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Replying to the answers received as of 17:02 20220127 GMT+1. Thanks A HUGE LOT to all and sundry for taking the time. I am the first one to understand that

*Replying to the answers received as of 17:02 20220127 GMT+1.* Thanks A HUGE LOT to all and sundry for taking the time. I am the first one to understand that theory is the only way to really grasp a problem (this is why differential equations and calculus and linear algebra are key in the education of an Engineer). This is something I guess all of you agree on (as a matter of fact, I am a pure mathematician by education). My problem with *specific algorithms* is that they are deemed to be obsolete, unless they are inherently theoretical. In this sense: a) Gauss reduction method (some of you have mistaken this for the iterative Gauss-Jordan method, I guess): this is not just a method but a way to understand a linear map (and a system of equations) in a much simpler way, and of getting information by itself (i.e. the eigenvalues). Same for the Jordan decomposition result (but this is a bit overkill to me). b) Newton-Raphson: the most important use of the "derivative as approximation" that exists, apart from showing the importance of iterations and stability. c) The condition number, and (in)stability of linear systems: this is a pure theoretical notion (nobody computes the condition number because if you can, then you can also invert the matrix) which has very important *applications as understanding*. However: a) Gauss-Jordan (i.e. the iterative method): I understand that it may be good to teach it as a tool to understand convergence and iterations but (you won't believe this): here they ask the students to *perform* iterations of this method BY HAND WITH A CALCULATOR... b) QR: I never understood teaching this to undergrad engineers (it is just the Gauss reduction method with a little care when your matrix is symmetric). What interest does this have in general for an engineer? Etc... Compare the two above with, for instance, the method of integration of rational functions in its most general form, which was taught in Spain in schools of engineering until twenty years ago. Nobody sees this as relevant any more, as it adds absolutely nothing to the understanding of the integral, and is just a waste of time (Wolfram|Alpha does it for free)... By the way, and you will not believe this either (I have been teaching this course several years by now). Where I work it is *in the first year*. This hurts a lot, as my students have absolutely no way to apply any of this to any engineering problem.

Tainnor 5y ago
Even as a pure maths student, I've rarely found it useful to have to carry out complicated computations in exam settings. Integrations methods I can even understand up to a point as it is useful for pattern matching – but I had to actually carry out the simplex method on paper in one exam, and worse, I had to memorise several variants of it with different pivoting strategies. Of course, I barely remember how that algorithm works by now. I guess one reason why such computations are asked for in exams, though, is because it gives people something concrete to study so that if they prepare well, they can score some points. If you only have "applied knowledge" exams, they get harder. And somehow, society wants to perpetuate the notion that you can achieve anything if you put in enough effort (no matter whether that effort is actually valuable). In an ideal world, we could instead maybe give students a high level description of the algorithm, have them carry it out explicitly on extremely simple input just to see it once, and then maybe ask them to implement the algorithm in a computer program. Sadly, at least for pure maths students, the coding skills are typically low even when there are explicit CS requirements, don't know what it's like for engineering students.
pfortuny 5y ago
OH MY! I intended to say Gauss-Seidel and said Gauss-Jordan! What a mess I have created. Sorry to all for the confusion. Of course, Gauss' reduction method is key to understanding systems/linear maps. Gauss/Seidel is totally different, though. My apologies.

*Replying to the answers received as of 17:02 20220127 GMT+1.* Thanks A HUGE LOT to all and sundry for taking the time. I am the first one to understand that

Tainnor 5y ago

Even as a pure maths student, I've rarely found it useful to have to carry out complicated computations in exam settings. Integrations methods I can even understand up to a point as it is useful for pattern matching – but I had to actually carry out the simplex method on paper in one exam, and worse, I had to memorise several variants of it with different pivoting strategies. Of course, I barely remember how that algorithm works by now. I guess one reason why such computations are asked for in exams, though, is because it gives people something concrete to study so that if they prepare well, they can score some points. If you only have "applied knowledge" exams, they get harder. And somehow, society wants to perpetuate the notion that you can achieve anything if you put in enough effort (no matter whether that effort is actually valuable). In an ideal world, we could instead maybe give students a high level description of the algorithm, have them carry it out explicitly on extremely simple input just to see it once, and then maybe ask them to implement the algorithm in a computer program. Sadly, at least for pure maths students, the coding skills are typically low even when there are explicit CS requirements, don't know what it's like for engineering students.

pfortuny 5y ago

OH MY! I intended to say Gauss-Seidel and said Gauss-Jordan! What a mess I have created. Sorry to all for the confusion. Of course, Gauss' reduction method is key to understanding systems/linear maps. Gauss/Seidel is totally different, though. My apologies.