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If I were every to have input into the curriculum for an engineering program, I'd stress adding more about verification and validation of models, not adding mor

If I were every to have input into the curriculum for an engineering program, I'd stress adding more about verification and validation of models, not adding more on numerical methods in general. All users of off-the-shelf models must do at least some sort of check on the model. You do not need to understand how the model works to check it, fortunately. Unfortunately, it's rare in my experience for engineers to do V&V. It might take some culture changes to fix this.

GlenTheMachine 8y ago
Yeah, that's a great point. In the example I had in mind, finite elements, the actual model is typically autogenerated by the software package. The CAD model is not meshed by hand. This issue was alluded to in the OP as well. But you are correct that this issue is not really with understanding the numerical method, it's with the model setup.
wenc 8y ago
Agree with this. Adding more numerical methods at the undergraduate level may or may not achieve the desired result due to limited time in undergrad and lack of mathematical maturity among undergrads. It might end up being just another thing to cram. I took a number of numerical analysis courses as a graduate student, and we had an entire course on how stuff could go wrong in numerics, e.g. catastrophic cancellation, ill-conditioning, nonconvexity, approximation errors due to discretization, etc. I don't think I could have appreciated all of this as an undergrad because I didn't see the practicality of this stuff until I had to solve large-scale numerical optimization problems as a grad student. Then it all started to come together. Also there was more time in grad school to step back and think more deeply about problems, as opposed to undergrad where you're just rushing to get as many courses done as possible. Furthermore, numerical computation is as much an art as a science. The only way to learn is through the repeated grind of trying and failing, and there's no way to fit that kind of practice into an undergrad curriculum. Most people learn this stuff on the job or in grad school. The role of an undergrad numerical methods course is usually only as an introduction to the landscape. In engineering, V&V requires an intuitive understanding of the physical system at hand, which requires experience, which in turn is usually acquired on the job. This is another reason why it is not taught in undergrad. These types of intuitions are best acquired in industry.

GlenTheMachine 8y ago

Yeah, that's a great point. In the example I had in mind, finite elements, the actual model is typically autogenerated by the software package. The CAD model is not meshed by hand. This issue was alluded to in the OP as well. But you are correct that this issue is not really with understanding the numerical method, it's with the model setup.

wenc 8y ago

Agree with this. Adding more numerical methods at the undergraduate level may or may not achieve the desired result due to limited time in undergrad and lack of mathematical maturity among undergrads. It might end up being just another thing to cram. I took a number of numerical analysis courses as a graduate student, and we had an entire course on how stuff could go wrong in numerics, e.g. catastrophic cancellation, ill-conditioning, nonconvexity, approximation errors due to discretization, etc. I don't think I could have appreciated all of this as an undergrad because I didn't see the practicality of this stuff until I had to solve large-scale numerical optimization problems as a grad student. Then it all started to come together. Also there was more time in grad school to step back and think more deeply about problems, as opposed to undergrad where you're just rushing to get as many courses done as possible. Furthermore, numerical computation is as much an art as a science. The only way to learn is through the repeated grind of trying and failing, and there's no way to fit that kind of practice into an undergrad curriculum. Most people learn this stuff on the job or in grad school. The role of an undergrad numerical methods course is usually only as an introduction to the landscape. In engineering, V&V requires an intuitive understanding of the physical system at hand, which requires experience, which in turn is usually acquired on the job. This is another reason why it is not taught in undergrad. These types of intuitions are best acquired in industry.