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/sci/ - Science & Math


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File: 2.61 MB, 4125x2400, Mathematics Guide(3).png [View same] [iqdb] [saucenao] [google]
9884591 No.9884591 [Reply] [Original]

CHART THREAD NOW

POST MATH AND SCI CHARTS NOW OR YOU WILL LOSE 87 IQ POINTS

>> No.9884636

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.

>> No.9884639

>>9884636
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).

>> No.9884643

>>9884639
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).

>> No.9884648

>>9884643
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.

>> No.9884651

>>9884648
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).

>> No.9884655

>>9884651
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).

>> No.9884657

>>9884655
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.

>> No.9884660

>>9884657
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)

>> No.9884671

>>9884636
>>9884639
>>9884643
>>9884648
>>9884651
>>9884655
>>9884657
>>9884660
But this is not a chart.

>> No.9884688

>>9884671
>But this is not a chart.
Of course it is.

>> No.9884696

>>9884688
>no image with cool book covers
>no dumb anime girl
Not a chart.

>> No.9884759

>>9884660
This the most retarded list ever
also not even a chart

>> No.9885483

>>9884660
Specialist (6th year of college):
What is a chart

>> No.9885488

should I follow this unironically?

>> No.9885490

>>9884636
>>9884639
>>9884643
>>9884648
>>9884651
>>9884655
>>9884657
>>9884660
this^
>>9885488

>> No.9885532

>>9885488
checked, same fagging

>> No.9885540
File: 6 KB, 413x304, 3458668456+wegf.png [View same] [iqdb] [saucenao] [google]
9885540

>>9884591
I think I lost some when I made this.

>> No.9885554
File: 3.07 MB, 776x5164, A Guide.png [View same] [iqdb] [saucenao] [google]
9885554

the only serious guide, can switch stewart with apostol tho

>> No.9885564
File: 36 KB, 600x501, 6EB23E7F-313F-4418-BDEE-CF5B25BABF5F.jpg [View same] [iqdb] [saucenao] [google]
9885564

ok

>> No.9885586

>>9885540
This makes me so fucking furious, because it doesn't make any sense. Do you know how fucking graphs work?

>> No.9885588

>>9884657
>>9884660
This "chart" is only pandering to Geometards

>> No.9885608
File: 22 KB, 177x284, A633D9D7-1E89-4F97-8B1C-6AB8CB18D36D.jpg [View same] [iqdb] [saucenao] [google]
9885608

>>9884696
Is this better

>> No.9885911

>>9885608
>ant-hology

>> No.9885965

>>9885490
>>9885488
Yes.

>> No.9887011 [DELETED] 
File: 81 KB, 613x531, 9FCF84E7-B356-483D-82BC-C97CF576A3FC.jpg [View same] [iqdb] [saucenao] [google]
9887011

>> No.9887728
File: 123 KB, 785x757, 1514177756593.png [View same] [iqdb] [saucenao] [google]
9887728

>>9884636
>>9884639
>>9884643
>>9884648
>>9884651
>>9884655
>>9884657
>>9884660
Saged, reported, thread hidden, cops called
Get the fuck off my board

>> No.9888596

hi guys do anyone have chart for biology, physics or electronics please.

>> No.9888612

>>9885586
The y axis and the red post should be swapped

>> No.9888622
File: 52 KB, 538x592, 5-years to be a mathematician.png [View same] [iqdb] [saucenao] [google]
9888622

>> No.9888634
File: 205 KB, 1100x1320, Cribsheet 1 - Stem Cell.gif [View same] [iqdb] [saucenao] [google]
9888634

>> No.9888640
File: 238 KB, 919x1100, Cribsheet 3 - Avian flu.gif [View same] [iqdb] [saucenao] [google]
9888640

>> No.9888646
File: 884 KB, 1000x1213, Cribsheet 5 - Nuclear Power.jpg [View same] [iqdb] [saucenao] [google]
9888646

>> No.9888649
File: 215 KB, 1000x1213, Cribsheet 6 - Hurricanes.gif [View same] [iqdb] [saucenao] [google]
9888649

>> No.9888652
File: 344 KB, 1000x1169, Cribsheet 7 - Extinction.gif [View same] [iqdb] [saucenao] [google]
9888652

>> No.9888655
File: 403 KB, 1000x1213, Cribsheet 8 - The elements.gif [View same] [iqdb] [saucenao] [google]
9888655

>> No.9888658
File: 687 KB, 1003x1217, Cribsheet 9 - String Theory.gif [View same] [iqdb] [saucenao] [google]
9888658

>> No.9888662
File: 297 KB, 982x1187, Cribsheet 10 -Photosynthesis.gif [View same] [iqdb] [saucenao] [google]
9888662

I have a few more. Will post thm tomorrow if this thread is still alive.

>> No.9888840

Why are all these meme guides so focused on algebra. There's more to math than p-addic numbers.

>> No.9889349

>>9888612
What do you expect. He lost IQ points by not posting charts

>> No.9889402

>>9885564
Where's the menopause?

>> No.9889730
File: 343 KB, 1003x1217, Cribsheet 11 - Plate tectonics.gif [View same] [iqdb] [saucenao] [google]
9889730

>> No.9889733
File: 277 KB, 1003x1217, Cribsheet 12 - Genetics.gif [View same] [iqdb] [saucenao] [google]
9889733

>> No.9889744
File: 182 KB, 1003x1217, Cribsheet 13 - Light.gif [View same] [iqdb] [saucenao] [google]
9889744

>> No.9889745
File: 186 KB, 1003x1217, Cribsheet 14 - Exoplannets.gif [View same] [iqdb] [saucenao] [google]
9889745

>> No.9889747
File: 206 KB, 1003x1217, Cribsheet 15 - Quantum Computing.gif [View same] [iqdb] [saucenao] [google]
9889747

>> No.9889748
File: 726 KB, 1675x2037, Cribsheet 16 - Synthetic Biology.gif [View same] [iqdb] [saucenao] [google]
9889748

>> No.9889751
File: 307 KB, 1215x1485, Cribsheet 17 - Solar power.gif [View same] [iqdb] [saucenao] [google]
9889751

>> No.9889752
File: 237 KB, 1003x1217, Cribsheet 18 - Biofuels.gif [View same] [iqdb] [saucenao] [google]
9889752

>> No.9889755
File: 2.58 MB, 2423x3632, Electronic Radiation Spectrum.jpg [View same] [iqdb] [saucenao] [google]
9889755

>> No.9889758
File: 1.41 MB, 3000x2275, Fundamental particles and interactions.jpg [View same] [iqdb] [saucenao] [google]
9889758

>> No.9889762
File: 545 KB, 1900x2200, How DNA works.jpg [View same] [iqdb] [saucenao] [google]
9889762

>> No.9889847
File: 884 KB, 4000x3758, How to lucid dream.png [View same] [iqdb] [saucenao] [google]
9889847

>> No.9889860
File: 1018 KB, 1365x1242, Hydrogen Wave Functions.png [View same] [iqdb] [saucenao] [google]
9889860

>> No.9889861
File: 800 KB, 3045x2300, Maths mind mapp.jpg [View same] [iqdb] [saucenao] [google]
9889861

>> No.9889864
File: 542 KB, 1575x1145, Nuclear Science.jpg [View same] [iqdb] [saucenao] [google]
9889864

>> No.9889868
File: 229 KB, 1865x632, Stars life.jpg [View same] [iqdb] [saucenao] [google]
9889868

>> No.9889870
File: 752 KB, 4600x2400, Universal reference sheet Maths.png [View same] [iqdb] [saucenao] [google]
9889870

>> No.9890105 [DELETED] 
File: 99 KB, 380x349, 1528348037738.png [View same] [iqdb] [saucenao] [google]
9890105

>>9884636
>>9884639
>>9884643
>>9884648
>>9884651
>>9884655
>>9884657
>>9884660

*snap*

>> No.9890118
File: 3.52 MB, 4000x3500, 1529667456541.png [View same] [iqdb] [saucenao] [google]
9890118

>> No.9890136

>>9890118
hmm this is probably the best chart i've seen on sci

>> No.9890188
File: 1.31 MB, 1860x1291, szeregipotegowe.jpg [View same] [iqdb] [saucenao] [google]
9890188

>> No.9890220

>>9890118
Is there any point in read those general physics books instead of jumping straight to Taylor, for example?

>> No.9890234
File: 309 KB, 662x2647, Observable universe.png [View same] [iqdb] [saucenao] [google]
9890234

>> No.9890239
File: 691 KB, 1104x1168, Relationship between mathematical structures.jpg [View same] [iqdb] [saucenao] [google]
9890239

>> No.9890246
File: 40 KB, 465x369, 1518192798182.jpg [View same] [iqdb] [saucenao] [google]
9890246

>>9890188
>wzór ogólny bardzo skomplikowany

>> No.9890382
File: 46 KB, 1282x620, Science - Homeschool curriculum.png [View same] [iqdb] [saucenao] [google]
9890382

>> No.9890458
File: 2.52 MB, 5000x8000, 1512144649094[1].jpg [View same] [iqdb] [saucenao] [google]
9890458

>>9885608
>>9885911

>> No.9890520

>>9890220
there's literally 1 (one) book retard

also because it holds your hand

>> No.9890539
File: 314 KB, 1698x2198, IntegralSummary-1.png [View same] [iqdb] [saucenao] [google]
9890539

https://www.vertex42.com/Files/pdfs/2/IntegralSummary.pdf
I have this one printed

>> No.9890571
File: 209 KB, 1700x2200, TrigSummary-1.png [View same] [iqdb] [saucenao] [google]
9890571

>> No.9890704

>>9888840
More like D a dick numbers am I right

>> No.9890929

>>9890458
>spivak's calculus is a "fail safe," apostol's calculus is "intro analysis"

>> No.9891079
File: 85 KB, 1387x702, 1529181985402.jpg [View same] [iqdb] [saucenao] [google]
9891079

need more math related charts