Much of your experience was Caltech specific, and will simply not translate to other schools. Caltech is famous for this - more so than schools like MIT, etc.
1. I learned the hard way, as did others, that one should still memorize with open book exams (or at the least make a 1-2 page cheat sheet). Why? Because there was a time limit and most professors would not alot enough time for people to even look up everything they needed in the textbook. Sure, if they increased the time by 50-100%, you'd do just fine with memorizing.
I'm not even hypothesizing there. After one open book exam I went and asked everyone who got a good score - most had incorporated some level of memorizing. And clearly most who did not memorize at all got a poor score (which is less surprising than it should be, because most students will do poorly regardless ;-) Still, I was the clear exemplar of one who improved from "below average" to "one of the top students" within the duration of one semester when I finally embraced that some level of memorization would be needed.
2. True, and I can relate to trig identities - most of which I remember 25 years later - and even after over a decade of not needing them. However, when I got to more advanced topics in math, the frequency with which I would need to use them dropped significantly, and the approach of "Just do lots of problem sets and you'll passively memorize" failed me in grad school.
> we were not expected to use the Laplace transform until its derivation was demonstrated. This applied to all the formulas used. FFTs too.
Did they teach you measure theory before those transforms? Did they teach you measure theory before probability? Did they teach you the theory of distributions before the Dirac-Delta function?
> Which is why some engineering schools are better than others. I applied to the USN&WR list of "top 10 engineering schools in the US". Caltech was #2.
I went to a top 5 engineering school. Can assure you Caltech's approach is not the norm.
I am sadly well aware of that. Caltech was known as unique at the time, I wonder what it is like 40 years later.
1. It was rarely necessary to look anything up. What was on the exam was reliably in the notes or in the assigned textbook. I don't recall ever memorizing things, and managed an A- average. My innate abilities were completely average there, and we all knew who the really smart ones were, like Hal Finney. What I did do to prepare, however, was ensure I attended every lecture and took comprehensive notes, make sure I could solve every homework problem, and every midterm problem (in trolling for the final). I did not look at prior year's stuff.
2. I didn't attend grad school, so can't comment there. But I did match wits with Masters engineers at Boeing, and would wind up fixing their work, too, though far more rarely. That group eventually offered me a position, though they had a Masters as a requirement.
Measure theory wasn't taught, at least in the undergrad courses I took. Neither was the theory of distributions.
> Can assure you Caltech's approach is not the norm.
1. I learned the hard way, as did others, that one should still memorize with open book exams (or at the least make a 1-2 page cheat sheet). Why? Because there was a time limit and most professors would not alot enough time for people to even look up everything they needed in the textbook. Sure, if they increased the time by 50-100%, you'd do just fine with memorizing.
I'm not even hypothesizing there. After one open book exam I went and asked everyone who got a good score - most had incorporated some level of memorizing. And clearly most who did not memorize at all got a poor score (which is less surprising than it should be, because most students will do poorly regardless ;-) Still, I was the clear exemplar of one who improved from "below average" to "one of the top students" within the duration of one semester when I finally embraced that some level of memorization would be needed.
2. True, and I can relate to trig identities - most of which I remember 25 years later - and even after over a decade of not needing them. However, when I got to more advanced topics in math, the frequency with which I would need to use them dropped significantly, and the approach of "Just do lots of problem sets and you'll passively memorize" failed me in grad school.
> we were not expected to use the Laplace transform until its derivation was demonstrated. This applied to all the formulas used. FFTs too.
Did they teach you measure theory before those transforms? Did they teach you measure theory before probability? Did they teach you the theory of distributions before the Dirac-Delta function?
> Which is why some engineering schools are better than others. I applied to the USN&WR list of "top 10 engineering schools in the US". Caltech was #2.
I went to a top 5 engineering school. Can assure you Caltech's approach is not the norm.