Real Analysis vs Abstract Algebra

I'm taking both classes next semester, and while I'm planning on studying both, which is the tougher course? Should I study more for one than the other?

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en.wikipedia.org/wiki/Metric_(mathematics)
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Real analysis if you are taking both at the same level.

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!"

Only if you take real analysis for brainlets.

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

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

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.

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

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.

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.

>what is a measure

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.

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

lol topology wtf you talking about

That might be true


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

>his analysis course didn't start with metric spaces

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

Why even waste your time?

t. brainlet

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

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

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

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