I think you and I mean different things by computational mathematics. Calculus isn't analysis, but it still has substantial rigor to it. You might not be able t

I think you and I mean different things by computational mathematics. Calculus isn't analysis, but it still has substantial rigor to it. You might not be able to develop calculus from scratch after studying it, like you could by working through real analysis, but that doesn't mean studying calculus has to be hollow and rote. For example, I find Spivak's Calculus to be a good compromise between full on analysis and the kind of formula memorization you're talking about. Ideally computational mathematics teaches more than just the simple "what" - it should address at least one of the "how" or "why", but it doesn't necessarily need to address all three. I also disagree that the point of the education should be for students to be capable of teaching themselves novel mathematics (and to be honest, I'm pessimistic most graduating math undergrads could do that simply because they made it through something like Rudin).