[jshowa1]

"Such a teacher will be successful if at the end of the course every one of his or her students feels they have taken “a good course,” even though they may not quite be able to pin down anything specific they have learned in the course."

Basically the equivalent of, if the course makes you feel good, then the course is good. Not something that I'd advocate.

By the way, a differential equation is simply an equation with a derivative in it. If you can't recognize that, then you didn't go far enough in math.

[freetime2]

Actually, I have degree in math from a reputable university. So while you are certainly entitled to think that isn't going "far enough in math", I do think that your opinion is in the minority here. If anything, I would say the fact that I have completely forgotten everything from that class is evidence I may have actually gone too far in math... or further than I ended up needing.

And I think it's evidence that the differential equations are not taught in a way that is beneficial for comp sci students (and other types of students too, but I can't speak to that). I took other classes that have not been applicable to my career after graduation - things like finite state machines, computability, and complexity theory. But I still remember a lot from those classes - due to their focus on fundamental ideas and proving things.

[jshowa1]

I've used state machines on the job. In fact, entire architectures are designed around finite state machines. I've also solved a complex logic problem a senior engineer couldn't solve by implementing K-maps.

And of course my opinion is in the minority because nearly everybody under the sun complains about how useless college is and how things should be taught with more application without realizing that things are taught minus application for a reason (so that you can apply things generally instead of specifically) and that many of the hot technologies are just re-purposed PhD research.

Also, the effort many students give to college is less than average (at least from personal experience going through a private engineering school) and probably for most college students. So their complaints are really just the result of laziness and lack of responsibility more than anything.

A minority opinion does not make it invalid or worth less, unless you have evidence to discredit it.

[freetime2]

> I've used state machines on the job. In fact, entire architectures are designed around finite state machines.

My point wasn't that FSMs are useless. My point was that despite the fact that I personally have never needed to convert an NFA to a DFA in my professional career or program a turing machine, I still have a deep appreciation for those courses because they fundamentally changed the way I think about computation.

> I've also solved a complex logic problem a senior engineer couldn't solve by implementing K-maps.

While you are clearly very proud of this fact, I'm not sure why that's relevant here?

> everybody under the sun complains about how useless college is and how things should be taught with more application without realizing that things are taught minus application for a reason (so that you can apply things generally instead of specifically)

This is basically the exact opposite of my complaint. I was complaining that differential equation courses essentially focus on teaching a bag of tricks for solving specific types of equations. I'm sure that behind each of those tricks there is a very fascinating how and why that - upon deeper exploration - may have changed the way I think about numbers. But that certainly was not the focus of the class that I took.

> the effort many students give to college is less than average

So you're saying in a given population, many of its members will be less than average? Very insightful. If only I had gone further in math maybe I would be capable of such insights, too. :)

> So their complaints are really just the result of laziness and lack of responsibility more than anything.

Be careful with this line of thinking. You could say the same thing to discredit any attempt to improve the way a course is taught. But surely you must agree there is room for improvement, right?

> A minority opinion does not make it invalid or worth less, unless you have evidence to discredit it.

Given that you made no attempt to substantiate your opinion - it seems to me that the logical thing to do here is to side with the majority.

[jshowa1]

>My point wasn't that FSMs are useless.

No, but your general point was that classes aren't taught in a beneficial manner, when in fact they are and are often directly applicable to what you're doing. It may be abstracted away to the point where you think you aren't using them, but you very much are. And this illustrates the point of not needing to know the how and why something works and why its often less beneficial to do so because knowing more detail often leads to more confusion.

>While you're clearly proud of this fact, I'm not sure why that's relevant here?

It was simply an example of a direct application of something I learned in college and is thus evidence that what you learn is useful and applicable. I mentioned that it helped a senior engineer because learning such abstractions can make experience irrelevant. You were the one that seemed to bring pride into the picture.

> This is basically the exact opposite of my complaint. I was complaining that differential equation courses essentially focus on teaching a bag of tricks for solving specific types of equations.

So why even mention that things like differential equations are taught in a inadequate manner?

> the effort many students give to college is less than average

Yes, its quite possible that student effort does not follow a normal distribution. All I can say is, from my experience, it was high. Do I have data to back this up? Not rigorously, but given the numerous complaints about how college isn't teaching things right and that professors and universities aren't stupid, I'm just assuming its lack of effort, priority, or skill.

>But surely you must agree there is room for improvement, right?

Be careful with this line of thinking. You could say the same thing to assume improvement must be made in the way a course is taught, when its really another factor that's the cause of peoples complaints that isn't mentioned (i.e. effort, professor, lack of skill, etc.)

> Given that you made no attempt to substantiate your opinion - it seems to me that the logical thing to do here is to side with the majority.

You haven't done the same either. And the most logical thing is to abstain from siding with any position until more evidence is present. After all, the majority of people believe in a religion as taught from selected texts, of which such texts have numerous factually incorrect statements in them.