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Old 3rd January 2013, 12:42 PM   #41
SY is offline SY  United States
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...in using them I wasn't sure I was really doing anything new which needed a special name for it.
Maybe that's my issue. So, if I write sqrt2 as √2 or 21/2, is it still a surd?
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Old 3rd January 2013, 12:58 PM   #42
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I went to a very good technical high school in the late 70's, and I don't remember doing any calculus, surds or any of the other stuff mentioned in this thread in my 'O' levels, physics or maths. Just basic manipulation of log tables in calculations. It certainly wasn't part of the exams, (I got a B in maths, and an A in Physics, so I would have noticed. )
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Old 3rd January 2013, 03:28 PM   #43
DF96 is offline DF96  England
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So that stuff disappeared from O-level some time between early 1970s and late 1970s. Grade inflation is not a recent phenomenon; early 1970s exams were a bit easier than the 1960s exams we used for practice.
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Old 3rd January 2013, 09:02 PM   #44
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So that stuff disappeared from O-level some time between early 1970s and late 1970s. Grade inflation is not a recent phenomenon; early 1970s exams were a bit easier than the 1960s exams we used for practice.
But they may have been marked harder. My JMB maths, further maths and physics A levels, taken around 1970, can't have been very hard to pass, and general studies must have been very easy because there was no course.

I'm always impressed by how much people in places like this know about the maths of feedback systems. My grasp of transforms is really shaky, and partial fractions drive me up the wall. If standards have been falling for years, how come so many people know so much?

Looking back, it's amazing that the expansion of higher education around the time of the Wilson government actually worked. How did so many more students pass their A levels so suddenly?

I don't see what politically-acceptable arguments drove the recent expansion. Unlike in my time, there isn't a credible vision of a future in which universal HE will be useful. The idea that a few countries will be fully occupied with clever stuff, whilst the others do all the menial tasks, should have perished ages ago. Assuming capitalism stumbles along indefinitely, we need to recreate our own downtrodden class of manual workers.

China may radically change the world. What's education like there?
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Old 3rd January 2013, 10:54 PM   #45
DF96 is offline DF96  England
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Originally Posted by PlasticIsGood
If standards have been falling for years, how come so many people know so much?
The smartest people still know a lot in every generation. However, their education may still have taught them less and less while not destroying their ability to learn more. I was surprised to hear a communications professor tell a combined MSc/MEng 4th year class (in response to a question) that radio receiver spurious responses were too complicated for the course - stuff which I began to learn as a teenager 30 years earlier. People capable of understanding stuff will still understand it if they find a need to do so, but they may no longer be taught it at university.

For example, servo systems was not part of my physics course but the required complex number stuff was. When I had to learn it in industry I managed OK, then realised that it also enabled me to understand negative feedback in audio.

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How did so many more students pass their A levels so suddenly?
They didn't. What happened was that university entrance criteria were relaxed, especially at the newer universities. The gradual A-level grade inflation then meant that over the next few decades the entrance criteria were 'increased' again. In the early 1970s you could get into Imperial College with 2 Bs; now you would probably need 3 As - which may actually be a reduction in requirements.

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I don't see what politically-acceptable arguments drove the recent expansion.
Suggestions would stray too far into politics for DIYaudio so I won't go there.
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Old 4th January 2013, 01:15 AM   #46
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Maybe that's my issue. So, if I write sqrt2 as √2 or 21/2, is it still a surd?
It's the algebra of surds that's important. Use whatever symbol you like. It's a surd for as long as you don't convert it into a number.

You covered the ground at school, I'm sure. At the most obvious level, you treat them algebraically so you can combine and simplify before evaluation, so avoiding the accumulation of error. You learned the rules.

Revision:Surds - The Student Room

I guess their peculiar rules of manipulation allow them to be used in transforms, rather like complex numbers? I vaguely remember some trick related to a proof of the binomial theorem.
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Old 4th January 2013, 01:18 AM   #47
SY is offline SY  United States
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But it is a number. You can't convert to an explicit numeral unless you have an infinitely large piece of paper, so the distinction still eludes me.
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Old 4th January 2013, 02:36 AM   #48
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Originally Posted by DF96 View Post
The smartest people still know a lot in every generation. However, their education may still have taught them less and less while not destroying their ability to learn more. I was surprised to hear a communications professor tell a combined MSc/MEng 4th year class (in response to a question) that radio receiver spurious responses were too complicated for the course - stuff which I began to learn as a teenager 30 years earlier. People capable of understanding stuff will still understand it if they find a need to do so, but they may no longer be taught it at university.

For example, servo systems was not part of my physics course but the required complex number stuff was. When I had to learn it in industry I managed OK, then realised that it also enabled me to understand negative feedback in audio.


They didn't. What happened was that university entrance criteria were relaxed, especially at the newer universities. The gradual A-level grade inflation then meant that over the next few decades the entrance criteria were 'increased' again. In the early 1970s you could get into Imperial College with 2 Bs; now you would probably need 3 As - which may actually be a reduction in requirements.
What? Ours has been an epoch of immense technical and scientific achievement. If the quality of general education was not important for this rate and breadth of advancement, then surely it quite simply doesn't matter at all. In that case, we may as well forget about it and do something else instead. If it is important, then it did a good job.

I don't feel we are close to agreement on grade inflation. At the very least, your highlighting of the issue seems reductionist: you are projecting a complex system onto too few axes ( that's my first ever pun).

One key element of the expansion in the 60s and 70s was the grants system, which made university free. Kids from poor families had something to aim for. Funding for schools, welfare benefits, women's emancipation, and advances in the technology of education were a few of many other factors.

I'm still hoping someone will chip in from somewhere that's still making progress. What's education like in Brazil, Ghana, China, ROK?
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Old 4th January 2013, 03:59 AM   #49
jcx is offline jcx  United States
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you are projecting a complex system onto too few axes
Quaternions or Gibb's abortion, the cross product, "axial vectors" lets you use one more axis - but you really want Clifford Algebras with exterior product, multivectors, Spinors...

(complex numbers are the "spinors" of the 2-d plane)

a really good education system could sieze on ideas like Hestenes' "Geometric Algebra", introduce it at the same time as complex numbers, vectors

Last edited by jcx; 4th January 2013 at 04:22 AM.
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Old 4th January 2013, 05:11 AM   #50
wahab is offline wahab  Algeria
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Originally Posted by SY View Post
But it is a number. You can't convert to an explicit numeral unless you have an infinitely large piece of paper, so the distinction still eludes me.
More precisely it is two possible numbers in the case of a square root ,
hence the surd cant be always removed since it would forcibly cancel
a solution , thus leading through intermediary operations to a false result.

Anectdoticaly , any entire number can be written as a never ending
decimal number in such a way :

1 = 0.99999999......
thus , 2 = 1.99999999......

And so on.....
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