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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)

#71

Post by wiredfool »

EsportToys wrote: post #10

Speaking of 2nd-order linear ODEs w/ const factor (a.k.a. mass-spring-damper systems), I wrote a blog post[0] deriving all possible general solutions in a concise matrix that makes it easily implementable in code. The following is the complete solution in Lua: function sprung_response(t,pos,vel,k,c,m) local decay = c/2/m local omega = math.sqrt(k/m) local resid = decay*decay-omega*omega local scale = math.sqrt(math.a…

My grad school was basically working through F=Ma-Cv-Kx in all it's expanding varied glory, working up to full blown finite element analysis.

Ultimately it all comes down to choosing the most convenient basis functions for the questions you're answering.

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

#72

Post by threatofrain »

distcs wrote: post #45
contrarian1234 wrote: post #41

Earlier quoted context omitted.

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…

> Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? I have. I went through Khan Academy, Brilliant and 3Blue1Brown. After spending more than 100s of hours I started getting the feeling that these are all good for elementary level math. But for any serious math (think real analysis, complex analysis, group theory and beyond), all these platforms did was leave me with a warm…

Note that 3B1B often warns you that his videos bring perspective for a book/class that you're doing or are already done with. And Khan Academy's focus is for K-12.

If you want anything past Analysis 1 I think you'll find that universities guard their content.

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

#73

Post by tux1968 »

TheOtherHobbes wrote: post #36
tux1968 wrote: post #5

Earlier quoted context omitted.

> I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on When the entire video is generated by an AI, that dynamic changes. It's no issue to improve "the script", and have it seamlessly regenerated. We can't be that far away from this capability, and it could have a profound impact on available learning resources.

The video won't be generated by AI, because there will no video. The mid-game is personalised, conversational, interactive tutoring. The end-game will be deciding how much humans need to know about any of this, because AI will be far better at 99% of it. If this seems unlikely, consider that Cauchy, Gauss, Laplace, and so on were all super-elite 0.001%-ers in terms of ability. No one knows whether AI will eventually…

> there will no video...

There will likely be video. Visual presentations can be an important part of learning. Perhaps it will be generated JIT, but likely AOT compilation of video will represent a useful savings in processing power. Students can always "put their hand up" to interrupt a presentation for a little one-on-one time with professor AI.

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

#74

Post by washadjeffmad »

mnl wrote: post #22
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…

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 application across every industry, breaking down the systems to the component level and manufacturers, deployment, and ordering, as they did the design and theory.

I learned how to evaluate a textbook from its structure and style. It certainly wasn't designed for discrete lessons, and the professor would have needed a diverse and practical understanding to teach it effectively.

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

#75

Post by marcosdumay »

mnl wrote: post #22
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…

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…

The problem is that there is no good textbook for Classical Mechanics out there. At least not on an introductory level.

It's funny that for the 19th century and the first few decades of the 20th one physicists were so eager to simplify and generalize their knowledge. With the side-effect of learning quite a few surprising things from the work. And yet for almost a century the goal is explicitly the opposite. (It's almost like if Academia is in crisis...)

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

#76

Post by zzbn00 »

zozbot234 wrote: post #42
zzbn00 wrote: post #17

Nicely written. But isn't a corollary that we should stop exams in Maths (and Physics/etc/etc) degrees and just teach people who want to learn, how much they want to learn? Exams are for people designing bridges and doing surgery. Basic science just learn and start doing some to see if it is for you.

Exams are ultimately for the students' collective benefit; they ensure that lecturers are teaching effectively, with good learning outcomes. If you're someone who "just wants to learn" and don't care for the rigor of a full Math/Physics curriculum, that's one thing. But if you do care, exams are great.

"The course is turned into a game of skill, where manipulative ability outweighs understanding"

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

#77

Post by marcosdumay »

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.

There are plenty of alternative teaching methods for instruments. (TBH, I don't even know what you are referring to by "classical music", but yeah, some places can be quite oppressive.)

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

#78

Post by pif »

michaelcampbell wrote: post #68
pif wrote: post #46

Earlier quoted context omitted.

> 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.

> > If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained. > 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. Hrm.

???

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

#79

Post by marcosdumay »

financltravsty wrote: post #25
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 b/c it acts as a mechanism to feed out the dummies. The system acts an an informal IQ test - that maintains the prestige of the departments. If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is main…

Yeah, the high-capability outliers are used to coast in any subject and may or may not have time to adapt to the laborious requirements before failing.

Also, anybody with "street-smarts" can see the cost-benefit ratio and perceive the benefit is kept much smaller than some other, easier subjects, while the cost is artificially inflated.

What it does select is people that really love the subject. And is at least a little bit smarter than average.

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

#80

Post by sesm »

Xcelerate wrote: post #24

I went to grad school for chemical engineering a decade ago and part of my frustration with the courses is that the math was never rigorous enough; when I asked for clarification, the inconsistencies were glossed over and hand-waved away. The linked article mentions differential forms, which is a perfect example. In engineering courses, these are often introduced without any rigor or formality. They just “appear” as…

How big a system can be while maintaining a quantum entanglement (also called 'quantum coherence') - is still an open question. A very important one, because it affects quantum computers. Experimentally researchers see, that a big enough system can't maintain quantum coherence for long. If you want to know about how this process is described mathematically, search for 'quantum decoherence'. If you want to know about possible physical interpretations, search for 'objective collapse theory'.
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