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Introduction to Differential Equations (2008)

tutorial.math.lamar.edu

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Re: Introduction to Differential Equations (2008)

#91
post #88

Earlier quoted context omitted.

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 ta…

> 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 computat…

>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.

Re: Introduction to Differential Equations (2008)

#92
post #86
post #71

Earlier quoted context omitted.

You need to learn the math before applying it. You don't apply things that you don't understand.

I need the concrete before the abstract just so my mind knows that what I’m seeing is not BS. Because in finance, 95% of the math is BS formulas that have no connection to reality.

Except for compounding interest, percent change, percent difference, multi-variate statistics... I'm quite dumbfounded to read this comment considering nearly all of finance is done through computers. Computers need algorithms in order to make predictions and algorithms are glorified formulas.

Re: Introduction to Differential Equations (2008)

#93
post #80

Earlier quoted context omitted.

The problem is math is entirely abstract. So you must learn the abstraction before applying it. Otherwise, you learn how to add 2 + 3, but you don't learn how to add n + m.

That strikes me as a strange way of looking at it. Most math taught to people who aren't pure mathematicians is taught precisely because of application to concrete situations. We value pure math largely because of the potential for future concrete applications. In case you aren't aware (and I wasn't until I trained to be a teacher, so this isn't meant to be condescending), there are alternative methods of teaching be…

I'm aware. Examples are given to demonstrate abstract concepts. However, that doesn't preclude you from needing to learn the abstract concepts eventually. Otherwise, you go back to knowing times tables for 2's and 3's, but not n's and m's.
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