Short rant against U.S. undergraduate Math programs.
1. Let me try to make a point by analogy with undergraduate C.S. programs.
I expect graduating C.S. students to be able to write and understand code.
But I also expect them to know and be able to do a lot more.
Code is just the bottom level of a hierarchy that
extends up to the conceptual design of the human interface and understanding what people actually use
computers to do.
Having a C.S. Major program of 9 courses, each teaching how to write a different sort of code,
would seem to me ridiculously narrow, and indeed if you look at
a typical C.S. Major program
you'll see they do indeed stray far from code.
Analogously, I expect graduating Math students to be able to write and understand
proofs (if emphasizing pure math) or the techniques of applied math. But these are just
the ``bottom level" techniques.
Surely we should expect graduating Math students to
appreciate and be able to articulate more of the spectrum that goes from
technicalities to the actual uses of mathematics in science, engineering and
human society?
But in fact when you look at
a typical Math Major program it is focussed solely on techniques internal to mathematics --
as if the primary purpose of an undergraduate Major were as the
first step on the road to becoming a research mathematician.
2. I am happy to acknowledge Fermat's Last Theorem as a great human cultural achievement like the Mona Lisa, but .......
- identifying "mathematics" with "pure mathematics" is like identifying
"graphic art" with "oil painting".
So having a Mathematics Department that focusses on Pure Mathematics is like
having a Graphic Arts Department
that focusses on oil painting.
Cambridge does it slightly better, with a Faculty of Mathematics split as
Pure Mathematics, Mathematical Statistics, Applied Mathematics, Theoretical Physics.