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"With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Student

"With a computational approach, we can go “top down”, starting with libraries that implement the most important algorithms, like Fast Fourier Transform. Students can use the algorithms first and learn how they work later." The "Learn how they work later" part sends out alarm bells to me. I don't have a lot of confidence that students will be particularly motivated to dig into how an algorithm works after their problem has been solved I fear this will lead to a generation of "just use $x package" and people blindly plugging in "magic algorithms" without understanding their choice. "Quicksort for everything" or "include leftpad" if you will... I see it a little in my industry (Engineering) "oh your data is noisy just apply a kalman filter" never mind if it is appropriate or not.

j2kun 9y ago
Another aspect, one that I've encountered many times, is that even when someone has to implement the idea from scratch, they don't work to understand it and instead just translate pseudocode. I once had an interview where I was asked to explain why a piece of code (that the interviewer wrote) worked, because the interviewer did not know. A benefit of the bottom up approach, of starting with the math and no reference implementation, is that you are less likely to implement it unless you understand it. And I should stress, these are tradeoffs.