Speaking for Linear Algebra, I learnt more reading for a few hours the appendix of "The Design of Rijndael: AES - The Advanced Encryption Standard" than I did in 6 months of theoretical university teaching full of useless technical terms and solutions in search of problems...
This sounds like it was meant to be pejorative, but it's what (applied) linear algebra, and applied mathematics more generally, is. Anyone can learn about a certain mathematical topic upon realising it's the one relevant to the problem they're facing—and learn it way more quickly, due to motivation and focus, than they would in a general-purpose course on the topic; the art is in recognising what mathematics is relevant, and you can't do that if you've never heard of it before. Having a library of (conceptual, not cookbook) solution hooks on which to hang your problems is how you get to be good at using mathematics.
Of course it was meant to be pejorative and that pretty much summarize my experience through university. In this particular case, the teacher wasn't giving a rat arse about his class and was merely there for the safe job, pension, sprinkles by some "research".
Anyhow, I disagree with that top-down approach, which seems to be very... European. I much prefer to follow a more logical path where the problem preclude the introduction to the solution.
Anyhow, I disagree with that top-down approach, which seems to be very... European. I much prefer to follow a more logical path where the problem preclude the introduction to the solution.
I agree that it's easier to learn that way, but it's not much use when solving real-world problems; you can learn the techniques relevant to the solution once you know what they are, but, if you haven't met them before, you won't recognise that they're the right ones.
Comments
Speaking for Linear Algebra, I learnt more reading for a few hours the appendix of "The Design of Rijndael: AES - The Advanced Encryption Standard" than I did in 6 months of theoretical university teaching full of useless technical terms and solutions in search of problems...
This sounds like it was meant to be pejorative, but it's what (applied) linear algebra, and applied mathematics more generally, is. Anyone can learn about a certain mathematical topic upon realising it's the one relevant to the problem they're facing—and learn it way more quickly, due to motivation and focus, than they would in a general-purpose course on the topic; the art is in recognising what mathematics is relevant, and you can't do that if you've never heard of it before. Having a library of (conceptual, not cookbook) solution hooks on which to hang your problems is how you get to be good at using mathematics.
Of course it was meant to be pejorative and that pretty much summarize my experience through university. In this particular case, the teacher wasn't giving a rat arse about his class and was merely there for the safe job, pension, sprinkles by some "research".
Anyhow, I disagree with that top-down approach, which seems to be very... European. I much prefer to follow a more logical path where the problem preclude the introduction to the solution.
I agree that it's easier to learn that way, but it's not much use when solving real-world problems; you can learn the techniques relevant to the solution once you know what they are, but, if you haven't met them before, you won't recognise that they're the right ones.