In my experience, it depends tremendously on the specific institution.
I've worked at two community colleges, where, by law, there are no entrance requirements other than the ability to pay the fees, and be at least 18 years old. Tragically, and almost unbelievably, by 2015, the majority - well over 50% - of adult students at those institutions had skills appropriate to 4th to 6th grade level in language,focus, attention span,science, math, personal responsibility, etc. (This matches the results of that large American study, where 50% of junior-college students couldn't use a bus time-table to plan a route from point A to point B to arrive at a specified time and day.)
I also worked for a while at a very prestigious technical Polytechnic university here in Canada (both trade certificates and 4-year degree programs are offered.) Twenty or more students apply for every seat available there, and evidently the laws governing admissions to public universities are different in Canada, so this institution is able to apply a drastic weeding-out process up-front. Applicants have to go through interviews and placement exams before gaining admission, and only the 5% or so who perform best are actually admitted.
Not surprisingly, I had many excellent, even exceptional, students in the classes I taught there. There was still a range of abilities, but the majority of students varied from good to excellent.
It's not that the entire human race has now become incompetent. Mercifully, there are still lots of smart, competent, young people out there.
But what concerns me is that clearly, there is now also a second, and much larger group of completely lost souls, stuck in adult bodies, but with the skills and abilities of a normal elementary-school student. Those are the young people I worry about, and that is the group that is dragging down standards in those educational institutions who don't have the luxury of filtering them out at the admissions level.
-Gnobuddy
British Columbia.
In California, four-year colleges (like the University of California campuses) all have entry requirements. But two-year colleges - junior colleges - have a different mandate, having been originally created to provide free education to anyone who wanted it, as a public service ( 4Faculty ).
California's junior colleges haven't been free for a long time now, and some include two-year transfer programs with articulation agreements with the University of California system, so that a good student can get the first two years degree courses at much lower cost at a junior college, then transfer to a four-year college to finish her degree. But traces of their origins remain, and the programs I taught into had no admission requirements - you had to be over 18, and able to pay the fees. That was it.
There were other unintended consequences of that policy. A significant percentage of JC students, it turns out, are recently paroled prisoners, attending college as part of their parole requirements. As a student, or a teacher, you never knew if you had a violent mugger with a hair-trigger personality in your class - the institution didn't tell you, because that would violate the mugger's right to privacy. Never mind that by denying the teacher that information, they were increasing the risk of violence to everyone in the classroom, including the teacher. And by denying that information to other students, they were denying them the option to maybe not take that particular class out of fear for their personal safety.
That scenario became scarily close to reality for me once, when I spotted peculiar body movements and facial expressions on one student. I asked him quietly if he was okay, if he wanted to leave, and he wordlessly shook his head "No", then nodded "Yes", and left. A few days later he told me that just before the incident, he'd just received a phone call that there had been a drive-by shooting outside the house where his girlfriend and baby were living.
And that he had once been in prison for going into a red rage and beating another man to pulp, with no memory of having done so after the fact. And that the phone call about the drive-by shooting had made him feel like he was starting to lose it. -Gnobuddy
Thanks to mention the integral of 1/x.
Indeed, the integral of 1/x is Log(x)
It is a bit peculiar because the integrals of
x, x^2, x^3,...or
1/x^2, 1/x^3, 1/x^4,....
are simple and don' t need a new function.
There is sort of a hole,
x^n has a simple integral which is x^( n+1)/( n+1) This works for all n, integer positif or negatif, except for n=-1 where the integral of x^-1 is log(x)
Going the other way, derivating, there is no hole, the derivative of x^n is nx^(n-1) for any n.
Mind boggling result:
Log(x) comes in to fill the hole when integrating x^n....A hole at x^-1 alias 1/x.
Indeed, the integral of 1/x is Log(x)
It is a bit peculiar because the integrals of
x, x^2, x^3,...or
1/x^2, 1/x^3, 1/x^4,....
are simple and don' t need a new function.
There is sort of a hole,
x^n has a simple integral which is x^( n+1)/( n+1) This works for all n, integer positif or negatif, except for n=-1 where the integral of x^-1 is log(x)
Going the other way, derivating, there is no hole, the derivative of x^n is nx^(n-1) for any n.
Mind boggling result:
Log(x) comes in to fill the hole when integrating x^n....A hole at x^-1 alias 1/x.
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Despite the fact that I'm not a "math" guy (in that I don't get excited about writing out proofs on the board), I do find this particular situation rather interesting, even more so when you consider the point that Gnobuddy brought up, which is just how many things it can describe.
The integral of 1/x with respect to x, is ln(x) + c, where ln is a natural/Napierian logarithm and c an arbitrary constant of indefinite integration.
There is absolutely nothing strange about this. In this case, the generic rule for polynomial term integration of the form ax^n, which in general is, { ax^(n + 1) }/(n+1) breaks down and connot apply. In fact, the denominator becomes n + 1 = -1 + 1 = 0 which does not apply for division, except in the case of a zero numerator.
There is absolutely nothing strange about this. In this case, the generic rule for polynomial term integration of the form ax^n, which in general is, { ax^(n + 1) }/(n+1) breaks down and connot apply. In fact, the denominator becomes n + 1 = -1 + 1 = 0 which does not apply for division, except in the case of a zero numerator.
My brain is wired like yours. Pure math for pure math's sake doesn't attract me, but its ability to explain things in the world around us always fascinated me.
There are so many cases of mathematicians proudly inventing some completely abstract thing, purely as an intellectual exercise, only for it to turn out to have actual applications years, decades, even centuries later. Like Bessel functions (which were described by Bernoulli in the early 1700s) turning out two centuries later to be the perfect tool to describe frequency modulation (radio).
-Gnobuddy
Switching power supplies look intimidating for the vast majority of members, but I think, it is time to try to break this intimidation.
A switching power supply does not necessarily need a feedback loop from the output to the controlling circuitry. This can be avoided. The advantage is getting a power supply with no intrinsic voltage regulation but with the advantage of avoiding the use of a bulky iron cored mains transformer. To achieve this, a square wave generator with a duty cycle of less than 50% can be used. The square wave would drive a switching MOSFET which drives the primary of a switching transformer. On power on, the duty cycle should be gradually increased from zero to just under 50%. This arrangement requires an additional flyback coil to return the magnetisation energy to the power source instead of letting it dissipate itself in damaging high voltage ringing of the switching transformer.
I would like to add, one can use variable frequency switching with a fixed duty cycle. The switching would be suspended when the output reaches the required voltage and restarted when it falls below a certain threshold.
The major issue in designing a switching power supply, is to keep dangerous ringing from destroying switching components and from dissipating too much power. There is also the issue of avoiding switching transformer core magnetic saturation as this results in the primary inductance dropping and the mains switching current rising to destructive values.
In short:
a) keep high voltage ringing well under control
b) never allow the core to magnetically saturate
The actual problem with switching power supply design is there are many ways to implement one.
A switching power supply does not necessarily need a feedback loop from the output to the controlling circuitry. This can be avoided. The advantage is getting a power supply with no intrinsic voltage regulation but with the advantage of avoiding the use of a bulky iron cored mains transformer. To achieve this, a square wave generator with a duty cycle of less than 50% can be used. The square wave would drive a switching MOSFET which drives the primary of a switching transformer. On power on, the duty cycle should be gradually increased from zero to just under 50%. This arrangement requires an additional flyback coil to return the magnetisation energy to the power source instead of letting it dissipate itself in damaging high voltage ringing of the switching transformer.
I would like to add, one can use variable frequency switching with a fixed duty cycle. The switching would be suspended when the output reaches the required voltage and restarted when it falls below a certain threshold.
The major issue in designing a switching power supply, is to keep dangerous ringing from destroying switching components and from dissipating too much power. There is also the issue of avoiding switching transformer core magnetic saturation as this results in the primary inductance dropping and the mains switching current rising to destructive values.
In short:
a) keep high voltage ringing well under control
b) never allow the core to magnetically saturate
The actual problem with switching power supply design is there are many ways to implement one.
I sometimes feel I have slipped into a parallel universe here. I left school (and home) at 16, never got to calculus, and that was the end of my formal education.
But I can read an analogue clock (unlike many of my 16 year old grandson's classmates) and a bus timetable. But the ferry timetables on Lake Como sometimes baffle me!
But I can read an analogue clock (unlike many of my 16 year old grandson's classmates) and a bus timetable. But the ferry timetables on Lake Como sometimes baffle me!
I feel like Rip Van Winkle, who went to sleep and woke up in a future in which nothing was familiar any longer (in the story, the American Revolution took place while he was asleep.)
Me, I woke up to find melting icecaps, 60% of all vertebrate life has gone extinct, an equal or higher percentage of invertibrates gone, dead or dying coral reefs everywhere, an ocean filled with plastic, and entire continents on fire. Oh yeah, and lots of adults who can't read a clock, can't make change, can't focus on any one thing for more than ten seconds, can't function without checking their pacifier, sorry, smartphone, ever two minutes.
What the heck happened while I was asleep?
-Gnobuddy
Back to the original topic: Youth
I just spent 2.5 days conducting job interviews with over 100 youths. All of the them were college students so mostly in their early 20s. None of them were stupid, not one. All were well dressed and well prepared, most of them very well spoken, fun and interesting to talk to. All had good technical skills and most had good people skills. They were just nervous, for the most part.
Yes, many were mentally young and inexperienced, but so were we at that age. I'd bet we were worse. Generally I was very impressed. I'd hire almost all of them, but fortunately I don't have to, since I have just 5 job openings. Basically I'm hoping they want to come work for me.
I'd say No - not more stupid.
I just spent 2.5 days conducting job interviews with over 100 youths. All of the them were college students so mostly in their early 20s. None of them were stupid, not one. All were well dressed and well prepared, most of them very well spoken, fun and interesting to talk to. All had good technical skills and most had good people skills. They were just nervous, for the most part.
Yes, many were mentally young and inexperienced, but so were we at that age. I'd bet we were worse. Generally I was very impressed. I'd hire almost all of them, but fortunately I don't have to, since I have just 5 job openings. Basically I'm hoping they want to come work for me.
I'd say No - not more stupid.
I went about 3 weeks into an easy statistics class in college without bothering to buy the text. I sat near the front, and one day after telling us again to turn to a specific example the professor look at me and said "do you HAVE a textbook?". I told him no, but I didn't need one, and he told me to get one before I come back to class...
Whose name did I see on the cover when I went to buy it?
Thanks for pointing that out. The poor fellow probably went into total panic mode when he got out of view. My 11th grade son lives with this problem, the trigger can be quite benign, and his life is often pure hell over such simple things.
Just something to keep in mind if someone's response seems out of proportion.
We sure didn't see much of it, Michael.
But I do remember one kid from 2nd grade, that would have been '72, who would get really nervous sometimes. He asked his older brother for a "nerve pill" in the lunchroom once, his voice was shaky. His brother was 4th grade or so and had real concern on his face. Now, I look back on that sadly and hope he's managed OK.
My son's stems from his tuberous sclerosis, in which autism/Aspberger's is common (25-50%). And yes, he is seriously concerned about being able to survive in this daunting world when he can't manage things that are simple for others. We have traced many episodes back to that root cause.
But I do remember one kid from 2nd grade, that would have been '72, who would get really nervous sometimes. He asked his older brother for a "nerve pill" in the lunchroom once, his voice was shaky. His brother was 4th grade or so and had real concern on his face. Now, I look back on that sadly and hope he's managed OK.
My son's stems from his tuberous sclerosis, in which autism/Aspberger's is common (25-50%). And yes, he is seriously concerned about being able to survive in this daunting world when he can't manage things that are simple for others. We have traced many episodes back to that root cause.
Let me guess.....there is a new version every year or two and the only things that change are the homework questions.
One of my brothers has "written" over 50 books, many are advanced level college texts in the medical field......many of those he has never read!
He is a well respected research PHD, and dean of a med school. Often unknown writers will ask him to "co-author" or "edit" a book, so that a well known author's name is attached to the book increasing the chances of it being used as a textbook or research volume in a very specific field. These are generally not seen in general circulation, but sold through specialty publishers like Elsevier. Occasionally one does show up on Amazon.
Amazon.com: Rickettsial Infection and Immunity (Infectious Agents and Pathogenesis) eBook: Burt Anderson, Herman Friedman, Mauro Bendinelli: Books
When I compare my upbringing with those much younger, there seesm to be a similar pressure but of a very different nature.
We were bullied and endured a very strict and austere ambience, with much physical abuse to ensure, often, terror.
Now with PC that is largely eliminated, but they have this avalanche of information, a greater expectation of personal decision making and achieving autonomy, earlier, and in what to many seems a world in disarray and ennui.
Even back in my college days, students would get wise to that crap and share xerox’es (remember those?) of the examples and problem sets at the end of the chapters. Not exactly legal, but neither is extortion.
There was however one class (basically EE101) where the prof used the same book and edition for years and years and years. They would show up in pretty tattered condition at the bookstore. He relied heavily on the example problems all throughout the semester. All exam problems were something like “Change the resistor from 2 to 3 ohms and re-work the problem”. Until the final. ALL new problems. Nothing harder than anything we had done for the past 3 months. It had students CRYING. The same ones that cried were the ones who had trouble with Thevenin-Norton. Fer crissakes, everyone knows you just put the two stupid resistors in parallel! Or put a load on it, and measure the current.... then do a little thing called math. They do teach that in grade school, don’t they? I would hate to see what it’s like today.
There was however one class (basically EE101) where the prof used the same book and edition for years and years and years. They would show up in pretty tattered condition at the bookstore. He relied heavily on the example problems all throughout the semester. All exam problems were something like “Change the resistor from 2 to 3 ohms and re-work the problem”. Until the final. ALL new problems. Nothing harder than anything we had done for the past 3 months. It had students CRYING. The same ones that cried were the ones who had trouble with Thevenin-Norton. Fer crissakes, everyone knows you just put the two stupid resistors in parallel! Or put a load on it, and measure the current.... then do a little thing called math. They do teach that in grade school, don’t they? I would hate to see what it’s like today.
When you have only enough money to choose between either food or textbooks, food always wins. Through my entire college career, I only bought a handful of textbooks, because that's all I could afford.
There were plenty of equally good textbooks in the local libraries, and plenty of classmates who would gladly let me copy down the homework problems from the book in exchange for my tutoring them on how to solve those same problems.
For what it's worth: a spouse of a friend wrote a college-level textbook that's used in several colleges in this area. It took him several years of long hard nights and weekends to write the book, not to mention the many years of hard work to get the Ph. D that qualified him to write it in the first place.
He earns about $100 a year in royalties from it.
The academic world tends to be quite different from the heavily money-driven world of most people. Academic prestige and reputation are prized far more than money, and so people will put out vast efforts to write a book that brings them virtually no money, but does bring them prestige, at least in their own imagination.
That doesn't make things any better for the unfortunate students who are expected to cough up hundreds of dollars a semester to buy textbooks that are, as others have said, barely different from hundreds of other textbooks. Fortunately, an increasing number of colleges are starting to use some of the many online free textbooks that are now available, at least at the lower levels of college education. (You are not going to find free books at a sufficiently advanced level to get you through, say, a Master's degree.)
For perspective: where I live, the workers who hold up the "Stop!" / "Slow!" signs at roadside construction projects make about $21 an hour. They earn more in one working day than that college professor earns in a year from his book royalties.
The sign-holders don't need any educational qualifications beyond a high-school diploma. They need their own pair of steel-toed boots, a bright safety vest and helmet, and a half-Saturday's "training", presumably to make sure they can tell the difference between the word "Stop" and the word "Slow".
-Gnobuddy
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