3 ms·

> On Wikipedia, unsuspecting visitors are usually greeted by some variant of this: As someone who studied 2 years of electronics I don't rememer everything and

> On Wikipedia, unsuspecting visitors are usually greeted by some variant of this: As someone who studied 2 years of electronics I don't rememer everything and certainly not the explanation of the Laplace transform. But I certainly remember writing like mad for a long time while trying to catch what the teacher told, only to be told somewhere around lunchtime I think that this wasn't actually important for engineering or even the exams, only included because it was interesting. One of a few reasons why I changed from electronics engineering to computer systems even if it meant a year more of studies and looked like a poorer choice wrt job security (at the time). I passed that course but that is partially why I applaud everyone who starts with the simple and interesting instead of diving head first into the mathier parts to try to shake off most students before they even know why this thing is interesting.

srean 2y ago
> But I certainly remember writing like mad for a long time while trying to catch what the teacher told, only to be told somewhere around lunchtime I think that this wasn't actually important for engineering or even the exams, only included because it was interesting. Depends what you are getting trained for. An acceptable cobbler who can patch up a broken shoe into something usable would have different pedagogic needs than one who is training to become a designer of the next-gen shoe. A vibrant economy needs both kinds. That said, a big part of 'hacking' used to be about the pleasure of deeply understanding a topic, not necessarily just as means of earning or employment. Was it Feynman who said something about whats the utility of physics and why do people engage in it ? I am paraphrasing his comment from faulty memory: sex is useful for reproduction but that's not why we engage in it. Many here are into it for that other reason of hacking.
- nonrandomstring 2y ago
  Much agree, and one of the reasons to try to make hacking and fun practical stuff part of a course is that the knowledge is stickier. You'll remember the Moog filter you built on a breadboard which made weird noises after you calculated the RC values wrong. Maybe not so much the perfect stopband you got a solver to make for you in a DSP simulator. Feynmann was all about that teaching realism. Also it takes about 6 months to a year of tinkering to really get "the pleasure of deeply understanding a topic". Many uni departments scrapped the electronics labs because it's all a bit messy, expensive and time consuming and I think the demand for people who teach it is getting smaller, at least here in UK. Last time I was asked to give an electronics class it was mainly digital switching of loads and hooking up I2C sensors. Still we had fun. That "just get the certificate" mentally of education doesn't leave much room for the play factor.
  - srean 2y ago
    The tension between who is the university for (students or their potential employer) and the tension around what is the university for (knowledge acquisition or for earning an accreditation) is a problem that society has not solved very well. I had hoped that online learning platforms such as Coursera and Edx would solve this by occupying the "for students" niche and the "for knowledge acquisition at the students preferred pace" niche. It did not quite turn out that way. Glad you and your students had fun tinkering.
mananaysiempre 2y ago
I’m not going to try and defend applied math courses taught to engineering students. The quality varies—some are superb, some are pretty meh, some are just bad, and it can be pretty difficult to tell the difference as a student, especially when a good course assumes you had a good one for a prerequisite when you only had a meh one. I am going to point out that repeatedly asking “why?” will get you into very mathy weeds very quickly, such that “foul” calculus will be the least of your problems. Like here: > As it turns out, most analog filters are relatively distortion-free only in one special case — a perfectly steady sine waveform[.] Ever wonder why? And not just in the sense of showing that’s the right answer, in the sense of setting off without the knowledge of the answer and deriving it. Well, the starting point is that the filter is linear and time-translation-invariant (i.e. doesn’t have a clock built into it); the fact that it is causal is somewhat important but not immediately so. But then things get interesting, and if you’re lucky you’ll get to hear such wonderful phrases as “group characters” and “representation theory”. I don’t blame people who got burned by their math courses, but I do want to emphasize that these kinds of “why?” questions are exactly what math is there for. If the math book in front of you doesn’t look like it works that way, take another one and try again—just don’t expect the specific question you have to be answered immediately. (I’m assuming I don’t have to explain the virtues of repeatedly asking “why?” on a forum called Hacker News.)
- srean 2y ago
  Those references to "group characters" and "representation theory" cracked me up, in a good way. For those who have an engineer's exposure to Fourier series and transforms, these would be the logical next steps to appreciate the big picture. As a pedagogic device I get some success with is by keeping things concrete, showing that shift in time (index) of a very high dimensional vector, is same as multiplying with a fixed matrix. Same with the difference operator, summation operators and so on. Then one can think of singular value, or eigen-decomposition of those matrices, that's the point were students realize why these operators "become" point-wise multiplications and divisions. Works with those who have some experience with finite dimensional matrices.
TheOtherHobbes 2y ago
The Laplace Transform is an easy(ish) way to transform differential equations into complex numbers. The response of a capacitor or inductor is a differential equation with an exponential solution. The Laplace transform replaces the exponentials with s = iω, where ω just means "a sine wave at some frequency". (It's actually jω in EE, because reasons, but it means the same thing.) So if you build a network of capacitors, resistors, and inductors, or springs and masses, or anything else that uses the same maths, you can turn it into a simple algebraic equation in s. This is called the transfer function. It literally defines the frequency and phase response with some simple algebra. In practice you don't bother with the calculus and just go straight to s. A single capacitor filter is 1/(1+sRC). Add more stages - the rules are pretty simple - and you get a more complex equation. Then you can put ω = 200Hz or whatever into the transfer function, and you get a complex number out. This tells how big the output is at that frequency, and how much it's phase shifted. If you graph ω, you get the complete frequency and phase response. Really all you're doing is replacing a static DC test voltage with a sine wave "probe" across the frequencies you're interested in. There's a bit more to it - which is where poles and zeroes appear - but not much. (It's also related to the Fourier transform, but that's a whole other thing.) It's incredibly impressive that all of this was invented in the early 19th century by a handful of French aristocrats and a couple of Germans, more or less as a hobby.
- aeronerd91 2y ago
  [dead]
- HeyLaughingBoy 2y ago
  > There's a bit more to it - which is where poles and zeroes appear - but not much. As someone who has bad memories of spending hours calculating Root Locus plots by hand, I'm going to have to take offense at that statement :-)
- eitland 2y ago
  I think you misunderstand. I love the Laplace transform. I just don't like how school decide to use three lecture hours to derive it and only afterwards explain what it is for and that this was only a demo of how one could arrive at the same result. We also derived the relativistic equations but then we got to know up front what was going on.
esafak 2y ago
I remember all of it. I just resent that it was useless to me and I could have learned more useful things instead.

srean 2y ago

> But I certainly remember writing like mad for a long time while trying to catch what the teacher told, only to be told somewhere around lunchtime I think that this wasn't actually important for engineering or even the exams, only included because it was interesting. Depends what you are getting trained for. An acceptable cobbler who can patch up a broken shoe into something usable would have different pedagogic needs than one who is training to become a designer of the next-gen shoe. A vibrant economy needs both kinds. That said, a big part of 'hacking' used to be about the pleasure of deeply understanding a topic, not necessarily just as means of earning or employment. Was it Feynman who said something about whats the utility of physics and why do people engage in it ? I am paraphrasing his comment from faulty memory: sex is useful for reproduction but that's not why we engage in it. Many here are into it for that other reason of hacking.

nonrandomstring 2y ago
Much agree, and one of the reasons to try to make hacking and fun practical stuff part of a course is that the knowledge is stickier. You'll remember the Moog filter you built on a breadboard which made weird noises after you calculated the RC values wrong. Maybe not so much the perfect stopband you got a solver to make for you in a DSP simulator. Feynmann was all about that teaching realism. Also it takes about 6 months to a year of tinkering to really get "the pleasure of deeply understanding a topic". Many uni departments scrapped the electronics labs because it's all a bit messy, expensive and time consuming and I think the demand for people who teach it is getting smaller, at least here in UK. Last time I was asked to give an electronics class it was mainly digital switching of loads and hooking up I2C sensors. Still we had fun. That "just get the certificate" mentally of education doesn't leave much room for the play factor.
- srean 2y ago
  The tension between who is the university for (students or their potential employer) and the tension around what is the university for (knowledge acquisition or for earning an accreditation) is a problem that society has not solved very well. I had hoped that online learning platforms such as Coursera and Edx would solve this by occupying the "for students" niche and the "for knowledge acquisition at the students preferred pace" niche. It did not quite turn out that way. Glad you and your students had fun tinkering.

mananaysiempre 2y ago

I’m not going to try and defend applied math courses taught to engineering students. The quality varies—some are superb, some are pretty meh, some are just bad, and it can be pretty difficult to tell the difference as a student, especially when a good course assumes you had a good one for a prerequisite when you only had a meh one. I am going to point out that repeatedly asking “why?” will get you into very mathy weeds very quickly, such that “foul” calculus will be the least of your problems. Like here: > As it turns out, most analog filters are relatively distortion-free only in one special case — a perfectly steady sine waveform[.] Ever wonder why? And not just in the sense of showing that’s the right answer, in the sense of setting off without the knowledge of the answer and deriving it. Well, the starting point is that the filter is linear and time-translation-invariant (i.e. doesn’t have a clock built into it); the fact that it is causal is somewhat important but not immediately so. But then things get interesting, and if you’re lucky you’ll get to hear such wonderful phrases as “group characters” and “representation theory”. I don’t blame people who got burned by their math courses, but I do want to emphasize that these kinds of “why?” questions are exactly what math is there for. If the math book in front of you doesn’t look like it works that way, take another one and try again—just don’t expect the specific question you have to be answered immediately. (I’m assuming I don’t have to explain the virtues of repeatedly asking “why?” on a forum called Hacker News.)

srean 2y ago
Those references to "group characters" and "representation theory" cracked me up, in a good way. For those who have an engineer's exposure to Fourier series and transforms, these would be the logical next steps to appreciate the big picture. As a pedagogic device I get some success with is by keeping things concrete, showing that shift in time (index) of a very high dimensional vector, is same as multiplying with a fixed matrix. Same with the difference operator, summation operators and so on. Then one can think of singular value, or eigen-decomposition of those matrices, that's the point were students realize why these operators "become" point-wise multiplications and divisions. Works with those who have some experience with finite dimensional matrices.

TheOtherHobbes 2y ago

The Laplace Transform is an easy(ish) way to transform differential equations into complex numbers. The response of a capacitor or inductor is a differential equation with an exponential solution. The Laplace transform replaces the exponentials with s = iω, where ω just means "a sine wave at some frequency". (It's actually jω in EE, because reasons, but it means the same thing.) So if you build a network of capacitors, resistors, and inductors, or springs and masses, or anything else that uses the same maths, you can turn it into a simple algebraic equation in s. This is called the transfer function. It literally defines the frequency and phase response with some simple algebra. In practice you don't bother with the calculus and just go straight to s. A single capacitor filter is 1/(1+sRC). Add more stages - the rules are pretty simple - and you get a more complex equation. Then you can put ω = 200Hz or whatever into the transfer function, and you get a complex number out. This tells how big the output is at that frequency, and how much it's phase shifted. If you graph ω, you get the complete frequency and phase response. Really all you're doing is replacing a static DC test voltage with a sine wave "probe" across the frequencies you're interested in. There's a bit more to it - which is where poles and zeroes appear - but not much. (It's also related to the Fourier transform, but that's a whole other thing.) It's incredibly impressive that all of this was invented in the early 19th century by a handful of French aristocrats and a couple of Germans, more or less as a hobby.

aeronerd91 2y ago
[dead]
HeyLaughingBoy 2y ago
> There's a bit more to it - which is where poles and zeroes appear - but not much. As someone who has bad memories of spending hours calculating Root Locus plots by hand, I'm going to have to take offense at that statement :-)
eitland 2y ago
I think you misunderstand. I love the Laplace transform. I just don't like how school decide to use three lecture hours to derive it and only afterwards explain what it is for and that this was only a demo of how one could arrive at the same result. We also derived the relativistic equations but then we got to know up front what was going on.

esafak 2y ago

I remember all of it. I just resent that it was useless to me and I could have learned more useful things instead.