/sci/ - Science & Math

[Anonymous No.6712599]

What do you think of Verbitsky's math curriculum?
http://imperium.lenin.ru/~verbit/MATH/programma.html

[Anonymous No.6712605]

No one here can read slavshit, idiot.

[Anonymous No.6712611]

I only skimmed through it and I didn't find any course on probability theory.

[Anonymous No.6712614]

>>6712605
I can, I just don't give a damn

[Anonymous No.6712622]

>>6712605
Google Translate does a doesn't job, asshole.

[Anonymous No.6712626]

>>6712622
*decent

[Anonymous No.6712632]

>>6712622
no it doesn't

[Anonymous No.6712644]

too focused on mathematical physics

⇒Мне не кажется, что все области математики одинаково ценные
top autism

[Anonymous No.6712652]

[Anonymous No.6712898]

>>6712644
The only meaningful math is that which can be applied to reality. All the rest is autistic puzzles.

[Anonymous No.6712901]

>>6712644
why is that autism? my russian isn't very good am i losing something in the translation?

[Anonymous No.6712921]

>>6712599
>http://imperium.lenin.ru/~verbit/MATH/programma.html

Damn. So I guess there's a reason why so many russians are the best mathematicians around.

[Anonymous No.6712923]

>>6712652
your potato computer sucks.

[Anonymous No.6712926]

>>6712923
>http://imperium.lenin.ru/~verbit/MATH/programma.html

there's no point to do pure math.
it's philosophically impotent.

[Anonymous No.6712929]

>Mathematical education in Russia.
>I have 6 years of reading training courses and lectures at the Independent University; overall benefits brought by these courses to anyone was almost zero; at least a mathematics student use was no. I will do this and more, but the occupation is obviously meaningless.

>My modest teaching abilities nothing to do with; I'll be even Oscar Zariski in half with Professor Yau, I did not work out to. Over the 6 years I have not seen in Moscow any student who would finish my studies to the state, which allows scientific work (I've seen quite a lot of good young scientists - Stephen Nemirovsky, for example - but they learned somewhere else, I do not know where, but I do not have). The sole function of the Independent University - to deliver frames to American graduate schools; but he copes with it, lately, very bad, because intellectual fund dwindled to complete devastation and kerdyk.

> Over the 6 years I have not seen in Moscow any student who would finish my studies to the state, which allows scientific work (I've seen quite a lot of good young scientists - Stephen Nemirovsky, for example - but they learned somewhere else
>I have not seen in Moscow any student who would finish my studies to the state, which allows scientific work

Now why would that be?

[Anonymous No.6713277]

Copy/pasting here:

Mathematical program must be designed so

School program (exam Matshkolnik)
Euclidean geometry, complex numbers, scalar multiplication, the Cauchy-Schwarz inequality. Principles of Quantum Mechanics (Kostrikin-Manin). Group transformations of the plane and space. Conclusion trigonometric identities. Geometry on the upper half (Lobachevsky). Properties inversion. The action of linear fractional transformations.
Rings and fields. Linear algebra, finite groups, Galois theory. Proof of Abel's theorem. Basis, rank, determinant, classical Lie group. Cross section Dedekind. Definition of the field of real numbers. Determination of the tensor product of vector spaces.
Set theory. Zorn's lemma. Well-ordered set. Basis of the Cauchy-Hamel. Cantor-Bernstein. Uncountable set of real numbers.
Metric spaces. Set-theoretic topology (Definition of continuous mappings, compactness, own display). Countable base. Definition of compactness in terms of convergent sequences for spaces with a countable base. Homotopy, the fundamental group, homotopy equivalence.
p-adic numbers, Ostrowski's theorem, multiplication, and division of p-adic numbers in a column
Differentiation, integration, Newton-Leibniz formula. Delta epsilon formalism lemma policeman.

[Anonymous No.6713280]

>>6713277
The first course
Analysis on $ R ^ n $. Differential display. lemma about contraction mappings. The implicit function theorem. Riemann integral and Lebesgue. ("Analysis" of Laurent Schwartz, "Analysis" Zorich, "Problems and theorems of functions. Analysis" Kirillov-Gvishiani)
Hilbert spaces, Banach spaces (definition). Existence of a basis in the Hilbert space. Continuous and discontinuous linear operators. Criteria continuity. Examples of compact operators. ("Analysis" of Laurent Schwartz, "Analysis" Zorich, "Problems and theorems of functions. Analysis" Kirillov-Gvishiani)
Smooth manifolds, submersion, immersion, Sard's theorem. Partition of unity. Differential topology (Milnor-Wallace). Transversality. Degree of the map as a topological invariant.
Differential forms, de Rham operator, Stokes' theorem, Maxwell's equations of the electromagnetic field. Gauss's theorem as a particular example.
Complex analysis in one variable (based on the book by Henri Cartan or the first volume of the Sabbath). Contour integrals, Cauchy formula, the Riemann mapping theorem of any simply connected subset of $ C $ in a circle theorem on the extension of borders, Picard's theorem on the achievement of an entire function of all values, except for three. Multivalent functions (for example, the logarithm).
Category theory, definition, functors, equivalence, adjoint functors (McLane, Categories for working mathematician, Gelfand-Manin, the first chapter).
Groups and Lie algebras. Lie group. Lie algebra as linearization. Universal enveloping algebra, Poincaré-Birkhoff-Witt. Free Lie algebra. Campbell-Hausdorff series and the construction of a Lie group on its Lie algebra (yellow Serre, the first half).

[Anonymous No.6713283]

>>6713280
The second course
Algebraic Topology (Fuchs-Fomenko). Cohomology (simplicial, singular, de Rham), their equivalence, Poincare duality, the homotopy groups. Dimensions. Bundle (Serre) spectral sequence (Mishchenko, "Vector bundles ..."). Calculation of the cohomology of classical Lie groups and projective space.
Vector bundles, connection, the Gauss-Bonnet formula, the Euler classes, Chern, Pontryagin, Stiefel-Whitney. Multiplicativity of the Chern character. Classifying spaces ("Characteristic Classes", Milnor and Stasheff).
Differential Geometry. Levi-Civita connection, curvature, algebraic and differential Bianchi identity. Killing Fields. Gaussian curvature of two-dimensional Riemannian manifold. Cell decomposition of the loop space in terms of geodesics. Morse theory on the loop space (the book Milnor's "Morse theory" and Arthur Besse "Einstein manifolds"). Principal bundles and connections in them.
Commutative algebra (Atiyah-MacDonald). Noetherian rings, Krull dimension, Lemma Nakayama adic completion, integrally closed, discrete valuation ring. Flat modules, local criterion plane.

[Anonymous No.6713284]

>>6713283
Beginning of algebraic geometry. (The first chapter of the Hartshorne or Shafarevich or green Mumford). Affine variety, projective variety, projective morphism, the image of a projective variety is projective (via resultants). Beams. Zariski topology. Algebraic variety as a ringed space. Hilbert's theorem on the zeros. Spectrum of the ring.
Beginning of homological algebra. Groups Ext, Tor for modules over a ring, resolvent, projective and injective modules (Atiyah-MacDonald). Construction of injective modules. Grothendieck duality (for a book Springer Lecture Notes in Math, Grothendieck Duality, numbers about 21 and 40).
Number theory; local and global fields, discriminant, norm, the ideal class group (blue book Cassels and Frohlich).
Reductive group of the root system, representations of semisimple groups, weight, Killing form. Groups generated by reflections, their classification. Lie algebra cohomology. Calculation of the cohomology in terms of invariant forms. Singular cohomology of a compact Lie group and its cohomology algebra. Invariants of the classical Lie groups. (Yellow Serre, the second half, Hermann Weyl, "Invariants of classical groups"). Design of special Lie groups. Hopf algebra. Quantum groups (definition).

[Anonymous No.6713287]

>>6713284
The third course
K-theory as a cohomology functor, Bott periodicity, the Clifford algebra. Spinors (book Atiyah, "K-theory" or Mishchenko "Vector bundles and their applications"). Spectra. Eilenberg-MacLane space. Infinite loop space (for a book Switzer or yellow book or Adams Adams "Lectures on generalized cohmology", 1972).
Differential operators, pseudodifferential operators, symbol, elliptic operators. Properties of the Laplace operator. Self-adjoint operators with discrete spectrum. Green's operator and applications to Hodge theory on Riemannian manifolds. Quantum mechanics. (Book R.Uellsa analysis or Mishchenko "Vector bundles and their applications").
The index formula (Atiyah-Bott-Patodi, Mishchenko), the Riemann-Roch theorem. Zeta function of the operator with discrete spectrum and its asymptotic behavior.
Homological algebra (Gelfand-Manin, all the heads of Prome latter). Cohomology of sheaves, derived categories, triangulated categories, derived functor, the spectral sequence of the bicomplex. The composition of triangulated functors and the corresponding spectral sequence. Verdier duality. The formalism of the six functors and perverse sheaves.
Scheme algebraic geometry, the scheme over the ring, projective spectra, the derivatives of, Serre duality, coherent beams, base change. Own and separated scheme valyuativny property and separability criterion (Hartshorne). Functors representability, the moduli space. Direct and inverse images of sheaves, higher direct images. With proper mapping higher direct images are coherent.

[Anonymous No.6713288]

>>6713287
Cohomological methods in algebraic geometry, semi-cohomology theorem of Zariski's connectedness theorem Stein's expansion.
Kahler manifolds, Lefschetz, Hodge theory, the ratio of Kodaira, the properties of the Laplace operator (zero head chapters of Griffiths-Harris, clearly stated in the book of André Weil "Kahler manifold"). Hermitian bundle. Line bundles and their curvature. Line bundles with positive curvature. Theorem of Kodaira-Nakano Vanishing (Griffiths-Harris).
Holonomy theorem of Ambrose-Singer, special holonomy holonomy classification, Calabi-Yau, hyperkähler, Calabi-Yau theorem.
Spinors on the manifold, the Dirac operator, the Ricci curvature, the formula Veytsenbeka-Lichnerowicz, Bochner's theorem. Bogomolov theorem on the decomposition of manifolds with zero canonical class (Arthur Besse, "Einstein manifolds").
Tate cohomology and class field theory (Cassels-Froehlich, blue book). Calculation of the factor of the Galois group of a number field by the commutator. Brauer group and its applications.
Ergodic theory. Ergodicity of billiards.
Complex curves, pseudo-conformal mappings, Teichmüller space, the theory of Ahlfors-Bers (from the book of Ahlfors thin).

[Anonymous No.6713293]

>>6713288
The fourth course.
Rational and profinite homotopy type of nerve cell étale covering space is homotopy equivalent to its profinite type. Topological definition of étale cohomology. Galois action on profinite homotopy type (Sullivan, "Geometric Topology").
Etale cohomology in algebraic geometry, the comparison functor, Hensel ring, geometric points. Base change. Any smooth variety over a field locally in the étale topology is isomorphic to $ A ^ n $. Étale fundamental group (Milne, a review of Daniel VINITI and SGA 4 1/2, the first article of Deligne).
Elliptic curves, j-invariant, automorphic forms, Taniyama-Weil and its applications to number theory (Fermat's theorem).
Rational homotopy (in the last chapter of the book Gelfand-Manin any article Griffiths-Morgan-Sullivan-length). Massey operations and rational homotopy type. The vanishing of Massey operations on a Kahler manifold.
Chevalley groups, their generators and relations (for a book Steinberg). Computation of K_2 from the field (Milnor, Algebraic K-theory).
Algebraic K-theory of Quillen, $ BGL ^ + $ and $ Q $ -construction (review Suslin in the 25th volume of VINITI, lectures Quillen - Lecture Notes in Math. 341).
Complex analytic manifolds, coherent sheaves, Oka's theorem on coherence, Hilbert's theorem on the zeros for ideals in the sheaf of holomorphic functions. Noetherian ring of germs of holomorphic functions, the Weierstrass theorem on division, Weierstrass preparation theorem. A theorem on the branched covering. The theorem of Grauert-Remmert (image of a compact analytic space under a holomorphic analytic morphism). Hartogs theorem on the continuation of an analytic function. Multidimensional Cauchy formula and its applications (uniform limit of holomorphic functions holomorphic).

[Anonymous No.6713295]

>>6713293
Fifth year
Kodaira-Spencer theory. Deformations of and solutions of the Maurer-Cartan. Solvability of the Maurer-Cartan and Massey operations on the DG-Lie algebra cohomology of vector fields. Moduli spaces and their finite (see. Lectures Kontsevich or Works Kodaira). Theorem Bogomolov-Tian-Todorov on deformations of Calabi-Yau manifolds.
Symplectic reduction. The moment map. Theorem of Kempf-Ness.
Deformation of coherent sheaves and bundles in algebraic geometry. Geometric invariant theory. The moduli space of bundles on a curve. Stability. Uhlenbeck compactification, Gieseker and Maruyama. Geometric invariant theory is the symplectic reduction (third edition of Mumford's geometric invariant theory, applications, Frances Kirwan).
Instantons in four-dimensional geometry. Donaldson theory. Donaldson invariants. Instantons on Kähler surfaces.
The geometry of complex surfaces. Classification Kodaira, Kahler and non-Kähler surface, the Hilbert scheme of points on the surface. Castelnuovo-Enriques criterion, the Riemann-Roch inequality Bogomolov-Miyaoka-Yau. The relations between the numerical invariants of the surface. Elliptic surface, the surface of Kummer K3 surfaces and Enriques.
Program elements Mori: Kawamata-Viehweg zero, the freedom theorem of base points, the theorem of Mori cone (Clemens-Kollar-Mori, "Multidimensional complex geometry", plus not translated Kollar-Mori and Kawamata-Matsuki-Massoud) .

[Anonymous No.6713296]

>>6713295
Stable bundles as instantons. Yang-Mills equation on a Kahler manifold. Theorem Donaldson-Uhlenbeck-Yau metrics Yang-Mills on a stable bundle. Its interpretation in terms of the symplectic reduction. Stable bundles and instantons on the hyper-manifolds; explicit solution of the Maurer-Cartan equations in terms of the Green's operator.
Pseudoholomorphic curves on a symplectic manifold. Gromov-Witten. Quantum cohomology. Mirror hypothesis and its interpretation. The structure of the group of symplectomorphisms (under the Kontsevich-Manin book Polterovich, "Symplectic geometry", the green book of pseudoholomorphic curves and notes of lectures McDuff and Salamon).
Complex spinors, Seiberg-Witten, Seiberg-Witten. Why the Seiberg-Witten invariants are Gromov-Witten.
Hyperkähler reduction. Flat bundles and Yang-Mills equation. Hyperkähler structure on the moduli space of flat bundles (Hitchin-Simpson).
Mixed Hodge structures. Mixed Hodge structure on the cohomology of algebraic varieties. Mixed Hodge structure on the fundamental group of Mal'tsev replenishment. Variations of mixed Hodge structures. Theorem on nilpotent orbit. Theorem on $ SL (2) $ - orbit. Close and vanishing cycles. The exact sequence of the Clemens-Schmid (the red book Griffiths "Transcendental methods in algebraic geometry").
Non-Abelian Hodge theory. Variation of Hodge structures as fixed points of $ C ^ * $ - action on the moduli space of Higgs bundles (dissertation Simpson).
Weil conjecture and proof. L-adic sheaves, perverse sheaves, the Frobenius automorphism, its weight, purity theorem (Beilinson, Bernstein, Deligne, plus Deligne, Weil conjecture II).

[Anonymous No.6713298]

>>6713296
Quantitative algebraic topology Gromov (by Gromov book "Metric structures for Riemannian and non-Riemannian spaces"). Gromov-Hausdorff metric, prekompaktnost plurality of metric spaces, hyperbolic manifolds and hyperbolic groups, harmonic maps into hyperbolic space, the proof of Mostow rigidity (two compact Kahler manifolds, covering the same symmetric space X of negative curvature, isometric if their fundamental groups isomorphic, and dim X> 1).
Of general type, Kobayashi and Bergman metrics, analytical stiffness (Sioux).

/curriculum

[Anonymous No.6713305]

>>6713277
>>6713280
>>6713283
>>6713284
>>6713287
>>6713288
>>6713293
>>6713295
>>6713296
>>6713298

>ctrl+f graph theory
>no results
It's shit.

[Anonymous No.6713314]

>>6713305
He excludes a lot of discrete math in general. Maybe he thinks it falls under algebraic topology or something.

[Anonymous No.6713333]

>>6713314
>discrete
http://en.wikipedia.org/wiki/Continuous_graph

[Anonymous No.6713341]

http://www.reddit.com/r/math/comments/10o6yo/what_do_you_think_of_this_guys_suggested/c6f7qyt?context=1

[Anonymous No.6713736]

>>6712898
you just called yourself stupid

[Anonymous No.6713777]

>>6712898
⇒The only meaningful math is that which can be applied to reality

That's why OP's masturbatory "muh string theory" curriculum is mostly useless. Please show me where you apply L-адические превратные пучки in reality. By your standards the curriculum should contain stochastic processes, financial mathematics, algorithmics, numerical anlysis etc. Unfortunately he forgot to include these and many other actually relevant topics.