Alright. Assume an oil refinery as part of a vertically integrated energy company. The issue is siting, storage and distribution. Run Vogel’s Approximation Method for no more than thirty variables and give me the results after a few hundred iterations. Do it longhand with paper and pencil.The point is that you need people who not only know how to run a program, but who understand what the program does. Any monkey can follow instructions. But I want people who can make an informed choice of which approximation algorithm is right, how many variables to pick, and how many iterations will give a result that is accurate enough for the problem domain.Millions depend on getting workable results so don’t make any math errors.
To be able to do that, you need a deep understanding of the background. You gain that understanding by thinking about the methods and techniques, and indeed working through a few exercises by hand. You also get a feeling for numbers that way, so that you can instantly see when results are an order of magnitude off, or when you are in a special case where your standard algorithm fails. This is something you should rather not learn “on the job.”
If you know and understand a numerical algorithm, learning how to use a program that implements it is easy and can be done in a few minutes. Understanding the background is harder, and why you need to spend some time in college before being allowed anywhere near a real project.
Yes, you need to spend time in college for most important jobs but you do not need a deep understanding of a tool that does the drudgery of your job. You need to understand that the tool exists, that it is accessible, generally (not deeply) how it works and when to use it. Repetitive, rote practice of manual calculation is a pointless waste of time for 10 year-olds. We don’t teach Ag students how to manage oxen and we don’t teach fighter pilots how to hand spin a prop driven biplane. They can learn those things on their own time if they have any interest
You are absolutely correct.