Is this guide still valid?

It's "possible" but not without a fat pile of cocaine and no life, and you won't retain very much of what you studied

there's absolutely no reason to go that fast, you're suffering through retarded work hours for worse understanding of the material

>Read THREE calculus books, baby Rudin, and then papa Rudin in rapid succession.

No.

>if you read a lot of Calculus books Rudin will be easy af :DDDD
No. Rudin is dificult because it's about hard problem solving, not because you need much background.

Wtf is baby rudin? The baseball player?

The red nosed reindeer

It's a candy bar made of peanuts, caramel and chocolate-flavored nougat covered in compound chocolate.

Stewart is trash.

That brown haired girl Arnold had a crush on in Hey Arnold.

...

I disagree with these guides. See and also . They focus on a lot of needless things which won't matter if you plan on doing math. Stuff like vector calculus or ordinary differential equations.

Here's what I would recommend to a bright student. Learn calculus non-rigorously from Thompson - Calculus Made Easy, it's a quick and easy read. Learn basic proof methods from anywhere. Stuff involving sets, induction, and simple number theory. Now you can start going through some books. Go through all the books in each section before moving on to the next.

Part 1, Foundations

Linear Algebra(Hoffman and Kunze or Axler): Pick one. I like H&K but many prefer Axler. You don't have to go through all of it now, just get the gist of vector spaces and linear operators. Linear algebra is very straightforward and most of it is just proving things you already expect to be true, so it's good practice for learning how to prove things.

Analysis(Rosenlicht and Rudin): Rosenlicht is wonderful for first learning because he is much more concrete using open balls instead of general sets and proving things by simple constructions. Rudin is best after this since you'll have much better motivation and intuition. Read the first 7 chapters of Rosenlicht and the first 8 of Rudin.

Calculus on Manifolds(Spivak): Here you'll learn how to put classical vector calculus on a modern grounding using manifolds. This is much more useful so everyone uses this language now in both math and physics. Electromagnetism courses for undergrads still use vector calc but that's because physics undergrads aren't expected to know it. Read all of it.

Group Theory(Armstrong): This is optional since you'll learn group theory in abstract algebra. I'm putting this here for people who don't wish to move on to part 2 but would still like to learn the most useful part of algebra. It's so useful even chemists use it. I also really like Armstrong's book.

Part 2, Abstraction

Abstract Algebra(Artin or Herstein): These books are very different even though they cover the same material. Artin focuses a lot on geometry and thus he spends a lot of time talking about linear algebra, groups and representation theory, stuff which is useful for physics. Herstein's Topics in Algebra is older and more abstract. Either one is fine.

General Topology(Armstrong or Munkres): Armstrong is a lot more interesting than the usual topology book because he focuses on stuff topologists are actually interested in, algebraic topology, instead of just general point set topology. Munkres is the standard. I like Armstrong but many people, like from Amazon reviews, dislike his casual style. You'll need to read it like a novel since it's organized poorly and important definitions and theorems are often not singled out.

Differential Topology(Milnor or Guillemin and Pollack): Read these after general topology. Milnor is just very good and short. G&P is basically just Milnor expanded. Read Milnor if you had to pick one.

Part 3, Graduate Material

Complex Analysis(Lang): I don't really like any one complex analysis book that much, but Lang is probably the best. Other options are Ahlfors, Conway, and Stein and Shakarchi.

Real Analysis(Rudin): Not very many options here, but thankfully Rudin is good. Has some problems but nice overall. Other options are Royden, Folland, and Stein and Shakarchi.

More Algebra(Lang): The only real general advanced algebra book. Covers just about everything you'll need to know. Not many alternatives and is the standard reference for just about everything. You should also learn categories from here or Maclane's Categories for the Working Mathematician.

Part 4, Advanced Material

Algebraic Topology(Bott and Tu or Bredon or Hatcher): B&T is very useful when first learning because it makes use of differential forms to give many results in AT geometric grounding and easier calculations. Similarly with Bredon making use of differential topology. Hatcher for when you want to learn the general theory.

Differential Geometry(Hicks and Spivak or Lee): Hicks for a quick overview with lots of theoretical physics applications. Reads a lot like Ahlfors except he is actually careful when explaining. Spivak is older than Lee and very long(5 volumes!) so if you don't wish to go to that effort read Lee instead.

Commutative Algebra(Atiyah and MacDonald): Short but problems teach a lot. Necessary foundation for algebraic geometry. You could also choose to go through Eisenbud's book instead but I think that's way too long.

Algebraic Geometry(Harris or Shafarevich): For an introduction at least. When you know these books and commutative algebra well you can tackle the serious books like Mumford, Hartshorne, and Eisenbud's geometry of schemes. You can also do algebraic geometry using complex analysis with Griffiths and Harris.

Why study a book when you can literally YouTube all these subjects for free? People think I'm lazy but those 100s I get on the calc exams sure didn't look lazy.

Kek

...

>french grammar

?

is stewart good enough for a brainlet engineering student?

>reading translated Bourbaki
Eww

>tenenbaum and pollard in brainlet

no user, that book is pretty good desu

>desu

>tfw it changes 't b h' to 'desu'

desu

slader is the tightest shit for undergrad math if you're going to follow that guy's advice

fuck srsly writing t b h changes it to desu when did this happen, why didnt anyone tell me that

Nee, senpai, why are you being such a newfag desuyo?

desu baka senpai cuck

Yeah, it's good for non-math majors because that's who it's written for

How much math should I know as an Mech E? Used Stewart for my first three calc classes and Pollard's ODE for the fourth. Also, good sources to learn about Fourier transformations?

I would put complex analysis before differential topology, and the second analysis before differential topology also.

Other than that, it's a bit rocky of a path you've built. Some jumps will be larger than others.

The only thing Stewart is good enough for is being reprocessed into toilet paper. Strang is an enormously better calculus-for-nonmathematicians text.

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

see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf

Tenenbaum ought to be in undergrad. Anyone who thinks it's a brainlet book hasn't been exposed to actual brainlet ODE books. I'm guessing it's supposedly-brainlet due to its lack of emphasis on existence/uniqueness, but isn't that basically a nonissue with ODEs? Admittedly I haven't studied ODEs beyond this book, and don't really care to.

The way I organized the list is more of a "what is your level of interest and how far are you willing to go".

tb.h i dont enjoy DEs that much

>Pretty much the life of a math undergrad who plans on doing well anyway.
Lol. Str8 A's and do 1hr of work a day at a top 15 school

That's fair. I just really didn't like any complex analysis books when I was learning but I loved differential topology. Graduate real could be switched with differential topology.