>there are people on this board who unironically like abstract algebra
>>8071873
As someone in an applied field I feel mislead in that I thought learning the field (and other "advanced" pure math fields) would make me better at mathematics in general, I invested a lot of time working for Pinter and not only were there no useful applications that aren't both simplistic and more easily solvable with unabstracted math in the sense that you can learn it on-the-fly in applied texts which is both easier and more useful. Worse still it doesn't even help you understand advanced applied math more easily. All learning abstract algebra does is to help you get better abstract algebra.
The only "advanced" math field that I actually found useful to study on its own is functional analysis. For everything else the applied textbooks teach it far better.
>>8071873
I don't really like it by itself. But I do like Algebraic Geometry, and you kinda need to know algebra to do algebraic geometry.
>>8071907
>you kinda need to know algebra to do algebraic geometry.
Nice meme.
>>8071907
Can you take algebraic geometry and whenever something comes up look it up? or is there just too much?
> I cannot get into abstract algebra
>>8071916
Algebraic geometry and commutative algebra are practically indistinguishable.
>>8071901
I don't know what Pinter is, but you must not have seen at lot of the applied math world if you never come across higher algebra.
>>8071916
No not really. Especially if you go for the Grothendieck Approach.
>>8071873
Abstract Algebra is awesome.
>>8071921
I've come across and I've studied algebraic topology (the textbook was self-contained by the way; zero need for previous algebra exposure) and I can't see how previous knowledge of the kind developed in pure algebra texts would've helped me the authors always very clearly define the operations/algebraic properties, studying various more difficult algebras does not help you understand a particular algebra better at all and the applied ones are usually very simple and understanding the algebra itself is rarely the point/bottleneck of the wider work.
>>8071873
>>there are people on this board who unironically like abstract algebra
>"smartest" board on the 4chins
>most people here don't know the definition of "ironic" or "literally".
Anyone who calls it "abstract algebra" is a dumb undergrad who doesn't know shit about math in general.
>>8071901
underrated post
>>8071916
Why do you want to do algebraic geometry if you don't even like algebra ? Like, what do you think it is about and what do you think you will gain by learning it ?
>>8071957
what. Are you saying that learning about homological algebra isn't going to help you with algebraic topology? You have to learn a requisite amount of algebra to even do algebraic topology. You're argument is like well learning algebra is useless because I can just learn algebra when I need it.
>>8072104
>your
not sure what I was thinking there.
Is it necessary to finish the Calculus series before taking Abstract Algebra? If I take Calc I-III then Linear can I jump into it?
>>8072109
Calc 3 isn't necessary for Abstract Algebra, but Linear Algebra gives you an idea of what certain topics in Abstract can be like, so I would recommend them if it isn't already required by your university. Also, take a proof-based class before Abstract. The whole class is literally proofs, so if you don't know how to prove (or disprove) mathematical statements, you're fucked.
>>8072041
Eventually algebraic completion and the fundamental theorem of algebra.
Its just a lot of these abstract books are so boring.
> heres a definition with no context
> heres ten theorems
> rinse and repeat
>>8072124
My uni requires a "Fundamentals of Higher Mathematics" class before all the proof based courses, so I assume that's what that is.
>>8072104
Perhaps the claim is that reading
tom Dieck, Hatcher, or May
might be more helpful than reading
Weibel if one wants to learn topology
rather than Ext, Tor, and all that.
Some people like holes.
>>8072041
Not that guy but the reason I study Algebraic Geometry is b/c I like Complex Geometry.
>>8072128
>Eventually algebraic completion and the fundamental theorem of algebra.
What?
>>8072164
You know...that every polynomial in Q has a root?
And I think the algebraic completion of Q is a pretty cool field.
Remember I dont really understand this stuff, hence the need to study it
>>8072197
What does this have to do with learning algebraic geometry?
>>8071873
>people on this board enjoy analysis
>>8072109
Don't listen to that guy. You can definitely jump straight into Abstract Algebra.
I've always sucked at calculus, and now I'm doing a math PhD in an algebraic field. And linear algebra was a mess before learning the general theory of modules.
>>8071901
What is your "applied field" exactly? Algebra has straightforward applications in control theory, most areas of physics (esp. particle physics), CS (obviously, esp information theory and cryptography), Bio (RNA computation), and Chemistry (crystallography).
If you study algebra from a book like Pinter, you're learning from a mathematician. You're gonna learn a bunch of proof techniques and details primarily of interest to prospective research mathematicians. But if you want to work in applied math, you need to have a solid basis in proof techniques, unlike in a field like physics.
If you take almost any advanced undergrad or graduate-level course in physics, you'll learn algebra pretty fast, in the straightforward way in which physicists teach it. Different disciplines tend to be good at teaching their students the aspects of 'pure math' fields most pertinent to their discipline. If you don't like the stuff for its own sake, you shouldn't read a book like Pinter.
>>8071873
I understand why learning the basics of abstract algebra, covering groups, rings, modules, fields, vector spaces, algebras would all be extremely important. And Galois Theory is a wonderful part of that. Anything beyond that I see no fucking point in learning.
>>8072250
if you dont understand analysis youre dumb
if you study anything beyond analysis youre autistic
>tfw took a year long graduate course in abstract algebra and passed
>tfw I still have almost no idea how to actually do abstract algebra at all
Same thing for a semester of complex analysis.
I just keep promising myself I've go back and actually learn this stuff correctly after I graduate. Except analysis. I get analysis.
Anyone else know this feeling?
>>8072308
It's far from uncommon that a problem in one discipline can be reduced to a potentially complicated problem in algebra. It would behoove you to know how to solve this algebra problem.
>>8071966
this so fucking much.
I hate this stupid shit site sometimes.
>>8072308
You're missing homological algebra.
>>8072456
Nice try, Weibel.
>>8072464
Homological algebra is widely applied in, uh, applied math, the standard buzzwords being persistent homology and big data. Of course, in pure math, the usefulness of its basics can't be argued (not talking to people to do fucking hyperbolic PDEs or some shit).
>>8072487
Barcodes, uh, find a way.
>>8071901
faggot
Literally what is there to analysis other than DOOD pdes n shiet
>>8072317
Same thing for me with undergraduate PDEs. We used Strauss' book. I did well but had no idea wtf was going on.
>>8072786
we used strauss's book too but my prof had beast notes he gave out.
when I took linear algebra, we used strang's book but I had no idea until I took numerical analysis and had to code up matrix manipulations in MATLAB
>>8072247
No clue o.o
I just cant into abstract algebra and someone told me I needed that.
I'm not really sure what algebraic geometry even is anymore. Someone said it was just like commutative algebra and commutative algebra is about things like modules and rings (which are polynomials) and compleation focuses on polynomials...I think I'm gonna stay over here in my analysis camp.
How are you supposed to learn general algebra without abstract algebra
>>8071901
>Pinter
did you work hard on Pinter? I'm working on it right now and it's mostly very easy. If it was your first time doing rigorous maths I can understand, but it only gets better when you're used
>>8072858
How retarded can someone be?
>Algebraic geometry? You mean like babby's second application of Zorn's lemma?
