Is Complex Analysis a meme? I really enjoy it and I am thinking about specializing in it...

Is Complex Analysis a meme? I really enjoy it and I am thinking about specializing in it, but I don't want my degree to become a meme.

everything is a meme
liking things is for redditards and normies

Should I just kill myself?

yup

Big bucks are in triple integrals

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.

Complex analysis is the ultimate integral solver.

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.

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.

>Complex Anal

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?

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.

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.

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

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

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

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.

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

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.

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

You forgot the most important applications in control.

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

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

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