As far as subject matter goes, and curriculum, what are the differences

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Pure math = Intellectual masturbation

Applied math = The stuff that actually matters.

>>8319666
Applied math is to pure math as experimental physics is to theoretical physics.
Pure math comes up with new and interesting ideas and applied mathematicians come up with some mundane way to apply it to the real world.
Creative vs practical. They're basically the engineers of math.

>>8319687
Engineering literally means creating

>>8319695
I think you want /lit/

>>8319666
Applied = more problem solving, less theorem proving
Pure= less problem solving, more theorem proving

>>8319695
No it doesn't.
It comes from ingenium.

>>8319730
ingenium and creativity are synonyms

>>8319681
which topics are intellectual masturbation, and which actually matter

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>>8319794
>which topics are intellectual masturbation
All the abstract stuff. Inter-universal Teichmüller theory is a good example of modern pure mathematics -- It's not useful since only handful of people even understands it. And it makes no difference whether the ABC theorem is proved or not. You don't send a rocket to space with Hodge theaters.

>which actually matter
Everything that non-mathematicians like engineers and scientists use regularly.

Applied math will do a lot of numerical methods class (making good approximations) and classes done with an emphasis on numerical methods (say "calculus for engineers" for instance), will have a lot of technical electives usually focused around computers, and some simple diffeq and linear algebra, all done with an eye towards approximations and modelling.

Assessments and goals will be computational, as in you'll be given a problem and be asked to find an "answer."

Pure mathematics will study a wide range of subjects in an abstract fashion, usually covering at least calculus up to multi variable and diffeq, abstract algebra, basic proofs, logic, topology, and analysis. Things will be done with an eye towards proofs, assessments will follow the same.