Real Analysis vs Abstract Algebra

Real analysis if you are taking both at the same level.

>>8974478
Learn linear algebra before abstract algebra
Learn topology before real analysis

real analysis is a troll course: "hey let's waste 3 months doing a bunch of shit with epsilon and deltas and a bunch of lemmas, then 1 week before the course ends: "oh btw in topology you can just define a metric and all this shit we talked about can be done with a metric and you don't need to worry about continuity just check inverse function of open is open lol!"

>>8974490
Only if you take real analysis for brainlets.

>>8974490
We didn't get to this in my analysis class, just Delta epsilon's all the way down

>>8974490
Yea, why don't we just teach stokes theorem in calc and end the course there...

>>8974490
my professor would always put every equivalent definition down at once. sometimes a simple eps delta is easier once youve been drilled to do them, too. they're still the least elegant thing in all of analysis.

>>8974601
The definitions are pretty elegant, doing the proofs of the important results are the ugly bit.

>>8974607
the definitions are simple and intuitive, which is good, but it leaves us with a not so elegant tool.

going all the way and defining infinitesimals with rigor, on the other hand, would give us very elegant tools, and just as powerful.

>>8974478
Wtf is that image supposed to mean? Is algebra going to get me a job in finance where all I have to do is sit in a chair and stare at a chalkboard?

Also algebra is fucking hard. toughest class I've taken at the graduate level.

>>8974490
>what is a measure

>>8974490
The definition of an open set makes zero sense if you didn't do the epsilon delta first though. You need that intuition in R where an finding an open neighbourhood of x ~ points arbitrarily close to x.

>>8974484

How much topology? I have a book on elementary point set topology. I wasn't sure if I should do that or Spivaks Calculus

>>8974835
lol topology wtf you talking about

>>8974831
That might be true


[spoiler]IF YOU ARE A BRAINLET[/spoiler]

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>>8974490
>his analysis course didn't start with metric spaces

>>8974484
>Learn topology before real analysis
most retarded thing I've ever heard
topology doesn't make sense if you don't know real analysis

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>>8974478
Why even waste your time?

>>8975235
t. brainlet

>>8974831
you don't need epsilons you can do everything with a delta(x,y) metric function

https://en.wikipedia.org/wiki/Metric_(mathematics)

>>8976364
But on metric spaces it still is full of epsilons and deltas. You still talk about distances.

>>8974478
Probably abstract Algebra because it introduces more new stuff. It's one of the courses that gives the most trouble to students in unis.