first chapter).
• Groups and Lie algebras. Lie groups. Lie algebras as their linearizations. Universal enveloping algebra, Poincaré-Birkhoff-Witt theorem. Free Lie algebras. The Campbell-Hausdorff series and the construction of a Lie group by its algebra (yellow Serre, first half).

[Anonymous No.9825477]

>>9825474
Sophomore:
• Algebraic topology (Fuchs-Fomenko). Cohomology (simplicial, singular, de Rham), their equivalence, Poincaré duality, homotopy groups. Dimension. Fibrations (in the sense of Serre), spectral sequences (Mishchenko, "Vector bundles ...").
• Computation of the cohomology of classical Lie groups and projective spaces.
• Vector bundles, connectivity, Gauss-Bonnet formula, Euler, Chern, Pontryagin, Stiefel-Whitney classes. Multiplicativity of Chern characteristic. Classifying spaces ("Characteristic Classes", Milnor and Stasheff).
• Differential geometry. The Levi-Civita connection, curvature, algebraic and differential identities of Bianchi. Killing fields. Gaussian curvature of a two-dimensional Riemannian manifold. Cellular decomposition of loop space in terms of geodesics. The Morse theory on loop space (Milnor's Morse Theory and Arthur Besse's Einstein Manifolds). Principal bundles and connections on them.
• Commutative algebra (Atiyah-MacDonald). Noetherian rings, Krull dimension, Nakayama lemma, adic completion, integrally closed, discrete valuation rings. Flat modules, local criterion of flatness.
• The Beginning of Algebraic Geometry. (The first chapter of Hartshorne or Shafarevich or green Mumford). Affine varieties, projective varieties, projective morphisms, the image of a projective variety is projective (via resultants). Sheaves. Zariski topology. Algebraic manifold as a ringed space. Hilbert's Nullstellensatz. Spectrum of a ring.
• Introduction to homological algebra. Ext, Tor groups for modules over a ring, resolvents, projective and injective modules (Atiyah-MacDonald). Construction of injective modules. Grothendieck Duality (from the book Springer Lecture Notes in Math, Grothendieck Duality, numbers 21 and 40).
• Number theory; Local and global fields, discriminant, norm, group of ideal classes (blue book of Cassels and Frohlich).

[Anonymous No.9825479]

>>9825477
Sophomore (cont):
• Reductive groups, root systems, representations of semisimple groups, weights, Killing form. Groups generated by reflections, their classification. Cohomology of Lie algebras. Computing cohomology in terms of invariant forms. Singular cohomology of a compact Lie group and the cohomology of its algebra. Invariants of classical Lie groups. (Yellow Serre, the second half, Hermann Weyl, "The Classical Groups: Their Invariants and Representations"). Constructions of special Lie groups. Hopf algebras. Quantum groups (definition).

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

[Anonymous No.9825481]

>>9825470
ur an idiot NEET

u do this 'plan' and gl seeing friends/having relationships/making money ever youll be on /sci/ and physicsforums till u die

[Anonymous No.9825482]

>>9825479
Junior (cont):
• Algebraic geometry of schemes, schemes over a ring, projective spectra, derivatives of a function, Serre duality, coherent sheaves, base change. Proper and separable schemes, a valuation criterion for properness and separability (Hartshorne). Functors, representability, moduli spaces. Direct and inverse images of sheaves, higher direct images. With proper mapping, higher direct images are coherent.
• Cohomological methods in algebraic geometry, semicontinuity of cohomology, Zariski's connectedness theorem, Stein factorization.
• Kähler manifolds, Lefschetz's theorem, Hodge theory, Kodaira's relations, properties of the Laplace operator (chapter zero of Griffiths-Harris, is clearly presented in the book by André Weil, "Kähler manifolds"). Hermitian bundles. Line bundles and their curvature. Line bundles with positive curvature. Kodaira-Nakano's theorem on the vanishing of cohomology (Griffiths-Harris).
• Holonomy, the Ambrose-Singer theorem, special holonomies, the classification of holonomies, Calabi-Yau manifolds, Hyperkähler manifolds, the Calabi-Yau theorem.
• Spinors on manifolds, Dirac operator, Ricci curvature, Weizenbeck-Lichnerovich formula, Bochner's theorem. Bogomolov's theorem on the decomposition of manifolds with zero canonical class (Arthur Besse, "Einstein varieties").
• Tate cohomology and class field theory (Cassels-Fröhlich, blue book). Calculation of the quotient group of a Galois group of a number field by the commutator. The Brauer Group and its applications.
• Ergodic theory. Ergodicity of billiards.
• Complex curves, pseudoconformal mappings, Teichmüller spaces, Ahlfors-Bers theory (according to Ahlfors's thin book).

[Anonymous No.9825485]

>>9825482
Senior:
• Rational and profinite homotopy type. The nerve of the etale covering of the cellular space is homotopically equivalent to its profinite type. Topological definition of etale cohomology. Action of the Galois group on the profinite homotopy type (Sullivan, "Geometric topology").
• Etale cohomology in algebraic geometry, comparison functor, Henselian rings, geometric points. Base change. Any smooth manifold over a field locally in the etale topology is isomorphic to A^n. The etale fundamental group (Milne, Danilov's review from VINITI and SGA 4 1/2, Deligne's first article).
• Elliptic curves, j-invariant, automorphic forms, Taniyama-Weil conjecture and its applications to number theory (Fermat's theorem).
• Rational homotopies (according to the last chapter of Gel'fand-Manin's book or Griffiths-Morgan-Long-Sullivan's article). Massey operations and rational homotopy type. Vanishing Massey operations on a Kahler manifold.
• Chevalley groups, their generators and relations (according to Steinberg's book). Calculation of the group K_2 from the field (Milnor, Algebraic K-Theory).
• Quillen's algebraic K-theory, BGL^+ and Q-construction (Suslin's review in the 25th volume of VINITI, Quillen's lectures - Lecture Notes in Math. 341).
• Complex analytic manifolds, coherent sheaves, Oka's coherence theorem, Hilbert's nullstellensatz for ideals in a sheaf of holomorphic functions. Noetherian ring of germs of holomorphic functions, Weierstrass's theorem on division, Weierstrass's preparation theorem. The Branched Cover Theorem. The Grauert-Remmert theorem (the image of a compact analytic space under a holomorphic morphism is analytic). Hartogs' theorem on the extension of an analytic function. The multidimensional Cauchy formula and its applications (the uniform limit of holomorphic functions is holomorphic).

[Anonymous No.9825488]

>>9825485
Specialist: (Fifth year of College):
• The Kodaira-Spencer theory. Deformations of the manifold and solutions of the Maurer-Cartan equation. Maurer-Cartan solvability and Massey operations on the DG-Lie algebra of the cohomology of vector fields. The moduli spaces and their finite dimensionality (see Kontsevich's lectures, or Kodaira's collected works). Bogomolov-Tian-Todorov theorem on deformations of Calabi-Yau.
• Symplectic reduction. The momentum map. The Kempf-Ness theorem.
• Deformations of coherent sheaves and fiber bundles in algebraic geometry. Geometric theory of invariants. The moduli space of bundles on a curve. Stability. The compactifications of Uhlenbeck, Gieseker and Maruyama. The geometric theory of invariants is symplectic reduction (the third edition of Mumford's Geometric Invariant Theory, applications of Francis Kirwan).
• Instantons in four-dimensional geometry. Donaldson's theory. Donaldson's Invariants. Instantons on Kähler surfaces.
• Geometry of complex surfaces. Classification of Kodaira, Kähler and non-Kähler surfaces, Hilbert scheme of points on a surface. The criterion of Castelnuovo-Enriques, the Riemann-Roch formula, the Bogomolov-Miyaoka-Yau inequality. Relations between the numerical invariants of the surface. Elliptic surfaces, Kummer surface, surfaces of type K3 and Enriques.
• Elements of the Mori program: the Kawamata-Viehweg vanishing theorem, theorems on base point freeness, Mori's Cone Theorem (Clemens-Kollar-Mori, "Higher dimensional complex geometry" plus the not translated Kollar-Mori and Kawamata-Matsuki-Masuda).
• Stable bundles as instantons. Yang-Mills equation on a Kahler manifold. The Donaldson-Uhlenbeck-Yau theorem on Yang-Mills metrics on a stable bundle. Its interpretation in terms of symplectic reduction. Stable bundles and instantons on hyper-Kähler manifolds; An explicit solution of the Maurer-Cartan equation in terms of the Green operator.

[Anonymous No.9825490]

>>9825488
Specialist (cont):
• Pseudoholomorphic curves on a symplectic manifold. Gromov-Witten invariants. Quantum cohomology. Mirror hypothesis and its interpretation. The structure of the symplectomorphism group (according to the article of Kontsevich-Manin, Polterovich's book "Symplectic geometry", the green book on pseudoholomorphic curves and lecture notes by McDuff and Salamon)
• Complex spinors, the Seiberg-Witten equation, Seiberg-Witten invariants. Why the Seiberg-Witten invariants are equal to the Gromov-Witten invariants.
• Hyperkähler reduction. Flat bundles and the Yang-Mills equation. Hyperkähler structure on the moduli space of flat bundles (Hitchin-Simpson).
• Mixed Hodge structures. Mixed Hodge structures on the cohomology of an algebraic variety. Mixed Hodge structures on the Maltsev completion of the fundamental group. Variations of mixed Hodge structures. The nilpotent orbit theorem. The SL(2)-orbit theorem. Closed and vanishing cycles. The exact sequence of Clemens-Schmid (Griffiths red book "Transcendental methods in algebraic geometry").
• Non-Abelian Hodge theory. Variations of Hodge structures as fixed points of C^*-actions on the moduli space of Higgs bundles (Simpson's thesis).
• Weil conjectures and their proof. l-adic sheaves, perverse sheaves, Frobenius automorphism, weights, the purity theorem (Beilinson, Bernstein, Deligne, plus Deligne, Weil conjectures II)
• The quantitative algebraic topology of Gromov, (Gromov "Metric structures for Riemannian and non-Riemannian spaces"). Gromov-Hausdorff metric, the precompactness of a set of metric spaces, hyperbolic manifolds and hyperbolic groups, harmonic mappings into hyperbolic spaces, the proof of Mostow's rigidity theorem (two compact Kählerian manifolds covered by the same symmetric space X of negative curvature are isometric if their fundamental groups are isomorphic, and dim X> 1).
• Varieties of general type, Kobayashi and Bergman metrics, analytic rigidity (Siu)

[Anonymous No.9825561]

>>9825470
good god fuck off

[Anonymous No.9826374]

>>9825490
Jeez.
Have you studied any of that?

[Anonymous No.9826382]

>>9825030
>Not true
Give a counterexample then. I cannot recall any relevant math frog after de Moivre and Cauchy. Give us proof.

[Anonymous No.9826429]

>>9825470
>>9825474
>>9825477
>>9825479
>>9825482
>>9825485
>>9825488
>>9825490
This pasta is old, unfunny and takes way too much fucking space in the thread. Fuck off or at least post it as a screenshot.

[Anonymous No.9826451]

>>9825490
lol. Verbitsky's curriculum detected

[Anonymous No.9826833]

>>9826429
>Fuck off or at least post it as a screenshot.
Turn it into a screenshot for me or fuck off.

[Anonymous No.9826866]

>>9824447
There's nothing wrong with this.

[Anonymous No.9826870]

>>9826866
>There's nothing wrong with this.
>Introduction to Proofs
>Humanity or Social Science Elective
>Physics I
>Physics II
>Physics III