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Anonymous Sat 06 Jun 17:22:01 2020 No.11768235 View Reply Original Report

Quoted By: >>11768247 >>11769258 >>11769294 >>11769566

Is it more important to learn pure math or applied math as an undergraduate? I have 2 options to fill my schedule pretty much
>PDEs
>Differential Geometry
>Complex Analysis
or
>General Topology
>Ring and module theory
>Real Analysis (lebesgue integration and such)
I want to be as prepared for grad school as possible.

Anonymous

Anonymous Sat 06 Jun 2020 17:28:26 No.11768247 Report

Quoted By: >>11768259

>>11768235
Math isn't important.

Anonymous

Anonymous Sat 06 Jun 2020 17:35:59 No.11768259 Report

Quoted By:

>>11768247
I know that. I'm saying what math is more important for math?

Anonymous

Anonymous Sun 07 Jun 2020 00:27:55 No.11769258 Report

Quoted By:

>>11768235
I'm speaking for someone interested in math grad school. Toplogy, ring theory, real analysis, and complex analysis comprise the basic core material for grad school. In fact, I'm surprised they aren't necessary for your major. Differential geometry only matters if you pursue that in grad school, but even then, the other courses will matter more and I cant imagine you'll cover any real content without toplogy. PDEs is completely irrelevant unless you're in applied math, but even then, it's only worthwhile if it's not an "engineering plug n chug" type course. So the second list for sure but try to get complex analysis in. I'm a second year PhD student in pure math btw.

Anonymous

Anonymous Sun 07 Jun 2020 00:43:30 No.11769294 Report

Quoted By: >>11769314

>>11768235
>engineering topics vs. core math classes
How is this even a question? Isn't the 2nd list required for your degree anyway?

Anonymous

Anonymous Sun 07 Jun 2020 00:51:09 No.11769314 Report

Quoted By:

>>11769294
The theory of complex analytical functions is an important fundamental, basic topic in math. So if complex analysis is taught at a decent level, it is totally worthwhile. But yes, it could possibly just be really a "complex calculus" course, which has some value, but is very bad if substituted for anything else in the other list. I cant imagine DEs at such a low level (without toplogy) will have any value. That is probably just another calculus (or an n-dimensional analysis course, which is also not that helpful compared to the other options). So yes, your dichotomy has truth to it.

Anonymous

Anonymous Sun 07 Jun 2020 02:30:20 No.11769566 Report

Quoted By:

>>11768235
Are real analysis, complex analysis, and ring/module theory not core requirements for a math major?
And to answer your question, most applied math classes are 90% formulas 10% intuition. You can git gud at pure and just apply yourself whenever you want. If you take pure and are serious about it, you can pick the hardest questions in the PDE book without reading anything else on the subject and simply figure it out on your own.

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