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> Determinants are kind of abstract and even inelegant. No they really aren't. Determinants represent the change in volume in a transformation. > Ideally [det
by rumanator 6y ago
> Determinants are kind of abstract and even inelegant.
No they really aren't. Determinants represent the change in volume in a transformation.
> Ideally [determinants] would not be taught at all, but it's useful for doing exam problems.
This is outright ignorant and wrong. Determinants are fundamental to a myriad of central concepts in calculus and also in engineering fields. For instance, volume integrals or any integral over a parametrization rely on determinants.
- llamaz 6y agoI did degrees in both math and engineering, please give me the benefit of the doubt that I'm not making a 1st year university level mistake. In the specific examples you give, 2-forms could be introduced instead to yield the final formula for the Jacobian. I don't think this is an overkill, because it's possible to use 2-forms without precisely proving the theorems etc about them. This is more convenient for math/physics people, and engineers care more about the final formula than about how exactly it was derived. As another comment here pointed to, the idea that linear algebra is better off without determinants was popularized by Axler - I'm not making this opinion up out of nowhere.
- llamaz 6y agoAs a practical example of what I would prefer be taught on the undergraduate level to e.g. engineering and physics majors: https://www.amazon.com/Vector-Calculus-Linear-Algebra-Differential/dp/B008VRPQV2 https://www.amazon.com/Vector-Calculus-Linear-Algebra-Differ... math majors would probably supplement this with additional material