Other:
>[S]cience
>[T]echnology
>[E]ngineering
>[M]athematics
Guides are welcome.
>I do not own the rights to the intellectual property of the posted guide, whoever made it, thank you.
Veeky Forumsence & Mathematics Guides:
Jordan Hernandez
Eli Johnson
...
Jaxson Wood
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.
Christopher Reyes
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).
Julian Reyes
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).
Nicholas Hill
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.
Joshua Collins
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).
Liam Roberts
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).
Gavin Myers
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.
Jordan Lee
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)
Juan Morris
Perfect, this is one of the pastas I was hoping for.
Alexander Wright
I'd say among the best I've seen yet. However, where's the functional analysis? It's basically modern day analysis.. (Harmonic analysis, Operator Theory / algebras, PDE's). What about representation theory?
William Cook
mathematician here
these images aren't very good, in general these sorts of "guides" are trash. most of them look like either "these are the books my courses used in undergrad" or "these are the top results for a google search in field X" - not that that invalidates any good advice that might be present in them, but just something to keep in mind. more important than deciding which textbook to read is actually reading a textbook.
if you manage to do this, please let me plead on behalf of the rest of humanity for you to not completely destroy the world.
Joshua Sullivan
>this pasta keeps getting posted
>still no image of it with anime girls
how are you supposed to study like this?
Andrew Flores
>how are you supposed to study like this?
Making an infographic with your own harem of waifus on it is the "middle school" step of the program (left as an exercise for the reader)
Easton Anderson
>If you manage to do this, please let me plead on behalf of the rest of humanity for you to not completely destroy the world.
I have Asperger's, I'll be fine.
Leo Hughes
...
Jack Johnson
I'm not a fan of Stewart over Spivak in Calculus, and Dummit & Foote over Artin or Herstein.
Other than that, I like this list.
You can edit it and add functional analysis if you'd like.
Henry Martin
A wonderful infographic, indeed, this should be taught as mandatory.
Alexander Wilson
several of my coworkers are pretty well along on the spectrum, and even they aren't nearly capable of that
Luke Murphy
Well, I live off of a trust fund and have eight hours a day to study.
Christian Foster
Going to start a math major next year, I already bought Spivak, and I can buy another book, what could be another essential book for the rest of courses? (say, Algebra)
(yeah I know about libgen but still)
Are you supposed to learn abstract algebra in high school in the first world? Fuck.
this
Ryan Edwards
This list is a troll, my friend.
Isaac Cox
Por those who seriously want to learn mathematics (in russian tho)
Brody Watson
That user here. I fall for the meme. I'll buy Logic: The Laws of Truth and Enderton's Set Theory. I'll save money for Herstein's Abstract Algebra and Meserve's Fundamental Concepts of Algebra next.
Jason James
...
Anthony Diaz
I made the list
As you can see, the last section is pretty rushed - i didnt care much for it. I made the list not to be entirely encyclopedic, plus I haven't done much analysis, I am doing a PhD in algebraic geometry so I veered more in that direction.
The purpose of the list is not for the experts, but for the beginners, and to see what to strive for. Mostly because every week there's at least 3-4 threads asking for the same thing "where to start?", and I thought I'd make it because the meme lists that recommend reading 10 books before calculus are a joke.
Jaxon Martinez
>This list is a troll, my friend.
What do you mean?
Ethan Powell
When I tried Spivak for the first time I had to drop it - I had no experience with proofs and I couldn't do most of the first exercises. Maybe it was because I am a brainlet, but I feel it's mostly because I had no exposure to the sort of thinking that goes into proving theorems in analysis. Further, to a layman beginning the journey, starting with a weakly motivated and rigorous text is going to push him away. That is the reason why I put Stewart - because it motivates the student by giving simple visual explanations as to why things work, and even if you have to take certain things as a given, developing the intuition at this stage is key.
I paraphrase what I read from some user: "if Newton had come up with Riemannian geometry, nobody would have listened to him and would have taken him as a hack".
Bentley Myers
...
Thomas Morris
>Are you supposed to learn abstract algebra in high school in the first world? Fuck.
There are several abstract algebra books geared towards high schoolers, i.e. pic related
Andrew Johnson
Anyone have the image that has all of the biochemical synthesis pathways? I think I remember it being from Sigma Aldritch.
Sebastian Long
Wait, so the best way to learn mathematics is to learn Russian first?
Jordan Reyes
Very nice, thank you.
Elijah Ward
Can you guys help me get some really good books on
>Probabilities/Statistics (I only know about Meyer's)
>Graph theory/algorithms/game theory idk
>Multivariable calculus
>developing the intuition
That's why logic, set theory and proof-related books are for, aren't they?.
Caleb Jackson
Precisely and is also why people should learn:
Ryder Nguyen
>>Multivariable calculus
Veeky Forums-science.wikia.com/wiki/Mathematics#Multivariable_and_Vector_Calculus
>>Probabilities/Statistics (I only know about Meyer's)
Veeky Forums-science.wikia.com/wiki/Mathematics#Probability_.28Multivariable_Calculus_based.29
Veeky Forums-science.wikia.com/wiki/Universal_Material#Statistics
>>Graph theory/algorithms/game theory idk
Veeky Forums-science.wikia.com/wiki/Mathematics#Combinatorics_and_Graph_Theory
Veeky Forums-science.wikia.com/wiki/Computer_Science_and_Engineering#Algorithms
Veeky Forums-science.wikia.com/wiki/Computer_Science_and_Engineering#Advanced_Algorithms_and_Mathematical_Optimization
Veeky Forums-science.wikia.com/wiki/Economics_Textbook_Recommendations#Game_Theory
Veeky Forums-science.wikia.com/wiki/Computer_Science_and_Engineering#Combinatorial_Game_Theory
Hudson Wood
>no meme list for physics
>Veeky Forums recommend hard textbooks without answers
suffering
I hate to be a brainlet
Daniel Hughes
You sure are helpful, user.
Juan Johnson
>autistically reading book by book
Fuck that, get a problem, try to solve it and learn as you go. Its the most effective way to learning anything.
The brain is made to be a problem solver, shoving it information that haves no inmediate purpose makes it discard it quickly.
Joseph Mitchell
It is best to have a rigid system in place, actually.
Mason Taylor
>le trivium meme because people did it hundreds of years ago
most of these books are terrible/superfluous, and phrasing it in as a trivium is unnecessary and limiting.
Hunter Carter
Reading it right now, it's so amazing how easy it is to read, like, it's not that the topic is easy but it keeps you entertained, I spend hours without noticing it.
Charles Martin
>most of these books are terrible/superfluous
>Even though I haven't read them.
Julian Williams
Both are great books, not a meme but you need to be interested in math from a foundational approach, have fun
Matthew Martinez
Young and Freedman - University Physics with Modern Physics
⇓
Taylor - Classical Mechanics
Griffiths - Introduction to Electrodynamics
Townsend - A Modern Approach to Quantum Mechanics
Reif - Fundamentals of Statistical and Thermal Physics
⇓
Fowles - Introduction to Modern Optic
Schutz - A First Course in General Relativity
Simon - The Oxford Solid State Basics
Griffiths - Introduction to Elementary Particles
⇓
Goldstein - Classical Mechanics
Jackson - Classical Electrodynamics
Pathria and Beale - Statistical Mechanics
Schwabl - "Quantum Mechanics" and "Advanced Quantum Mechanics"
⇓
Wald - General Relativity
Feynman, Hibbs, and Styer - Quantum Mechanics and Path Integrals
Schulman - Techniques and Applications of Path Integration
Schwinger - Selected Papers on Quantum Electrodynamics
⇓
Peskin & Schroeder - An Introduction to Quantum Field Theory
Schwartz - Quantum Field Theory and the Standard Model
⇓
Nathan Thomas
>Herstein's Abstract Algebra
No, get Herstein's "Topics in Algebra". Herstein's "Abstract Algebra" is just Topics with stuff deleted to fit a single semester course.
Jeremiah Davis
Nice, thank you.
Elijah Cooper
wrong board, fuck off
Brayden Bennett
The wikia is a thing
Veeky Forums-science.wikia.com/wiki/Physics_Textbook_Recommendations
Jaxon Watson
>Learning formalized logic is bad.
Oh, so you hate math too?
Bentley Scott
Sorry, but Topics in Algebra hasn't a spanish translation, and abstract algebra is pretty dense to me and I'm a native spanish speaker. Sometimes I try Dummit & Foote anyways. But I'll reconsider it anyways.
Yeah, I'm really interested in the foundations of math. I hope to take foundations courses later on the major. I'm trying to "build" my path into math by learning through the most rigorous and proof-heavy material out there. If there's any concept I don't understand, there's plenty of youtube channels out there for me to check, so I can get back to the rough material.
I got really bored of the 'applications'-type math books.
Cooper Brown
>pop phil nonsense and "how to write lmao" is formalized logic
fuck off
Adam Morgan
There's a whole section on FORMALIZED LOGIC, you fucking retard.
There's also a nice book on a mathematical mindset, which isn't half-bad.
But of course, you're just trying to desperately hard to fit in with Veeky Forums 'purism'.
You sad pusillanimous puerile punk.
Matthew Wood
>I-I can justify one of my books!
then stop posting that shit and literally just post that one???
idiot
Leo Hall
You can't count, that's 3.
Christopher Miller
you expect anyone here to take a book on "mathematical mindset" or "creative and critical thinking" seriously? you're wrong.
copi's book is shit too, despite the title.
Connor Sanchez
What books on pure logic would you suggest then? And mathematics ISN'T pure logic, it is a subset of logic.
Jaxson Parker
>mathematics [...] is a subset of logic
you're such a fucking retard it's hard to reply to you at all
Enderton is a serious author, so his book "A Mathematical Introduction to Logic" should do
Cooper Anderson
Mathematics is the system that we use to describe logic, you fucking retard.
Nicholas Bell
>says the humanities freshman, proudly, to the math grad
sure showed me
Oliver Wilson
Its really worth it, my first semester of college was pretty bad because I kept coming back to logic/set theory and a lot of people would give me shit for it, but when you really understand something, like, being able to explain it all the way through it feels so nice, and it was worth it, now I learn a lot faster so definitely keep it.
Also I'm sorry but Spanish books are sometimes not enough, (también es mi Idioma natal) but your English seems fine, you may need to check the meaning of some words but this way you will improve both your Math and English skills, use youtube videos as a review but stick to the book, you have the right ideas already so just keep going, you got this :)
Daniel Parker
>The symbols we draw are actually a pre-defined part of the universe.
How can a supposed "grad" be so fucking dense?
Josiah Ward
you have a very limited exposure to either topic, and that's why you're approaching it with a scripted discussion in your mind (that nonsense you greentexted). that's not how it works.
logic and math are different disciplines in many ways. math is (only formally) logic applied to a specific set of axioms. but that's a retarded way to see math, it's not a game of symbol manipulation. the other side is clear I think, no one would claim logic is math.
Easton Flores
>Who is Bertrand Russell?
And you say I have a:
>limited exposure to either topic
Gosh, this must be awfully embarrassing. :/
You have logic, which should be axiomatic.
You then have mathematics to signify logical truths (axioms).
It's not really that hard to understand, certainly for a "graduate" in the subject. :/
Easton Miller
It depends on your way of thinking, I actually believe the foundation of math is logic, but of course there are differences when you compare them as formal languages, your approach covers that first bit of intuition you need to understand math in order to formalize its study, but when comparing logic books from a mathematical point of view it's hard to beat Enderton, except for maybe Smith? kinda of between math and logic though (as formal languages) but I loved it, nice guide.
John Rogers
Thank you, at least someone is willing to step away from the dogmatic Veeky Forums purism that has degraded the intellectual content of this board.
Lincoln Myers
the way you approach discussions is terrible. you just assume people who say things you don't understand are wrong and don't know the first thing about the topic (e.g. hurr who is bertrand russell)
>logic is axiomatic
>math "signifies" (???) axioms
what's the point? whatever you tried to say, it's nonsense.
Brandon Wright
>I don't care about math or logic but let me post pop philosophy books and complain about the intellectual content of the board
Landon Nguyen
you don't need that shit to be able to formalize a study in math. it has nothing of value for that route. those books are meant for trash courses in humanities and for pseudo intellectuals
Charles Cooper
>I try to rebuke something by attacking my opponent not the argument.
Maybe you SHOULD try the trivium, it seems you have a "limited exposure" to the topic.
>>logic is axiomatic
I said "should be" to try and rewire your headcanon.
>signifies
Symbols, you retard.
>hurr who is bertrand russell
Someone who showed that mathematics and logic are the same thing.
>I like to post misdirection instead of actually offering an argument as to why learning logic is bad, but instead I'm hung up on the fact that he also included rhetoric and grammar, it isn't like I need those to write a decent grant proposal.
Just because you dislike the books, doesn't mean that formalized logic is worthless, you philistine and attempted sophist.
Jaxon Morales
I didn't ask who russell was, you unmeasurable idiot.
>showed that mathematics and logic are the same thing.
it's amazing that you keep saying such idiotic things and then try to claim you have any knowledge of the topic
no one said learning logic is bad. the books you posted aren't formalized logic. they aren't logic. they are nothing. honestly stop
Sebastian Wood
This isn't about the books anymore, if you had a solid grasp of rhetoric, you might've picked up on that.
>I didn't ask who russell was, you unmeasurable idiot.
>It's amazing that you keep saying such idiotic things and then try to claim you have any knowledge of the topic.
Apparently you still need the direction though, even after your quick 5 minute Google:
>en.wikipedia.org
David Peterson
you're the worst kind of poster on Veeky Forums: the wikipedia scholar who doesn't know shit but posts wikipedia articles to justify whatever fucked up beliefs he has.
have you noticed wiki calls it "an attempt"? have you noticed there's a big criticism section? the letters are big enough that only a tremendous fucking retard like you could have missed it.
either way, back off. the main point is this: this is a board of science and math. this is a thread for science and math book guides. your books, whether you consider them absolute trash or not, have nothing to do with science or math. you want to argue that they do, because they motivate a "mathematical mindset" or some idiotic nonsense, but you aren't a math student. you don't know any higher math. so you wouldn't fucking know, you imbecile.
Luis Gutierrez
isnt all of Veeky Forums people linking obscure hard to figure out wiki articles to flex their e-peen of the info they learned in the 10 mins reading it?
Gabriel Morris
I posted that article because it is comprehensive enough for the discussion and drawn from valid sources, sources that might crop up in an actual peer reviewed paper (gosh, the horror), just because it is an aggregate doesn't make it any lesser. You're just attacking ME AGAIN, because you're too retarded for the fucking topic.
Also, Wikipedia is constantly reviewed by bots and volunteers, many of who are experts in certain subjects, including mathematics and logic.
Daniel Taylor
I dream of a world where it isn't like that, there are some knowledgeable people who post in the right threads.
Logan Russell
Fuck off defending his retarded bullshit.
Jason Nguyen
save me your nonsense you fucking idiot, I'm not going against wikipedia. i'l spell it big and clear since you're a retard:
YOU DID NOT READ THE FUCKING WIKIPEDIA ARTICLE YOU LINKED, BECAUSE IT EXPLAINS HOW GODEL'S THEOREMS IMPLY YOU ARE FUCKING WRONG
Brandon Kelly
BECAUSE IT SHOWS THE LIMIT OF LOGICAL POSITIVISM, NOT LOGIC ITSELF, YOU ABSOLUTE CRETIN.
IT STILL SHOWS A LINK BETWEEN LOGIC AND MATHEMATICS, AND IF MATHEMATICS IS BASED ON LOGIC (WHICH IT IS), THEN IT IS A FORM OF LOGIC, DUHHHHHHHHH.
Jacob Phillips
wow
Ayden Barnes
>people ITT having early 20th century discussions
thanks mate:) what are your thoughts on proof books? are they useful or unnecessary for studying uni maths? I like Velleman's How to Prove It and Solow's How to Solve it
Brandon Ross
You don't need to read those books but you certainly need the intuition, some people achieve it by reading and practicing, some people are naturally good at this so they just "get it"
Noah Harris
I know right, mind-blown?
Jaxon Robinson
no, it's impossible to talk to you. hence "wow"
definitely, intuition is arguably the most important part of math. but it won't come from this kind of book. not a chance.
Aiden Cook
no1 here actually read any of these listed books... they need khan level explanations of linear algebra at best
Connor Wilson
>>no meme list for physics
staff.science.uu.nl
Ryder Hall
>no, it's impossible to talk to you. hence "wow"
You started the caps bullshit first?
Love it though: I do the same thing, yet imply I'm childish for doing it too. And then, because I am now 'childish' in your mindset, you don't have to reply.
It's a good thing I know the real reason you aren't replying, that is, that I've shown how little about the core of mathematics you truly know.
It is certainly very disconcerting knowing that an apparent "graduate" knows so little about mathematics, I worry for academia.
Nolan Lee
>And mathematics ISN'T pure logic, it is a subset of logic.
Other way around, actually.
Jack Turner
Semantics much.
Chase Clark
>Semantics much.
You incorrectly wrote the converse of a true statement, hardly "semantics".
Julian Allen
Mathematics is built on-top of logic.
Therefore, mathematics is a form of logic.
Logic is the base.
Mathematics is the base plus the symbolism.
Aiden Fisher
>Therefore, mathematics is a form of logic.
Non-sequitur.
Connor Cox
Which makes the difference semantic, because you're trying to redefine logic as mathematics and vice versa in the statement.
Dominic Harris
Mathematics is built on-top of logic. -> Therefore, mathematics is a form of logic.
Jaxon Perry
Or better yet (semantics again):
Therefore, mathematics is a subset of logic.
Evan Lee
>Mathematics is built on-top of logic. -> Therefore, mathematics is a form of logic.
My house is built on-top of the ground -> Therefore, my house is a form of the ground.
Benjamin Howard
They are nice, it's not like you need them but they certainly help, I read Velleman's book and its good but I think this one is better
fac.ksu.edu.sa
But if you already finished one that's probably enough.
With logic, sets and proofs covered you are ready for some serious math! try real analysis, Tao is good, Rudin is though but worth it, once you finish you will know pretty much all the content of undergraduate calculus classes, getting ahead of everyone else and with a better understanding! but keep in mind this is a hard topic, so don't worry if it takes a long time
Nathaniel Sanders
>Therefore, mathematics is a subset of logic.
Don't you mean subcategory?
Brandon Reed
False analogy.