I'm a math professor. In my opinion, no. This would be possible, but I don't believe it would be a good idea.
I firmly believe that, if you want to learn any math subject, whether elementary or research-level or anywhere in between, you have to do a bunch of computations. Trying to skip this would be like trying to master chess by reading books and learning theory, without ever playing against live opponents.
I think it's very plausible that we could do with much less symbolic computation by hand, and more use of computers and calculators. Doing integrals and derivatives by hand is often overemphasized, because that's the easiest thing to test for. But I believe that even in an ideal world, this should have a prominent place in the curriculum.
I firmly believe that, if you want to learn any math subject, whether elementary or research-level or anywhere in between, you have to do a bunch of computations. Trying to skip this would be like trying to master chess by reading books and learning theory, without ever playing against live opponents.
I think it's very plausible that we could do with much less symbolic computation by hand, and more use of computers and calculators. Doing integrals and derivatives by hand is often overemphasized, because that's the easiest thing to test for. But I believe that even in an ideal world, this should have a prominent place in the curriculum.