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Lessons I wish I had learned before teaching differential equations [pdf] (1997)

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Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#91

Post by narrator »

washadjeffmad wrote: post #74
mnl wrote: post #22

Earlier quoted context omitted.

What's the problem with a good book, age? Baby Rudin's first edition is 70 and the latest one is from 1976. It's still widely used and will be for a while. Honestly your problem was that you didn't know any Classical Mechanics yet and you were assuming that the volume of recent developments made old books obsolete. Maybe in Biology, in Physics getting to recent developments would mean that you're familiar with Goldst…

I had a 1930s edition of a "radio physics" textbook as a child, and because there could be no prior assumptions about exposure or familiarity, it was filled with very complex ideas explained so cohesively and coherently that, well, I could understand. The author knew that this book was for people who might be as involved in the business of radio as its science or engineering, so they wrote as much about the applicati…

Do you have any ore information on that book? I would like to dig it up at a local library. Is is this one perhaps? https://archive.org/details/dli.ernet.16412/page/n9/mode/2up

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#92

Post by AnimalMuppet »

contrarian1234 wrote: post #65
mnl wrote: post #61

Earlier quoted context omitted.

There are excellent textbooks on Classical Mechanics, probably because it's a crystal clear subject and you can give a detailed account of the essentials in a single volume without handwaving. Of course everything can be improved, but it also can be muddled. If it works think twice before fixing it. Kind of what happens with Rudin and introductory Real Analysis. On the other hand, there's for instance Optics where yo…

I think you have the perspective of somehow who's succeeded in Physics. In your typical introductory physics class less than half the students will walk away with a very solid understanding of classical mechanics. To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement But sure.. Thermodynamics.. things could be worse :) Someti…

> In your typical introductory physics class less than half the students will walk away with a very solid understanding of classical mechanics.

That's probably true.

> To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement

In my view, that's probably false. I don't think the problem is masochism, gatekeeping, and people holding on to old textbooks. I think the problem is that classical mechanics is actually hard, at least for most people. If you come in to beginning classical mechanics wanting to have learned it, rather than wanting to learn it, no textbook can save you. And I think that many people come in that way. They want it out of the way as a prerequisite for something else, rather than really wanting to know it for itself.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#93

Post by starcraft2wol »

contrarian1234 wrote: post #41
mnl wrote: post #22

Earlier quoted context omitted.

What's the problem with a good book, age? Baby Rudin's first edition is 70 and the latest one is from 1976. It's still widely used and will be for a while. Honestly your problem was that you didn't know any Classical Mechanics yet and you were assuming that the volume of recent developments made old books obsolete. Maybe in Biology, in Physics getting to recent developments would mean that you're familiar with Goldst…

You're conflating things. This issue isn't that Classical Mechanics has somehow evolved or changed. It's that people continue to find new and better ways to explain and illustrate concepts. At lest personally I don't know of any field or book where I've felt "Hmm, this is basically perfect and I can't imagine a better way to explain these concepts". Have you looked at for instance Khan Academy's Grant Sanderson (aka…

> people continue to find new and better ways to explain and illustrate concepts

I strongly disagree. All the best math and CS books I have are old.

New books about old topics tend to be less informed about the context and core ideas that led to their development.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#94

Post by starcraft2wol »

marcosdumay wrote: post #90
jampekka wrote: post #87

There seems to be something similar in other branches of mathematics too (and lots of other fields). A clear example I recall was studying Fourier transforms in math and I couldn't make any sense of it. To me it was just some by-rote algebra with integrals of exponentials of complex numbers. But then I happened to do some audio signal analysis, and when I saw a magnitude spectrum of a waveform, it was instantly obvio…

I'd say that the Fourier Transformation doesn't belong in the calculus program at all. It should be taught in linear algebra, where it does not only make sense, but is a non-trivial example of application that the textbooks have so little of.

You need analysis to make sense of infinite series, indefinite integrals, exponential functions, etc.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#95

Post by BenjiWiebe »

washadjeffmad wrote: post #74
mnl wrote: post #22

Earlier quoted context omitted.

What's the problem with a good book, age? Baby Rudin's first edition is 70 and the latest one is from 1976. It's still widely used and will be for a while. Honestly your problem was that you didn't know any Classical Mechanics yet and you were assuming that the volume of recent developments made old books obsolete. Maybe in Biology, in Physics getting to recent developments would mean that you're familiar with Goldst…

I had a 1930s edition of a "radio physics" textbook as a child, and because there could be no prior assumptions about exposure or familiarity, it was filled with very complex ideas explained so cohesively and coherently that, well, I could understand. The author knew that this book was for people who might be as involved in the business of radio as its science or engineering, so they wrote as much about the applicati…

I'd like to know which book it was.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#96

Post by acjohnson55 »

quacked wrote: post #53

Nearly every educator I've ever learned from has unconsciously insisted that learning material remain sterile, and never become as funny and opinionated as this essay. For most students, "learning" is outrageously boring until you get out of college (or into graduate school) and suddenly learn through essays and memoirs that what was presented to you for 12-16 years in a bone-dry format as established gospel truth wa…

> Nearly every educator I've ever learned from has unconsciously insisted that learning material remain sterile, and never become as funny and opinionated as this essay.

As a former teacher, I think the reason for this is the educational system as we know exists to (attempt to) have reproduceable learning outcomes, at scale. We try to transmit the hard-won knowledge of centuries of geniuses into the minds of adolescents. It's kind of a weird thing to do. It's actually surprisingly successful when I think of it that way, even though I think that it is not great at transmitting the actual insights behind the knowledge.

I suspect a better way to educate people is the more student-led, discovery driven approach. But that is both seemingly harder to scale and less deterministic. Instead, we play out the same cycle of boring, mildly effective education over and over.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#97

Post by gosub100 »

j7ake wrote: post #23
contrarian1234 wrote: post #3

“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…

This masochism also applies to classical music (eg violin). Decades of rote before you’re allowed to express your own musical thoughts.

I was going to make a variant of this comment. $FAMOUS_COMPOSER's $REALLY_HARD suite is right there, you can get the sheet music and it clearly says "play this note, then play that one, then stop for a specific duration...and so on". That doesn't $EXPLETIVE mean that if you watch Khan Academy's video on how to play notes[1..n] you can play the music according to the composer's specification.

I think people who are frustrated they can't grok diff eq in a n-week course are likewise deluded. There is such a deeper meaning those symbols on the page, and I suspect there is simply no way to spoon feed it.

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#98

Post by [deleted] »

pif wrote: post #46
contrarian1234 wrote: post #3

“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…

> Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable I have a PhD in particle physics, and I've been a researcher at CERN with colleagues from multiple countries. And I cannot understand what you are saying there.

[deleted]

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#99

Post by xaellison »

samvher wrote: post #83

> 4. Teach changes of variables This has been something that always seems a bit magical to me, when someone comes up with an obscure change of variables that completely simplifies the problem. I'd love to learn this in a more structured/rigorous way. Does anyone have any recommendations for picking this up?

I think there is less of unifying theory than an assortment of artful tricks - and it's a pretty small assortment, too.

If you want to be able to reproduce every clever mathematical trick of the last 200 years you probably can (I believe in you!). But everyone short of Ramanujan learns them by studying many problems, repeated exposure, and either systematically or organically memorizing them. Afterwards, using them in a problem is more about pattern recognition. This is my experience as a physics phd-master-out ymmv

Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)

#100

Post by angra_mainyu »

SaintRomuald wrote: post #33
siftrics wrote: post #15

Earlier quoted context omitted.

You have to have a pretty helpless attitude to blame someone else (teachers) on your inability to learn from a good textbook. How are you ever going to learn anything truly novel in the world if you always delegate teaching to a teacher?

I shouldn't need to read a 500page textbook to understand a class that a teacher has been 'teaching' for 20 years. He's there to give me an understanding of the subject. I have at least 5 classes each semester which are very technical and difficult, it's impossible for me to read a textbook on each while also reading a 20-30 page lab instruction each night, all written in a technical language which I barely understan…

The entitlement in your comment is staggering...

Why such a desire to be spoonfed, whining about having to put in the work?

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