There is very little room for computing in pure math research. The Four Color Theorem is still an exception and not just because mathematicians can’t program. That said this is irrelevant because the article is about the undergraduate program. Only a minority of undergraduate math majors end up as PhDs in math. The rest do something else. Sadly some of them end up teaching high school or as actuaries (no offence). If they want to do something else but still math related then yes, they definitely need a programming course!

GAP? Pari/GP? Mathematica? Magma? There is much room for programming in modern pure math research. In fact, I think we will end up seeing much more computer-aided-math than you think.

>>GAP? Pari/GP? Mathematica? Magma?

Are you suggesting these as tools for mathematicians? Now what is supposed to happen? They have to find problems for these tools? It should be the other way around...

It's called experimental mathematics. It's gathering data about known structures to make conjectures about all structures satisfying certain properties.

Not to mention that, even outside of experimental math, there are plenty of pain-in-the-ass calculations that computer algebra systems make so much easier.

I disagree with your statement and wish you would provide a counterargument.

I think the four color theorem is an exception because mathematicians weren't impressed and excited to find that computers could prove theorems. Instead they were disappointed and considered it somehow "wrong". We should be pushing forward with automatic theorem provers, and we would be if more mathematicians could program.

I was not commenting on the way things should be, only on the way they have been.

when i took math courses, we used maple, and R (for statistics)

engineering courses i took focused on matlab, and C (for embedded microcontrollers)

I never use java as 'domain-specific-language' for those projects.

The intro to CS was java; however, i took C for engineering course for uni requirement (counted as intro to cs)

I'd recommend haskell, smalltalk, scheme or lisp for pure mathematics.

If they are into numerical analysis then Mathematica, C and Java are still important and potentially necessary depending on what they are researching.

For a mathematician, I'd recommend a dialect of ML (or Haskell). It's based on a theorem prover, even.