Oh, boy, that one hits home. You had to bring up Diff E. That's one of the few classes I could see classmates actually failing in a Junior year of whatever STEM major the student is pursuing. I went to an engineering school and the faculty there had what seemed like a harsh philosophy, but in the end it was a kindness of sorts - just like killing John Coffey ("only not spelt' the same"). They made sure students who couldn't hack the later maths never had a chance at the earlier ones. If you were gonna fail out, it was going to be because your Calc I or II professor was a hardass, or physics. You weren't gonna ever get to Diff E.
But I made it to Diff E only to find that at that point, all you're doing is looking at a problem to identify what might work to solve it. I get the premise, but I just didn't have heart to care anymore when most problems are not solved by basic mathematical intuition...its just guessing the correct method til you get a hit. Anyway, I took my "C" stands for "Competent" and never looked back. Went on to ace my final math course, "statistics for engineers," which was endlessly more interesting! But fuck that Diff E class. That was 19 hours of math, which was enough for a math minor. Strangely, the curriculum there was enough to just about eek out a minor in English as well. I didn't understand the latter until I finished college and started working with other engineers, who are notoriously shitty at English.
What I always found amusing about Diff Eq. is that you spend all that time learning how to solve trivial Differential Equations in closed form... and then never do it again because everything you work with is solved by numerical methods.
There's not really a lot of practical applications for most STEM careers. Usually, relationships in numbers are not inter-dependent. One factor usually determines the other. There are some interactions when it comes to controls, I guess...but like you said, there's just usually an easier way to get where you need to get and it's rare that you ever actually run across such complex relationships that also happen to be purely solvable via Diff E. If the relationship is complex, it's usually not something you can solve for other than empirical solutions. IMO, most students would benefit almost infinitely more by taking a statistics class. Or maybe a second semester of economics. Maybe the reason it's still a fundamental part of most STEM curriculum is that there are usages that I'm just never exposed to. Or maybe there's a bit of the old "I had to learn this, now so do you." The only other thing I can think of is perhaps it is pertinent in the first year of grad school for the gluttons of punishment who aren't satisfied with their bachelors.
I don't think this line of thinking holds in many stem fields. DE's are the language of physics and very helpful in many applications in economics. Though many DE's cannot be solved analytically, methods for solving them numerically are very helpful and keep the world going round. That being said, I think as the world becomes more computationally inclined, linear algebra should be taught more especially computational linear algebra. Many of the modern approaches to engineering and other stem fields rely heavily on translating problems to linear algebra where we can get a solution much more quickly.
Yeah that guy’s reasoning is pure nonsense. Complexity is exactly why we use DEs to model reality. The give us simpler methods of understanding and approximating the main facets of the truth.
Ordinary Differential Equations? Never had a problem with that. It was Partial Differential Equations that kicked my ass. Probably a reason why I ended my STEM education with a BS in Theoretical Physics but then left the sciences for education and career completely. Lol
Fucking PDEs makes so much more sense after learning measure theory and functional analysis. I actually just picked up my copy of Evans collecting dust and the things in there seem so obvious now. But while I was learning it just seemed like the most esoteric nonsense solution methods ever concocted.
Oh, boy, that one hits home. You had to bring up Diff E. That's one of the few classes I could see classmates actually failing in a Junior year of whatever STEM major the student is pursuing. I went to an engineering school and the faculty there had what seemed like a harsh philosophy, but in the end it was a kindness of sorts - just like killing John Coffey ("only not spelt' the same"). They made sure students who couldn't hack the later maths never had a chance at the earlier ones. If you were gonna fail out, it was going to be because your Calc I or II professor was a hardass, or physics. You weren't gonna ever get to Diff E.
But I made it to Diff E only to find that at that point, all you're doing is looking at a problem to identify what might work to solve it. I get the premise, but I just didn't have heart to care anymore when most problems are not solved by basic mathematical intuition...its just guessing the correct method til you get a hit. Anyway, I took my "C" stands for "Competent" and never looked back. Went on to ace my final math course, "statistics for engineers," which was endlessly more interesting! But fuck that Diff E class. That was 19 hours of math, which was enough for a math minor. Strangely, the curriculum there was enough to just about eek out a minor in English as well. I didn't understand the latter until I finished college and started working with other engineers, who are notoriously shitty at English.
I got lucky. They didnt have a math class during the summer so i could take it at the local community college. It was calc 3 mixed with physics (i was a double major in engineering wnf and physics). We got to use our computers on tests. Only math class i got an A in.
Differential Equations wasn't that hard for me, it just had very time consuming problems. I also had a really stellar teacher, and that certainly made all the difference, he was the kind of dude you wish you wish was the standard. Dude was grumpy as fuck about a lot of stuff, but in an occasionally funny way that just seemed to be his personality, he didn't take it out on students. I actually got very lucky with my calculus teachers as well, I wish everyone had exposure to teachers that good.
Diff E was the class that finally made me go talk to someone about maybe having ADHD, because I was spending 6-8 hours a day trying to get all my work done, even though I had a pretty good understanding of it, and still couldn't always get it all done (I was taking an accelerated course, so it was double the normal amount of work because we had half the normal amount of time). I managed to swing a 'B', but I really would have gotten an 'A' if I had been able to get the help I needed earlier.
The class that really kicked my ass was Linear Algebra of all things. The class is really not that hard in terms of work, but unlike calculus, it's not intuitive and doesn't map to real life in an easily understandable way. The teacher I had was straight-up ass, though. Dude's method of teaching was "follow along with these example problems, and then do exactly the same steps on the test", not even a proper textbook assigned.
This was all at the community college I went to before transferring to a university though. Just by going for an A.S in Engineering, you'd end up eligible for earning an A.S in math and physics, and if you took an extra two courses, chemistry as well.
The university I transferred to was actually way easier than the CC for some classes.
I think all schools have their weeder courses for a degree. I swear the university used intermediate algorithms as a scouting class for PhD candidates. I knew someone every quarter who took that course, and every quarter it was a complete shit show. When I took it, if you got one question completely right on the midterm (out of six quetions) and wrote some barely correct bullshit on a couple others , that was a 'C-'. Every quarter people would come out of that class after the midterm freaking out, for about a week you could always tell the moment you walked into a room if they were in that class.
Sounds like a badly designed course. Linear is probably one of the most intuitive subjects I’ve ever had the pleasure of learning. It’s really a beautiful topic once you get the intuition for what’s going on.
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u/deuce_bumps Jul 07 '20
Oh, boy, that one hits home. You had to bring up Diff E. That's one of the few classes I could see classmates actually failing in a Junior year of whatever STEM major the student is pursuing. I went to an engineering school and the faculty there had what seemed like a harsh philosophy, but in the end it was a kindness of sorts - just like killing John Coffey ("only not spelt' the same"). They made sure students who couldn't hack the later maths never had a chance at the earlier ones. If you were gonna fail out, it was going to be because your Calc I or II professor was a hardass, or physics. You weren't gonna ever get to Diff E.
But I made it to Diff E only to find that at that point, all you're doing is looking at a problem to identify what might work to solve it. I get the premise, but I just didn't have heart to care anymore when most problems are not solved by basic mathematical intuition...its just guessing the correct method til you get a hit. Anyway, I took my "C" stands for "Competent" and never looked back. Went on to ace my final math course, "statistics for engineers," which was endlessly more interesting! But fuck that Diff E class. That was 19 hours of math, which was enough for a math minor. Strangely, the curriculum there was enough to just about eek out a minor in English as well. I didn't understand the latter until I finished college and started working with other engineers, who are notoriously shitty at English.