Veeky Forums approved guides

Let's have dump all our best material!

Other urls found in this thread:

topology.org/tex/conc/differential_geometry_books.html
ocf.berkeley.edu/~abhishek/chicmath.htm
sgsa.berkeley.edu/current-students/recommended-books
ocf.berkeley.edu/~abhishek/chicphys.htm
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
ahilado.wordpress.com/book-list/
jmilne.org/math/
math.harvard.edu/~lurie/
math3ma.com/mathema/2016/8/22/resources-for-intro-level-graduate-courses
math.harvard.edu/quals/index.html
csd.cs.cmu.edu/content/sample-undergraduate-course-sequence
eecs.mit.edu/docs/ug/6-3.pdf
alpha.math.uga.edu/~pete/MATH2400F11.html
math.uga.edu/~pete/2400full.pdf
Veeky
amazon.com/Introduction-Linear-Algebra-Dover-Mathematics/dp/0486664341/
amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
amazon.com/Finite-Dimensional-Vector-Spaces-Second-Mathematics/dp/0486814866/
twitter.com/NSFWRedditImage

Got one from /g/ too

Does anyone have any guides for biology, chemistry or physics?

why would you take book recommendations from a hivemind comprised of underage roleplayers, autsitic neckbeards, ledditors, and other people who take book recommendations from the former three groups, rather than do your own research?

Because I'm bored

topology.org/tex/conc/differential_geometry_books.html

ocf.berkeley.edu/~abhishek/chicmath.htm

sgsa.berkeley.edu/current-students/recommended-books


ocf.berkeley.edu/~abhishek/chicphys.htm
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
ahilado.wordpress.com/book-list/
jmilne.org/math/
math.harvard.edu/~lurie/

math3ma.com/mathema/2016/8/22/resources-for-intro-level-graduate-courses

...

...

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

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

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

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

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

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

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

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

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

>its the highschool guy again

>No SICP
Shit-tier

>wasting time with highschool level surveys

What to read or do make the introduction of Apostol much easier to understand? Some of the theorems and exercises I can do but some of them I don't even know where to begin to prove.

Have you read a proofs book like Smith or Hammack?

help I'm stuck at 0

You improved it! Now it's perfect. Great job! This is the first math book list I approve. Save and repost everywhere.

Just the set theory part of Hammack.

>algebraic geometry

>Algebra by Lang
>Commutative algebra
and the only real algebraic geometry book and its
>Algebraic geometry by Shartstorm
neck yourself

how did you write this then user?

what do you think of Principles of Mathematics by allendoerfer and oakley as a replacement for basic mathematics by serge lang?

The only books you need to read

Middle class LARPING pseudointellectual loser, the list.

>t. Bluepill

Is this new age bullshit?

I'm reading The One Year Manual right now, a guy in /occult/ at 8ch recommended it for newbies.

Not really, perhaps with the internet it had a revival but most of the teachings from these books (at least the nonpolitical ones) come from long time ago.

>Middle class LARPING pseudointellectual loser
Internet in nutshell

Yes it is.
Those teachings come from the 19th/20th century occult fad which was the root of New Age, i.e. they are new age bullshit.

No, you can't classify all those books as new age bullshit. Many of those books discuss Gnosticism, Hermiticism, Neoplatonism and other Western Esoteric traditions. I can maybe see how R. A. Willson, A. Crowley, etc might be considered
>19th/20th century occult fad
But books like the Nag Hammadi Library and Three Books On Occult Philosophy are old books from antiquity. Also I wouldn't consider every book written in 19th 20th century about the subject "new age". The Western esoteric tradition is pretty interesting desu.

It certainly isn't Veeky Forums in any way though.

>that last one

That's outdated.

math.harvard.edu/quals/index.html

...

What's with the fucking anime people

It's leddit barriers.
You have to go back.

What's "leddit"? What does that sentence mean? Why do you people always try so hard to be special. If feel excluded by the most retarded shit on this website

...

Anime is turbo normie trash. All normies watch anime, you stupid retard.

>he doesn't read anime

>why would you take book recommendations from a hivemind comprised of underage roleplayers, autsitic neckbeards, ledditors, and other people who take book recommendations from the former three groups, rather than do your own research?
what's wrong with that? it works so well with politics after all amirite?

>analysis is the study of rigorous calculus

As long as it has IceCat and ungoogled-Chromium, it doesn't matter

August 2017 isn't "outdated" anyway---Firefox Quantum is even more botnet than before, so why bother noting it

>galois theory
>high school

what the fuck

u muss be woss, fwen
wet me kaw u an oobah bak 2 fasebuk

Thanks buddy

...

anything about science/physics?

This is too basic. You should move the high school recommendations to middle school and your college recommendations to high school. There is also NO reason you shouldn’t start Artin level algebra at 6th grade. This is why our math education is utter trash, people like you thinking you have to wait until high school to get to cohomoly and k-theory. DESU you should be comfortable with k theory end of middle school year.

The best and only guide is to find a university you like, and go through their program path recommendation, and then look up each class' syllabus and lecture schedules where often you'll find all you need. These are put together by actual educators and not a meme.

Here's one csd.cs.cmu.edu/content/sample-undergraduate-course-sequence
Here's another eecs.mit.edu/docs/ug/6-3.pdf

I seriously hope nobody uses these guides. There's no need to spend so much time on completely trivial foundations. Most introductory books on algebra or analysis have a section that quickly reviews basic set theory and definitions. Going through 8 books on foundations just to study calculus is complete overkill. Do some algebra, analysis, topology, number theory, or literally anything but this, and you will figure out how to write a proof way quicker than any of these will teach you.

leddit loves anime, normies love anime.

thanks i wanted to read spivak this summer after already completing stewart (physics major) and that chart gave me a panic attack

Any good analysis books to use?

The list is obviously not serious since it lists Landau. Personally I would never recommend any of those books to students. They would definitely die from boredom.
In order of difficulty. Rosenlicht. Tao. Pugh. Rudin. Note that I haven't really read Pugh but it looked good and is recommended highly by others. Once you finish one, if you want to learn more analysis Royden, Folland, and Rudin are good choices. Though I think the later editions of Royden contain many more typos and incorrect proofs.

I can't say anything about books I haven't read, and what I've done might not be optimal, so do what recommends and see what actual professors recommend.

If you've never seen an [math]\epsilon/\delta[/math] proof, an easy introduction is Ross's Elementary Analysis. It is essentially just proofs of basic facts from single-variable calculus, with the occasional aside about more general metric spaces.

The classic introductory text for a more advanced reader is Rudin's Principals of Mathematical Analysis.

What's a good book that goes in depth with the properties of real functions? Stuff like composition, parity, monotony, periodicity, bounds, injections/sujerctions.

Every calculus/analysis book I've tried defines the concept of a function, goes to continuity, then limits and immediately skips to derivatives/integrals.

a good book on relation theory would be appreciated as well

I think Pugh is more difficult due to its sheer number of exercises, it's more than triple than Rudin's.

>being this new

There's no pre-reqs for Spivak, but it's helpful to have Polya or somebody else's 'Problem Solving' proof book lying around while you read it if you get stuck on exercises. Spivak is self-contained.

You may also be interested in this, a course which uses Spivak as the textbook with really good course notes alpha.math.uga.edu/~pete/MATH2400F11.html specifically the notes here math.uga.edu/~pete/2400full.pdf

Advanced Calculus by Sternberg/Loomis covers all that though not in depth like an Analysis book would. Try Tao's Analysis books they're famous for not leaving out any details and he has an entire chapter on functions.

>lynx worse than chrome
I beg to disagree

Anyone have any recommendations for cryptography intro?

Veeky Forums-science.wikia.com/wiki/Computer_Science_and_Engineering#Computer_Security_and_Cryptography

>Mozilla has been compromised and can't be trusted
/g/'s conspiracy theories are the reasons their guides should not be posted in this thread.

Where is Metanoia?

How to learn Veeky Forums english? Specifically math/physics related. I have a hard time reading english textbooks (spanish is my mother tongue), and I really want to get into books like Jackson or Rudin (which aren't translated)

Just read more books and you'll get the hang of it. Also, Rudin is translated.
Babt: 9686046828, papa: 8420506516 and grandpa: 842915115X

>What's with the fucking anime people

You're not aware "Veeky Forums" is full of people who are weebs on the down low?

Doable.

Where do I start if I want to master college algebra?

I want to refresh myself with functions, graphing, set notation, etc and then lead into the calculus ie Spivak/Stewart

Lang's Basic Mathematics

>No "On Lisp"

Axler's Precalculus is the best, because it includes fully worked out answers for some questions so you can see exactly how he solved it. However you can just start any calculus book. Whatever you don't remember look it up directly in Axler or just Youtube search for a 30second lesson. As you go through the book's exercises, you will solidify you knowledge of precalc over many exercises. Stewart's "Early Transcendentals" book is good for this with it's hundreds of applied exercises, or Apostol's Calculus which is totally comprehensive and covers absolutely everything. So many exercises in Apostol's book you'll have mastered trig identities and basic algebra manipulation half way through.

Trying to get into college maths, I can't get into linear algebra. Abstract algebra, calculus, number theory, geometry, they all seem pretty easy to handle for me, but linear algebra seems like a weird place with their own language and stuff. I'm ok with matrices and the operations, but vector spaces and basis look really weird to me. Typically, if I were to divide a common linear algebra course, I can handle the first third, but the rest two thirds are chinese to me.

what would be a good introductory book? is lang a meme?

amazon.com/Introduction-Linear-Algebra-Dover-Mathematics/dp/0486664341/
amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
amazon.com/Finite-Dimensional-Vector-Spaces-Second-Mathematics/dp/0486814866/

Well this thread has brought me to the conclusion that I will always suck at math and be retarded

Thanks user

>try to look smartest
>muhh high school education
>DESU
what a brainlet

>going to high school
>not being whisked away when they saw your test scores
>not studying advanced topics in a mountain redoubt
>not bonding over calculus with other ultra-gifted children
>not coming to terms over time with your rapidly developing psionic abilities
>not being called upon at last to defend the earth from an extraterrestrial menace
Who keeps letting these brainlets onto Veeky Forums?

I made the guide. I knew some people would have issues with the heavy focus on foundations. That's why I put "foundational" in the sub-title. Apparently it didn't help. There's a reason the guide starts with a book on logic and not algebra.

>SICP
>good
how autistic do you have to be to not prefer the clearly superior "How to Design Programs"

just like your waifu.

Veeky Forums was first and foremost an anime website.

>on an anime image board
>complains about anime characters

Literally book or proof or how to solve it, maybe elements of set theory and you’re ready to read Spivak/Apostol. Why so many foundational books?

thanks user

Not OP. But he clearly said it's a foundational [math]\text{approach}[/math] in mathematics. He never said the entire list is made so that you can grasp Spivak. Spivak/Apostol are part of the approach. If you wanted to just go for Spivak and have no foundational or atleast less foundational approach then yes, lots of those books can be skipped. But clearly this is an optional list for people who want to have great foundations, not for people who just want to Do calculus after they finish their algebra course, there are lots of other list for non-fondations.

>anime
>not hentai

Why does this have people reading stuff on set theory and foundations of analysis before they even start doing basic arithmetic and algebra problems?

They are drunk on the wine of formalism and have spurned the milk of geometric motivation.

Is there any for artifical intelligence/machine learning?

only decent list ITT desu

bump
Also, can we make this a general?