What's the sequel to this?

way too long winded. cut it to 3 books (book of proof, basic mathematics and apostol/spivak calculus) and at most 2 optional ones and we'll talk.

differential geometry and topology before real analysis is dumb. a boner for shakarchi is dumb. weird order of topics.

Linear Algebra - Hoffman & Kunze
Analysis I - Terrence tao

that's it. when and if you finish both, make a post and ask for more, will probably follow up with abstract algebra and multidimensional analysis. long guides with shitloads of books aren't worth shit.

Algebra:
Algebra by Lang
Commutative Algebra Atiyah Macdonald
Group Theory by Robinson
Commutative Algebra by Eisenbud

Number Theory (Algebraic and Analytic):
Algebraic Number Theory by Neukirch
Course in Arithmetic by Serge Lang
Multiplicative Number Theory by Davenport
Elliptic Curves by Silverman
Algebraic Geometry by Hartshorne (hard)

Topology:
Algebraic Topology by Hatcher
Differential Topology Guilleman and Pollack

Mathematical Logic:
Model Theory by Chang and Keisler
Set Theory by Kunen
Set Theory by Jech (long)
Real & Complex Analysis by Rudin or Real Analysis by Folland
Complex Analysis by Ahlfors

It seems I have a lot of reading to be doing.

Well the books on the 3rd list are first-year grad books. If you look at the questions asked on the general qualifying exams at Princeton math you can see that most people don't necessarily know all of these areas but rather specialize.

How would you rate the reading list on the Wiki for mathematics?

Yeah...a whole two intro to proof books. With one of them being optional...

Draft, another suggestions.

There are honestly a lot of problems with this.
Strang shouldn't be there, use a rigorous linear algebra book (Hoffman and Kunze is probably the best one).
I think you should move ODES and Complex to the medium level (both of those should be done after analysis).
Zorich is bad, and you should really have rigorous calculus books on the basic level (Spivak, Apostol, Tao Analysis I), and then more serious analysis books on the medium level (Pugh, Rudin, Tao Analysis II).
You don't really need the category theory book, and if you want to include it, also give some options for traditional set theory (for example, Naive Set Theory by Halmos).
I think it's ok to give people multiple options as long as it's clear that the books are covering the same content, so maybe you could try and set of the diagram by topic with a list of possible books instead of just listing one.
So here's what I might do:
Basic: Rigorous Calculus Books, Linear Algebra Books, Geometry, Basic Foundations Books
Medium: Analysis, Algebra, Topology
Advanced: Analysis Related Stuff (ODEs, Complex, Measure Theory, Functional Analysis), Topology and Geometry Stuff (Differential/Algebraic Geometry/Topology), Other Algebra Stuff, Logic/Set Theory

Can't I just skip Basic Mathematics and go straight into Allendoerfer?

Second Draft, More suggestions.

>Bland pointless logic book (mathematical logic should be studied much later)
>intro proof book
>one of the best undergrad set theory books but seemingly misplaced
>baby analysis book, maybe
>high school math book
>`advanced' high school math book
>transition to bullshit (why not an analysis, algebra, or topology book)
>calculus

This doesn't seem retarded to you? Learning proofs should be done with something in mind to prove. Intro proof books should be burned.

Legit question. How does Apostol stack up against pic related? I mean both in content and learning curve.

>Bland pointless logic book (mathematical logic should be studied much later)
why tho?
what if you are a philosopher?

can someone put a pic like this but about programing and python ?

good I already have anal 1 & 2 by tao

why not get comfortable with proofs? that way when you have something difficult to prove, it's easier.

I like where this is going

I feel the OP was more aesetheticly appealing tho (smaller font, anime girl didn't have border, smaller and more neutral colored lines, etc)

post a better one then, getting real good takes a lot of practice. I'd rather read too much than too little

Stewart (and most other American calc books for that matter) is a poor commercialization of George Thomas's Calculus and Analytic Geometry which was the standard text in the sixties. Any book with >3-5 editions should be an immediate red flag for you because it means the publisher is revising ever few years to push a new edition. I had to buy Stewart for a class and it's atrocious to try to learn from on your own, however there are a lot of problems to work from and it's extremely common, which means you can find them worked out (check out slader.com). If you're looking for a intro text search elsewhere but if you need it for a class you can supplement it with online resources like video lectures for understanding concepts. As far as Apostol is cconcerned, don't bother if this is your first encounter with calculus, the content is much more dense than intro books and much of the concepts are assumed to be understood implicit by the reader. Leave it for a summer or two when you have some free time. I'd recommend working through Spivak *slowly*, making sure you understand everything, while also doing problems.

Why do you _have_ to buy it? Is not okay to borrow from library?

that is a nonsense chart. it's out of order in a ridiculous way, too. this is why undergrads aren't allowed to design these things.

How's this book? Heard some good things about it.

you have no idea what you are doing. for starters, real analysis by stein IS measure theory

I honestly think a little topology before real analysis is fine, I just think it needs to be a dumb, quick book and not Munkres.

then at least post something constructive, like a correction or alternative

I was thinking about picking up Thomas's Calculus here soon, have you read it?

never heard of it, why are you interested in this over the traditional memes of spivak, apostal, courant and hardy? Coincendtially I just stumbled upon this very same book and heard it briefly described as being "a more advanced textbook which focus on problem solving/applications rather than theory", if that helps.

I'm not even sure this is getting better... I'm only going to comment on books I have experience with, I'm sure some of your other picks are questionable.
>PMA
Garbagio.
>Artin then Dummit and Foote
They're both comparable in depth. Really a better double exposure to algebra would be something like Fraleigh/Hungerford to D&F/Lang/Artin
>Ahlfors
Kind of a meme text. You really need topology to read it. Con Jonway's text is much better for a first exposure.
>Ahlfors then Papa Rudin
Both are suitable for a second exposure to complex analysis, only Rudin is, as previously stated, garbagio. Papa Rudin is more of a reference text than a textbook. Con Jonway CONplex variables II: Revenge of the holomorph also exists.
>Analysis on Memefolds by James R. Memekres
I do not like this book. Some people do. It does not have those prereqs, it's not actually a book about analysis on manifolds. Put it after a real analysis textbook. Replace it with Lee- Intro to Smooth Manifolds.
>Separate textbook on multilinear algebra
I haven't read this book, but I'm going to say what everyone is thinking. If you need multilinear algebra for smooth manifolds, the info will be in the book. If you need multilinear for AG, then you need to do Atiyah MacDonald then do Eisenbud. I have neither heard of nor seen a separate course in multilinear algebra, at least at the undergrad or 1st or 2nd year graduate level.

Not really relevant to books, but is Wildberger's linear algebra series on youtube meme or worth watching? I'm not really sure because I know he's kinda controversial.

worth watching, don't let the memes stop you

Another Draft, More suggestions, something geometry or PDE.

Look up old Putnam problems and try to solve them.

You should add a legend.

looking better and better

Replace Halmos's Naive Set Theory with Elements of Set Theory by Enderton or with Introduction to Set Theory by Hrbacek and Jech. Tao's Intro to Measure Theory is way better than Royden. Too many algebra books, the image is cluttered, it should be Pinter A Book of Abstract Algebra to D&F to Lang (really could even skip D&F). Also you should add off the algebra section Ideals, Varieties and Algorithms by Little and O'shea. Rotman or Hatcher's algebraic topology book should go after Munkres. Also on the left of the image springing from the intro set theory book should be Enderton's Mathematical logic, then Set theory by Kunen.

Evans for PDE

Tu's new book for Differential Geometry

>No linear algebra done right or elementary lingear algebra by anton
wtf

why don't you make ur own image and I'll follow one image, another low level user follows the other, then you and this lovely gentlemen can battle off your pupils in a math showdown to prove superiority

ITT: Undergrads recommend books they've never read to other undergrads who'll never read them.

Im reading laws of truth so fuck you

You're projecting.

— — — — — — — —

0. Remedial Mathematics
Khan Academy
Algebra - Gelfand

— — — —

>1. The Prerequisites of University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
How to Prove It - D. J. Velleman

(Can replace Stitz with Axler, Knisley with Kline, and Velleman with Hammack, same stuff)
— — — —

Pick One Path:

>2a. Introduction to Applied Mathematics (Some Proofs)
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross

>2b. Introduction to Pure Mathematics (Proof-Based)
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter

>2c. The Mixed Approach
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter

— — — —

>3. Foundations for Advanced Pure Mathematics
Linear Algebra - K. M. Hoffman & Ray Kunze
Analysis I & II - Terence Tao
Visual Complex Analysis - Tristan Needham
Algebra - Michael Artin

>Pre-Calculus - Carl Stitz & Jeff Zeager
I found this to be really dry and needlessly verbose. Would recommend Lippmann and Rasmussen instead.

itt: memelists

What book isn't a meme?

>What book isn't a meme?

i just get the most popular book

James Stewart is killin it homie

Ehhh fuck Tao. That book is way too fucking long-winded and put me to sleep. In the beginning he tries to """"motivate""" the subject by giving you a lot of examples of situations where you need to know the concepts in the book, but I just go away wondering I should give a shit about any of those examples. Knowing how to swap integrals and summations just isn't very exciting for a dumb undergraduate brain. How about showing something COOL you can do with analysis? That would be motivating.

2b needs a linear algebra text

nice projections

Is Apostol II not good enough of an introduction for Hoffman & Kunze? jc

Can you give a legend please, it's terrible without one, where should i begin ?

I second this. What do the colors mean?

I'm not saying that, it's just that one can become familiar with linear algebra right alongside, even before, learning calculus. Why postpone exposure to it until more advanced studies?

bump

can someone break down the top linear algebra books for me

You can learn linear algebra before calculus, calculus before linear algebra, etc. People just do the latter path more often.

I'm aware, but that doesn't quite answer the question of why you'd be going through Apostol, Topology, Abstract Algebra before Hoffman and Kunze. It seems an earlier introduction would be beneficial.

Nigga google how to optimize youre png's.
Nice guide btw, don't mean to be dick

Bump

come on flowchart user I'm counting on you for this sweet sweet update

matrices n shit

The sequel is realizing "Oh fuck I spent 2 years learning nothing" and then going to a university to actually start your studies.

Veeky Forums-science.wikia.com/wiki/Mathematics#Linear_Algebra

HEY GUYS
How useful is linear algebra? (I'm a future software engineer.) Idk why but it seems cool, it's just not a required course for my degree. Is it worth it?

>>baby analysis book, maybe
Nah, that is just building the complex from the natural numbers. It's fun, but quite bland.

Might not be useful if you just want to be a fucking code monkey writing throwaway applications but it is indispensable if you want to do ANY of the actually cool shit like machine learning, computer vision, computer graphics, etc. etc.

If you want to be a software engineer and only a software engineer, you won't need math at all. If you wish to do anything more "computer sciency" take it.

Is it possible to take it without having taken Calc II? Calc II is a prereq but I might be able to get it waved if it's irrelevant.

Depends on your specific university. But no, linear algebra doesn't depend on knowledge from calculus (unless they decide to touch on applications to calculus, of course. I don't know what the specific course at your school covers).

Linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations Euclidean spaces.
Sounds like nah

You seem to take a discriminatory stance towards autodidacts.

>Zorich is bad
why do you think so

do you know the course textbook?

I don't know what the calcs in the US cover, but a lot of examples in LA use the space of continuous functions, derivatives and integrals as linear operators, etc.

What do you need for the riemannian geo book?

What list?

Hoffman isn't introductory LA material though

>t. Brainlet

If you're talking about Do Carmo, you need general topology (first half of Munkres), differential topology (Lee chapters 1-15 at minimum, although go a little further to get Stokes' theorem and de Rham's theorem for funsies) and a lot of linear algebra knowledge and intuition. The book is written assuming that you're familiar with the classical differential geometry of surfaces. It's not necessary but you might be disoriented if you try reading it without exposure to that.

Do Carmo has one of my favorite "wtf how is that true" theorems in it, the quarter pinched sphere theorem.

Rudin
Pedersen
Evans

The one true sequence.

what a terrible fucking list.
Jesus Christ.
Is this actually suggesting people actually read Landau?

That Landau book is amazing.

Why would anyone read three proof books?
Here is what I have actually done and felt was useful

Calculus 1,2 -some Stewart book
Multivariable calculus - Marsden and tromba ("vector calcus". Not a great book but it's pretty rigorous and has nice problems)
Linear algebra - Linear algebra and its applications by Later

Proof book: how to prove it by velleman, this is literally all you need

Intro analysis: understanding analysis by Abbot
Better analysis: baby rudin (the way you read this book is to TRY prove all the theorems yourself before you read the actual proof)
Algebra: herstein or Artin

After that you know enough math to have your own opinion and make your own list.

I would probably just skip Abbott's book and go straight to Rudin. Keep it handy for intuition, but honestly trying to prove all the theorems in rudin is THE way to learn math. It's far more active, interesting, and fun.

Fuck, I mean linear algebra and its applications by LAY. Sorry was phone posting like a pleb

Does anybody have a pdf to Smith's Logic? Already looked up on bookzz, but all links are deleted.

>Does anybody have a pdf to Smith's Logic?
gen.lib.rus.ec/

Just to with C++ user.
There are a lot of decent infographics out there. However you could use thenewboston to learn the basics.
Personally I used Chilitomatonoodle tuts and did wonders (also they're game oriented so that's a plus for me)

I started reading Enderton book on logic, but when it started to deal with first order logic, I felt that I first should have studied set theory, so I started reading his book on set theory that is in that list.

So, my question is, how does enderton book on logic compares to Laws of Truth?

Should I really read Laws of Truth before enderton book on set theory?

Exclusively python programming? Is language agnostic acceptable?

I think you would benefit from functionalcs.github.io/curriculum/

This list is nice but in my opinion I would have changed the LISP-like options for more employable counterparts.