Essential textbooks for each of the major topics in math

your opinion for the essential textbooks that are a must for each of the topics in mathematics

is this a good book? dunno, i didnt find it rigourous

>Ahlfors

for your information ahlfors is good, albeit of course not as rigorous as rudin, still good nevertheless.

Concrete Mathematics (Knuth & Graham)
Applied Combinatorics (Roberts & Tessman)
A Course in Combinatorics (Van Lint & Wilson)
Analytic Combinatorics (Flajolet & Sedgewick)

I wish every analyst who griped about combo had to work through these books like I had to work through Apostol, Rudin, Royden, that greek guy, and the Russians before I was allowed to gripe.

Maybe not, but it helps you through a course of complex analysis.

Anybody recommend me two and three dimensional geometry books?

Two dimensional geometry the best of the best is Coxeter. Just read anything he published, it doesn't even matter. Once you've wet your whistle find texts by Marcel Berger. He has two and three dimensional geometry books.

Analysis is a pre-requisite for combinatorics while combinatorics is not a pre-requisite for analysis at all so how does your point make sense?

Why complex analysis when you can just study topology? Please somebody can answer this?

>Analysis is a pre-requisite for combinatorics

In what universe is that remotely true?

the one where it's much often much easier to work with integrals than it is to work with sums.
The one where you often need to approximate a discrete function with a continuous version in order to evaluate it or get a lower or upper bound because the discrete version is far less tractable.

Have you actually done any combinatorics beyond highschool counting problems or did you just look up some book titles to sound smart?

>the one where it's much often much easier to work with integrals than it is to work with sums.

Ok, its clear you are actually the one who has never studied enumerative combinatorics.

Cool. Anyone who knows about combinatorics knows that I'm right and you're wrong so who are you trying to save face in front of?

Categories for the Working Mathematician
Sipser for computer science
A Concise course in algebraic topology

I just took topology and am about to take complex. Don't you miss something by ignoring the fact that you have a function, with like, derivatives and integrals and shit? Or are you just meming?

I can only really say this about analysis and linear algebra since they're the only two topics in which I've taken a look at the various different textbooks:
Linear Algebra Done Right - Axler
Principles of Mathematical Analysis - Rudin

Someone continue this list.

He's just memeing. Topology and complex analysis are very different.

>Cool. Anyone who knows about combinatorics knows that I'm right and you're wrong so who are you trying to save face in front of?

You're just wrong though. You could work through three of the four books I posted without having taken undergrad analysis and you wouldn't miss out on a thing. If you had studied those topics you might know that.

He was right.

He listed a couple of instances in which you'd want to use calculus while studying combinatorics. That does not make analysis a prerequisite for studying combo. It's nowhere near that.

Leave it to analysts to assert their subject is foundational to everything though.

>conformal mappings
hngghhhh

I'd say Shilov is more essential than Axler

>Sipser for computer science

Sipser is high school tier. At least read Arora and Barak or Kozen.

>muh CS classes didn't use calculus so calculus is useless

>one example of calculus being used in one area of a field means real analysis is a prerequisite for that entire field

>has never studied generating function

Clearly the only exposure to combinatorics must have been in a CS discrete math course.

Analysis is a prerequisite for studying analytic combinatorics. Nothing I have said in this thread contradicts that.

he is completely right. reading introductory combinatorics and concluding "hurr combinatorics doesn't use analysis" is retarded of you. stop trying to save face.

>generating functions and counting through polynomials and series isn't something used in enumerative combinatorics

STOP TRYING TO SAVE FACE. DONT POST. YOU'RE NOT GAINING ANYTHING. THIS IS AN ANONYMOUS BOARD. WALK AWAY.

>J.P. May
My nigga. Do you have recommendations for algebraic geometry for someone comfortable with higher category and topos theory?

You have yet to provide any substantive evidence that one cannot learn combinatorics without first learning analysis. Since you are so buttmad, maybe you should walk away?

>I can study Probability for Business majors without calculus/analysis so Probability can be studied just fine without calculus/analysis
>I can study Combinatorics for CS majors without calculus/analysis so Combinatorics can be studied just fine without calculus/analysis