Lessons I wish I had learned before teaching differential equations [pdf] (1997) • Hacker News Board

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

#181

Post by da39a3ee » Mon, Nov 13, 2023, 6:36 PM UTC

elteto wrote: post #156

da39a3ee wrote: post #143

Earlier quoted context omitted.

> If you want anything past Analysis 1 I think you'll find that universities guard their content. Not so; there's an absolutely vast amount of freely available undergraduate mathematics resources available at all levels. Honestly, so much that it makes it confusing to choose and not get distracted by the options -- perhaps AI-mediated distillation could be helpful in the future.

Really? Can you link some for Analysis and beyond? I wanted to find good analysis video lectures from a real university complete with problem sets, homeworks and their solutions. I couldn’t. I think MIT OCW now has one analysis course like that, but it’s relatively “recent”.

What about these amazing resources from Daniel Murfet at University of Melbourne:

http://therisingsea.org/post/mast30026/

They have videos as well as everything else. I'd love to study them with someone/some group of people one day.

But, you don't need videos if there are carefully-written course notes PDFs.

Try Oxford: https://courses.maths.ox.ac.uk/course/index.php

E.g. two random Analysis-related courses (second more advanced than first)

https://courses.maths.ox.ac.uk/course/view.php?id=65

https://courses.maths.ox.ac.uk/course/view.php?id=4988

And there are tons of others, but with videos is a bit harder.

Berkeley exam papers with solutions: https://tbp.berkeley.edu/courses/math/113/

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

#182

Post by sheepshear » Mon, Nov 13, 2023, 6:38 PM UTC

mnl wrote: post #141

sheepshear wrote: post #106

Earlier quoted context omitted.

Your response does a pretty good job demonstrating the internal challenges universities face. The interest in making a change was motivated by unmet needs, and it's not going away until those needs are met. The only way to deal with people who won't meaningfully engage in the problem solving process is to go around them.

A textbook should be provided for reference. Copying its contents on a blackboard isn't teaching. You still have to design your course. There's goals to meet, you have to evaluate where your students come from and your job is getting them there. Besides pedagogy, in college you have to respect your students as studying adults and give them a proper bibliography, emphasizing references for independent study if they do…

I actually completely agree with everything you wrote. I'm also very familiar with the ongoing battle between education and training.

What I'm talking about is expanding options to meet additional education needs. Since universities are a shared resource, any solution must be carefully designed to preserve the ability to continue providing existing services. That's difficult to achieve, so I understand the obstructionist response.

All I'm saying is that if you position yourself as an obstructionist, don't be surprised when you're treated like one.

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

#183

Post by [deleted] » Mon, Nov 13, 2023, 6:51 PM UTC

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…

[deleted]

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

#184

Post by __rito__ » Mon, Nov 13, 2023, 6:55 PM UTC

Here's the most intuitive introduction to Differential Equation that I have ever seen: https://www.complexityexplorer.org/courses/31-introduction-t...

Explains DEs from scratch, physical significance, one or two traditional methods, then goes on to numerical methods.

If you ever want to learn DEs, I HIGHLY recommend this tutorial. This is short, too.

I have never found a resource where the concepts behind DEs are explained better.

This tutorial won't prepare you for a course, or tell you everything there is to know about DEs, of course.

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

#185

Post by not2b » Mon, Nov 13, 2023, 6:56 PM UTC

Lots of good criticisms of the traditional way of teaching in here. The only issue I would raise is his claim that Bessel functions should be dropped. In physics and engineering they come up all the time when the geometry is cylindrical.

I suppose he could argue that they could wait for a second course, perhaps.

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

#186

Post by elteto » Mon, Nov 13, 2023, 6:57 PM UTC

da39a3ee wrote: post #181

elteto wrote: post #156

Earlier quoted context omitted.

Really? Can you link some for Analysis and beyond? I wanted to find good analysis video lectures from a real university complete with problem sets, homeworks and their solutions. I couldn’t. I think MIT OCW now has one analysis course like that, but it’s relatively “recent”.

What about these amazing resources from Daniel Murfet at University of Melbourne: http://therisingsea.org/post/mast30026/ They have videos as well as everything else. I'd love to study them with someone/some group of people one day. But, you don't need videos if there are carefully-written course notes PDFs. Try Oxford: https://courses.maths.ox.ac.uk/course/index.php E.g. two random Analysis-related courses (second m…

Fantastic, thanks!

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

#187

Post by Q_is_4_Quantum » Mon, Nov 13, 2023, 6:58 PM UTC

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…

>I really wish textbooks with open licenses would take over and they could be reworked and improved year after year by different people

Could anyone explain to me how they think this might work in practice?

I am presently producing an undergrad textbook in quantum theory. I have two motivations: 1. IMO the "qubits first" (ie teach finite-dimensional QM before wave mechanics) approach to introducing the theory is superior (basically only Feynman did it of all the "classic" books) and 2. I'm involved in third world education and I want the book to be freely downloadable.

Now its a lot of work despite having taught the course multiple times and produced comprehensive lecture notes etc. Once its done I am sure I will not have the time to keep updating it, expanding on the problem sets and so on. A former student on the course is helping with the conversion and he will be a co-author, but like me he sees it as a service not at all about producing a product. So I think we're both very open to the idea of such "open license".

Given all that here are the kinds of questions that immediately arise:

- Mechanically how should one make the book available for such re-working? Put the source files on github? (Not something I've ever used, but I know roughly how it works).

- Via what mechanism does someone get to be credited for work they might do on better versions?

- Who decides what is the current "definitive" or "best" version? I will have a separate website for the book so I guess new versions can be announced there. But one way or the other I won't be involved forever.

- QM is fraught with crackpots, people who have whacky ideas on how to explain things and so on. Can they be prevented from "taking over", rewriting large chunks into (what I would view as) nonsense and so on? Note that presumably my name would still be associated with the new versions, so the issue is primarily not lending credence to stuff I fundamentally disagree with, not that they shouldn't be allowed to go do their thing.

- We will make a POD service available for purchasing hardcopies, the (expected to be small) royalties from which would be donated to third world physics/math education. Is there some license that can ensure any subsequent use of the material is also similarly non-profit?

I can see some (though not perfect) analogies with open-source software, so perhaps someone here has useful ideas about this kind of thing already...

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

#188

Post by ajkjk » Mon, Nov 13, 2023, 6:58 PM UTC

ink_13 wrote: post #158

ajkjk wrote: post #32

Earlier quoted context omitted.

Yeah it's not rigorous. The tragedy is that the organizations responsible for teaching math, like how to do it and how to understand things mathematically, for other purposes , would rather waste their time on rigor. No problem with there being a rigorous math department. For mathematicians. But, quite literally, no one else cares. Mathematicians and everyone else are at crossed purposes, and the mathematicians are w…

> No problem with there being a rigorous math department. For mathematicians. But, quite literally, no one else cares As someone who did an undergrad in mathematics, I have to disagree with you here. People think math is about numbers and computation, but that's like saying literature is about letters and composition. Fundamentally, mathematics is the study of things that are provably true. Without rigor it's not mat…

That's just false. What physicists (and engineers, etc) are doing is also math and it's way more useful and insightful.. and (imo) the world would be a better place if that's what everyone else was also learning in college. The idea that math is only about rigor isn't intrinsic; it's a historical accident that people seem to not realize is optional. It is also about understanding things and being able to wield concepts to accomplish goals or convey understanding to others.

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

#189

Post by fredgrott » Mon, Nov 13, 2023, 7:01 PM UTC

Interesting, I wonder if the same things exist in teaching programming? Well, yes!

Let me give you an example. Both Dart and Flutter borrow from Google's own lessons learned and innovations they did with the native Android OS and widget stack. In fact the testing stack of widgets, goldens, and re-using storyboarding as BDD come directly from the same practices on native Android.

In programming we have a legacy of borrowing from the language and frameworks that came before the current stack that is helpful to know about as everyone uses human knowledge and human language shortcuts to refer to past programming languages and frameworks.

The problem with this area of math is that you need a good basic grasp of geometry as that is how it was built and discovered, see this history chart to see why I state that from wikipedia:

https://en.wikipedia.org/wiki/Geometric_calculus#/media/File...

Of course I always found it easier to think and solve things in geometrical terms and methods. It drove one of my Calculus professors crazy, that and sleeping in class and yet still passing class with an A, getting As on all the tests.

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

#190

Post by mnl » Mon, Nov 13, 2023, 7:02 PM UTC

sheepshear wrote: post #182

mnl wrote: post #141

Earlier quoted context omitted.

A textbook should be provided for reference. Copying its contents on a blackboard isn't teaching. You still have to design your course. There's goals to meet, you have to evaluate where your students come from and your job is getting them there. Besides pedagogy, in college you have to respect your students as studying adults and give them a proper bibliography, emphasizing references for independent study if they do…

I actually completely agree with everything you wrote. I'm also very familiar with the ongoing battle between education and training. What I'm talking about is expanding options to meet additional education needs. Since universities are a shared resource, any solution must be carefully designed to preserve the ability to continue providing existing services. That's difficult to achieve, so I understand the obstructio…

I'm very adaptable nowadays. It's just that I think I know which things should work, but I'm not fighting society, particularly not on this.

The thing with giving the public what they want and being too much of a pragmatist is that we've seen it before.

Consider Western universities in the 17th century, they were still there churning out degrees, but modern science, mathematics and technology developed elsewhere.