/sci/ - Science & Math

[Anonymous No.9847214]

How do I get gud at math

[Anonymous No.9847218]

Stop posting here and read a book
>http://www2.math.umd.edu/~jcohen/402/Pinter%20Algebra.pdf
>http://148.206.53.84/tesiuami/S_pdfs/Linear%20Algebra%20Done%20Right.pdf
>file:///C:/Users/Manitan/Desktop/epdf.tips_calculus-a-complete-course-plus-mymathlab-global-2.pdf
>http://mttk.no/AdamsCalculusACompleteCourse8thEditionc2014solutionsISM.pdf

[Anonymous No.9847221]

[Anonymous No.9847261]

>>9847214

All of this >>9847221 is outdated—see exclusively https://www.youtube.com/channel/UCXl0Zbk8_rvjyLwAR-Xh9pQ

[Anonymous No.9847267]

>>9847221
What a shitty guide. You don't learn any deep mathematics by completing it. I would say you only need to read like a half or a quarter of those books and instead read about the mathematics that really interests you.

[Anonymous No.9847315]

>>9847214
>How do I get gud at math
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.9847320]

>>9847315
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.9847323]

>>9847320
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.9847326]

>>9847323
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.9847331]

>>9847326
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.9847335]

>>9847331
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.9847337]

>>9847335
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.9847340]

>>9847337
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.9847366]

>>9847315
Who are you and why do you always post this same shit?

[Anonymous No.9847373]

>>9847366
>Who are you and why do you always post this same shit?
What do you want to know about me? And I usually post other things.

[Anonymous No.9847405]

>>9847373
>>>9847366
>>Who are you and why do you always post this same shit?
>What do you want to know about me? And I usually post other things.
you,ve posted this multiple times now. no one would ever go this far to git gud at math

[Anonymous No.9847415]

>>9847405
NTAYRT but yes plenty of people do

it's not objective-oriented about getting good, but more a thread to follow or inquisitively curious people
it's a very good list of suggestions and it's not as difficult as it seems if you're the type of person who finds reprieve in mathematics

[Anonymous No.9847417]

>>9847315
>>9847320
>>9847323
>>9847326
>>9847331
>>9847335
>>9847337
>>9847340
do I have to direct you to the right board again?
>>>/hm/
stay there

[Anonymous No.9847421]

>>9847417
>do I have to direct you to the right board again?
No, I only use this board.

[Anonymous No.9847425]

>>9847405
>you,ve posted this multiple times now.
Anons have asked questions for which this list is a suitable answer multiple times now.

> no one would ever go this far to git gud at math
What do you mean?

[Anonymous No.9847446]

>>9847425
>>>9847405 (You)
>>you,ve posted this multiple times now.
>Anons have asked questions for which this list is a suitable answer multiple times now.
>> no one would ever go this far to git gud at math
>What do you mean?
What I mean is yes this list has fundamental value but realistically no one on the board would ever go throw with it to the degree brought up

[Anonymous No.9847456]

>>9847446
>realistically no one on the board would ever go throw with it to the degree brought up
Speak for yourself.

[Anonymous No.9847467]

>>9847456
What do you mean

[Anonymous No.9847470]

>>9847467
>What do you mean
Instead of what you wrote, write "realistically I would never go throw with it to the degree brought up".

[Anonymous No.9847477]

>>9847470
>>>9847467 (You)
>>What do you mean
>Instead of what you wrote, write "realistically I would never go throw with it to the degree brought up".
Thanks for the suggestion

[Anonymous No.9847479]

>>9847315
"I really really want to feel special and smart, please look at this list of topics"

op the answer is to read a lot of books and be really strong willed about not letting frustration stop you. Getting started is hard because you don't know what books to get but there are a lot of fundamentals books and they're mostly good. Mine was "A concise introduction to pure mathematics."A lot of people (me included) would tell you to learn some analysis and abstract algebra. I think they're both more ways of thinking about problems than subjects. But once you've cleared a fundamentals book you might have some idea of what you're interested in and if not, just ask again.

[Anonymous No.9847494]

>>9847479
>"I really really want to feel special and smart, please look at this list of topics"
Who are you quoting?

[Anonymous No.9847511]

>>9847494
It's a quote of me at my house just now making fun of whoever posted this autistic manifesto

Did they think it would be helpful to op? Only a fucking idiot would think that so either they are a fucking idiot or they're only posting it because it's in a completely scrambled fuckwad order and they want to feel like a smart little boy

Oh yeah I'm sure homotopy and p-adic numbers were just standard stuff at this ass blaster's high school. This is the most useless, piece of shit list, and I can't believe somebody would bother making it, posting it, and then having posted it continue to not realize how dumb they looked and continue to post it

[Anonymous No.9847566]

>>9847511
>Did they think it would be helpful to op?
Yes.

>Oh yeah I'm sure homotopy and p-adic numbers were just standard stuff at this ass blaster's high school.
Which high school for brainlets do you go to?

[Anonymous No.9847573]

>>9847566
"Hey I think I might like to learn medicine where should I start" "Here is a list of every bone in the human body, you're welcome"

Please, reveal to us mere mortals your high and mighty school o wise one so that we may be in awe

[Anonymous No.9847590]

>>9847573
>"Hey I think I might like to learn medicine where should I start" "Here is a list of every bone in the human body, you're welcome"
Who are you quoting?

[Anonymous No.9847596]

>>9847511
>Oh yeah I'm sure homotopy and p-adic numbers were just standard stuff at this ass blaster's high school.
Well, I mean, not him, but it is in Russian high-schools.

Soviet era ones at least. I know this from memoirs of Russian mathematicians.

[Anonymous No.9847603]

>>9847315
>>9847320
>>9847323
>>9847326
>>9847331
>>9847335
>>9847337
>>9847340
This is actually a pretty good list. It skips over a lot of fields that are now redundant or generalized by modern fields. The only minor complaint I have is that specialist lists assume that you want to do research in AG or MP and neglects other frontiers.

I don't know why people are giving you so much shit.

[Anonymous No.9847604]

Dieudonné's 5 year 'How to be a Mathematician, not a mathematician' plan (published as "A Letter from
Dieudonne")

>1st year (Elementary algebraic geometry)
Borel and Bass - Linear algebraic groups (first part)
Cartan-Chevalley Seminar 1955
Chevalley Seminar 1956 'Classification des groups algébriques'
Mumford - Introduction to algebraic geometry (chapter 1)
Semple and Roth's - Algebraic geometry
Serre - Faisceaux algébriques cohérents (cohomology parts)
Serre - Géométrie Algébrique et Géométrie Analytique
van der Waerden - Algebraische Geometrie

>2nd year
Borel and Bass - Linear algebraic groups (the rest)
Borel-Tits - Groupes réductifs
Serre - Groupes algébriques et corps de classes

>3rd year
Borel-Harishchandra - Arithmetic subgroups of algebraic groups
Borel - Introduction aux groupes arithmétiques
Weil - Adeles and algebraic groups
Seminaire Borel-Serre - Complex multiplication notes

>4th year
Mumford - Introduction to algebraic geometry (chapters 2-3)
Read Elements de géométrie algébrique until Mumford's 'Abelian varieties' makes sense
Mumford - Geometric invariant theory
Serre - Algèbre locale
Samuel Ergebnisse - Méthodes d'algèbre abstraite en géométrie algébrique

>5th year
Abelian varieties over finite fields, formal groups
Automorphic funtions, modular functions
Jacquet-Langlands theory
Algebraic geometry of surfaces
Advances theory of schemes (Grothendieck topologies, étale cohomology...)

[Anonymous No.9847606]

>>9847603
>he only minor complaint I have is that specialist lists assume that you want to do research in AG or MP and neglects other frontiers.
The only other frontier worth considering is the Langlands program.

[Anonymous No.9847608]

>>9847604
>This shit again

Not everyone wants to be a fucking geometer.

[Anonymous No.9847613]

>>9847606
I meant AT*.

Langlands programme I consider to be mostly in the interest of MP (mathematical physics).

Since when is pure number theory, pure group theory, combinatronics, analysis, chaos theory etc. not considered worth pursuing anymore?

[Anonymous No.9847615]

>>9847613
>Langlands programme I consider to be mostly in the interest of MP (mathematical physics).
I meant arithmetic Langlands, not geometric Langlands

[Anonymous No.9847620]

>>9847615
Ah.

Alright, well that's all your opinion. But there are many fields other than AT and AG frontiers that are worthy of study. If they weren't they wouldn't be funded, which they are.

I find it funny that they are more popular because they are often applied in MT, but people who work in it are the most insistent that their work is about "pure mathematics".

[Anonymous No.9847622]

>>9847620
>using funding as a criterion for whether something is worthy of study

[Anonymous No.9847625]

>>9847620
>MT
was this a typo for MP?

[Anonymous No.9847632]

>>9847622
Well what alternative criteria would you suggest? Impact factors and h-indexes? Because the most worthy fields of mathematical study are review articles of graphics processing techniques.

>>9847625
Yes, sorry.

[Anonymous No.9847636]

>>9847632
>Well what alternative criteria would you suggest?
Inherent value to mathematics

[Anonymous No.9847644]

>>9847636
By "mathematics" do you mean "all of mathematics" or "my field of mathematics"?

Follow up question. Do you consider geometry to have more inherent value than foundational fields (set, cat, number)?

[Anonymous No.9847670]

>>9847644
>By "mathematics" do you mean "all of mathematics" or "my field of mathematics"?
The former

>Do you consider geometry to have more inherent value than foundational fields (set, cat, number)?
Geometry is a foundational field: set and category theories yes, number theory no.

[Anonymous No.9847673]

>>9847670
>Geometry is a foundational field:
Since when?
>set and category theories yes,
Okay, so you consider set and category to be "worthy of study"
>number theory no.
Fair, though I would argue that the main reason you consider category theory to be fundamental and number theory not is because you see the applications in geometry.

[Anonymous No.9847679]

>>9847673
>Since when?
Thousands of years ago

>Okay, so you consider set and category to be "worthy of study"
>Fair, though I would argue that the main reason you consider category theory to be fundamental and number theory not is because you see the applications in geometry.
I meant that I consider geometry to have more inherent value than set and category theories, but not more than number theory. I do consider number theory to be fundamental. I do not consider set theory to be worthy of study.

[Anonymous No.9847682]

>>9847679
Alright, we're done here.

Fucking hell geometers are next level elitist cunts.

[Anonymous No.9847683]

>>9847682
>Fucking hell geometers are next level elitist cunts.
I'm not a geometer

[Anonymous No.9847685]

>>9847679
>I do not consider set theory to be worthy of study.
To be more precise, I think set theory was at one point worthy of study, but that worth has been exhausted.

[Anonymous No.9847690]

>>9847683
What is your field of research then if I may ask?

>>9847685
I admit that truly breakthrough papers have been sparse in the last few decades. But that doesn't mean we've thoroughly exhausted the digsite.

[Anonymous No.9847695]

>>9847690
>What is your field of research then if I may ask?
Cryptography

[Anonymous No.9847802]

>>9847695
Crypt-...

FUCKING CRYPTOGRAPHY?

I feel disgusted for even posting in the same thread as you.

[Anonymous No.9847804]

>>9847802
>FUCKING CRYPTOGRAPHY?
Do you need to swear?

[Anonymous No.9848390]

>>9847214
just b urself lmao

[Anonymous No.9848509]

>>9847802

I'm a newbie here, what's not okay with cryptography?

[Anonymous No.9848525]

>>9848509
think about it, the only problem is there is a key which if not given you only can guess between millions of combinations. What's so interesting about it to do reasearch?

[Anonymous No.9848533]

>>9847218
I want to learn math not reading

[Anonymous No.9848543]

>>9848525
Man's attitude goes some ways, the way his life will be.

[Anonymous No.9848555]

>>9848525
Think about it, geometry is just about drawing shapes with a straightedge and compass, what's so interesting about that? You can do the same thing to any subject.

[Anonymous No.9848570]

>>9848555
This.
I tend to think that any problem is good enough if you can't come up with it's solution the moment you hear it

[Anonymous No.9848573]

>>9848555
>found the cryptograph
You can draw laws from geometry.
Cryptography isn't an actual research field.
>you don't have a key
you're fucked there's too much combinations to go trough all of them
>same as above but encryption is shit
brute force until something matches
Prove me wrong, seriously. Not trying to be an ass, I'm just so brainlet I don't get what's there to investigate in cryptography, for me is just engineering. Explain if not.

[Anonymous No.9848613]

>>9848525
Isn't that cryptoanalysis, not cryptography? There's a big difference

[Anonymous No.9848619]

>>9848573
>>Actually hate cryptography

Thinking cryptography is trying to decrypt encrypted messages is like thinking a number theorist just does arithmetic. I assume you would be researching new encryption techniques, trying to break existing ones, etc., but it's not my field so idk the details.

[Anonymous No.9848639]

>>9847315
This list would be a lot better if it was condensed

"Linear algebra ... basis ... rank ... determinants ... Schwarz inequality" Just "Linear algebra" would do imo. Also "scalar multiplication"? You mean like normal ass multiplication?

[Anonymous No.9848656]

>>9848525

[Anonymous No.9848997]

>>9847456
you speak so much like an idiot who can't stop bragging about an iq score.

[Anonymous No.9849010]

>>9848997
>you speak so much like an idiot who can't stop bragging about an iq score.
I've only told a handful of people about my IQ, and I was surprised at how high it was

[Anonymous No.9849012]

>>9848525
anon i think you don't understand what cryptography is
you're thinking the most singular applied use case
it'd be better to think about it like dynamic systems interfacing as a subset of information theory and the expression/transduction of signals between dynamic systems

it's got nothing to do with developing SHA256 algorithms
static systems are trivial

[Anonymous No.9849017]

>>9847315
>>9847320
>>9847323
>>9847326
>>9847331
>>9847335
>>9847337
>>9847340
How much would all these textbooks cost?

[Anonymous No.9849019]

>>9849017
.pdf, anon

[Anonymous No.9849020]

>>9849017
a few bucks to print off copies you download from libgen

[Anonymous No.9849535]

>>9848509
It's literally applied number theory, something that that Anon dismissed earlier in the thread.

[Anonymous No.9850962]

>>9847479
>A concise introduction to pure mathematics
Thanks, anon. This book is precisely what I needed right now. There's other books that cover the same material but this is more concise. I've only looked through the first chapter on sets but it gets to the point faster, sure it isn't as in depth or formal or whatever, but this seems an ideal text for my current requirements (being introduced to the basics of notation and concepts underlying pure mathematics). Seems a great starting point before delving deeper.

[Anonymous No.9852534]

ain't nuthin' to it but to do it