Is Complex Analysis a meme? I really enjoy it and I am thinking

>>8389909
everything is a meme
liking things is for redditards and normies

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>>8389912
Should I just kill myself?

>>8389945
yup

Big bucks are in triple integrals

>>8389909
I will assume you are a math major. Complex analysis is an incredibly important branch of mathematics. It shows up everywhere in pure math and even physics. They are also important for electricity and wave equations.

>>8389977
Complex analysis is the ultimate integral solver.

>>8389909

pls stop extending perfectly good functions into realms I don't understand.

If you're actually going into math as a career, you're going to need to specialize in something higher than Analysis. Normies think Real/ Complex Anal is the top tier, it's more like in the middle.

Number Theory if you're a genius or memer, otherwise Algebraic\ Arithmetic Geo.

>>8390090
It is fine to specialize in Analysis. There are tons of deep problems that are analytic in nature, and analysis itself has many connections to many different fields of math.

Its funny that you mention Number Theory and denounce Complex Analysis, even though many important problems and concepts from Number Theory require knowledge of analytic continuation.

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>>8390090

>Complex Anal

>>8390090
What actually goes on in Real Analysis class? I get the impression from people talking about it that it's some kind of ultimate weeder course where people who are "good at math" learn how stupid they are, and some kind of deep, profound realizations about mathematical theory that leave you in awe are revealed. Is this correct?

>>8390147
Its just very rigorous/terse. All the concepts from analysis are at least somewhat geometrical/intuitive in nature or can be viewed from a geometrical lense (you can picture neighborhoods, open/closed sets, compact sets, etc). Formally defining all of this stuff is hellish and its very easy to get lost in the details. If you are not extremely strong in formal logic and good at coming up with strategies for proving things, analysis typically gives you at least some trouble.

>>8390152
Also what im describing here is literally the very babby basics of undergrad analysis, which is what I thought you were referring to since you called it "Real Analysis class" and "ultimate weeder course". An actual graduate level real analysis class I have not taken yet, so I cannot comment on that.

>>8390104

>first lecture of functional analysis
>70+ year old professor
>writes "math-519 Fun. Anal." on the board

>>8390166
>Functional analysis
If the dude is anything like our prof is its anal fun minus the fun.

>>8390913
functional analysis is fun as fuck though
the intro is basically linear algebra on steroids

>>8390147
You listen to some poo-in-loo ramble about theorems then go home and prove shit that takes 2 hours.

And the exams are like 1 or 2 proofs so if you fuck up early on you fail.

>>8390102
Pure analysis is sort of a mathematical backwater nowadays. Really, what are the important open problems that will impact math as a whole?

>>8390147
Real analysis is usually used as an introduction-to-proofs class for pure math majors, mainly for historical reasons. It's arguable whether it should be, though. Topology and abstract algebra are probably fine starting points too.

>>8390989
My uni has a course called Fundamentals of Higher Math for intro to proofs/ set theory, then Analysis I, Analysis II, Real Analysis.

>>8390048
You forgot the most important applications in control.

>>8390934
I don't even know what functional analysis is anymore, such a wide assortment of different math gets the "functional analysis" sticker.

>>8391139
from the top of my head, the introductionary class included
operators / linear functionals
dual space/predual
locally convex vector spaces
riesz representation Theorem
banach steinhaus
hahn banach
baire category theorem
spectral theorem

what i meant with linear algebra on steroids, was that a lot of LA results can be obtained by looking at their generalised FA equivalents, like the spectral theorem or least squares fitting

>>8391099
Most engineers study signal processing, nor complex analysis. You don'the need to know complex analysis to understand signals.

>>8391241
Do you see the word engineering anywhere post? Do you see the word signals? I'm talking about mathematical control theory research.

Drink bleach you half witted major politics ugrad cuck.

>>8390090
>every professional mathematician works in algebraic geometry or number theory
Damn I knew /sci/ was ignorant but this is just... wow

>>8390989
>Pure analysis is sort of a mathematical backwater nowadays
Analysis is central in all parts of math, from differential geometry to number theory, representation theory, group theory, dynamics, etc. What is pure analysis ? Functional analysis ? It's very useful to group theorists and probability theorists, off the top of my head.

> Really, what are the important open problems that will impact math as a whole?
Uh RH ? Navier-Stokes ? Yang-Mills ?

Don't believe everything /sci/ tells you. Not every mathematician works on (oo)-categories and all that (I'd even go as far as to say that more computer scientists work on these things than mathematicians)

>>8391187
>what i meant with linear algebra on steroids, was that a lot of LA results can be obtained by looking at their generalised FA equivalents, like the spectral theorem or least squares fitting

Is LA in american schools just vector spaces instead of generalised linear spaces? In my first year of uni we had LA with general spaces and also studied LS fitting and spectral theorem there.

>>8391767
can't talk about american universities, but I don't quite believe you, when you say, you tell me you discussed the spectral theorem in a general hilbertspace setting and not just C^n in first year of linear algebra unless your highschool tought you measure theory

>>8391767
>Is LA in american schools just vector spaces instead of generalised linear spaces?
This is the first-semester linear algebra type of stuff. It isnt until a 2nd course in LA where you learn the rest of what you mentioned

>>8391775
You're right, looks like we just barely touched it when discussing symmetric matrices.

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Complex Analysis isn't a meme, it's just you may rip your hair out with when and when not to use Cauchy's Theorum.

>>8390147
Very roughly, think of it as "calculus with proofs". So the "good at math" people you are refering to are those who think that math IS calculus, i.e. it is about solving a bunch of integrals. And real analysis is the beginning of real math. That's where they introduce you to rigorous proofs etc. You will have to learn to prove things you have always taken for granted.

>>8392115
Why do i need to take complex analysis for my geophysics degree /sci?

>>8392369
To solve integrals with the Residue Theorem.

>>8391706
>every GOOD AND RELEVANT professional mathematician works in algebraic geometry or number theory

>>8392115
The answer is always, anon. Always

>>8391533
Lame math major detected.

>>8393528
I'm a chemical engineer. Stop thinking everything is about major politics jesus christ. It doesn't matter beyond your own insecurities.

>>8391746
>Analysis is central in all parts of math, from differential geometry to number theory, representation theory, group theory, dynamics, etc. What is pure analysis ? Functional analysis ? It's very useful to group theorists and probability theorists, off the top of my head.

Of course. But no one really calls themselves an "analyst" anymore, they would call themselves by whatever more specific/interdisciplinary area they work in.

>>8393636
And of course RH is really analytic number theory.

>>8389945
suicide is a meme

Complex analysis is the one subject I respect above all else.

https://www.youtube.com/watch?v=k0Aqis660VI

I love how this man connects everything to the complex plane.

>>8391775
>measure theory
bah. little l2 is the best Hilbert space... assuming there is more than one... which there isn't really.

>>8391241
Really? Fourier transform? Analytic signal and Hilbert transform? Roots and poles of rational functions?

>>8391241

I did learn quite a bit of complex analysis in my ECE education. Some fields will require it more than others, i'm sure; but it is certainly not a useless course.

I also think that it is unfair to compare it to a 'signals and systems' type of course, which is the most essential course in all of electrical engineering curriculum anywhere.

>>8393926
Ok, let me make myself clear.
I know that both Fourier Analysis and signal processing in general are heavily dependent on Complex analysis.
However, engineering professors just teach the formulas and the applications, without the mathematical proofs.

>>8390050
this

>>8393999
Bait taken.

>>8393919
what exactly is your point? Just because you can identify every separable hilbert space with an l2 doesn't mean that there isn't a huge difference between finite and infinite dimensional vector spaces.
also once you get into applications those isomorphisms don't mean shit anymore anyways

>>8389909
itt high school dropouts arguing about "specializing in one class"

next you'll tell me that some people specialize in calc 2, others in calc 1

>>8394881
The point is you don't need measure theory to learn about Hilbert space. Little l2 is an infinite dimensional Hilbert space, just as big L2 is.

I agree with you about practical differences.

>>8396323
>The point is you don't need measure theory to learn about Hilbert space
which i never implied.
you need it to have a framework for the spectral theorem though

>>8396268
Complex analysis is not only a class, anon, but a whole branch of mathematics. Plus, it is a pretty important branch.
Two words: Residue Theorem.