Re:Why do many math books have so much detail and so little ...
by jessriedel on Monday May 15, 2017 @08:54AM
(#14341149)
>> Based on my own experience as both a student and a teacher, I have come to the conclusion that the best way to learn is through "guided struggle".
> This is the only way to "properly" learn mathematics or science. Anything else is only making you think you've learnt something.
My point is not just that most textbooks make it too hard/inefficient to learn this stuff. My point is that most of it is never learned. The Legendre transform connects the Lagrangian and Hamiltonian mechanics, the two fundamental formulations of both quantum and classical physics, and yet most physicist cannot tell you why the transform is defined as it is. The reason is they don't take seriously the possibility that we'll find non-Lagrangian phenomena, and so they have not been forced to consider what observational and theoretical evidence led to it's identification in the first place.
> This is the only way to "properly" learn mathematics or science. Anything else is only making you think you've learnt something.
My point is not just that most textbooks make it too hard/inefficient to learn this stuff. My point is that most of it is never learned. The Legendre transform connects the Lagrangian and Hamiltonian mechanics, the two fundamental formulations of both quantum and classical physics, and yet most physicist cannot tell you why the transform is defined as it is. The reason is they don't take seriously the possibility that we'll find non-Lagrangian phenomena, and so they have not been forced to consider what observational and theoretical evidence led to it's identification in the first place.