Differentiation P1

[Samsonknight]

Hi,

A-level Maths is going well, making good progress with the tutor from
imperial college - well I guess its going 20 times better then 2 years
ago....Anyway! I have a question , and would anyone be kind enough to
help me out here:

How would differentiate the following:

y = 4/3(pie)r^3

What would happen to the fraction as there is no power as normally the
rule would be dy/dx=nx^n-1 - would the fraction just disappear when
differentiated like a single whole number? (because theres no power
next to it) How do you differentiate PIE? does the same rule apply ,
or would it be different because its pie. If I were to take a pot
guess at answering this question I would probably use the rule
dy/dx=nkx^n-1 and come to the following conclusion:

dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".

Thank you all!

P.S.

When is the deadline for the UCAS forms, my tutor said its now moved
from December to April.

[Robert de Vincy]

Post by Samsonknight
Hi,
A-level Maths is going well, making good progress with the tutor from
imperial college - well I guess its going 20 times better then 2 years
ago....Anyway! I have a question , and would anyone be kind enough to
y = 4/3(pie)r^3
What would happen to the fraction as there is no power as normally the
rule would be dy/dx=nx^n-1 - would the fraction just disappear when
differentiated like a single whole number? (because theres no power
next to it) How do you differentiate PIE? does the same rule apply ,
or would it be different because its pie. If I were to take a pot
guess at answering this question I would probably use the rule
dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".
Thank you all!

Pi. Pi, pi, pi, pi. PI, PI, PI, PI, PI!


That feels better.

Post by Samsonknight
P.S.
When is the deadline for the UCAS forms, my tutor said its now moved
from December to April.

When I applied (for 2003 entry), the "deadline" (I'm sure MMH will
enlighten you as to how it's not really a deadline in any strict sense
of the word) was in the middle of January. Did it change to December
last year?

[Millie]

Post by Samsonknight
When is the deadline for the UCAS forms, my tutor said its now moved
from December to April.

According to the UCAS website...

http://www.ucas.ac.uk/student/faqs/pre_app.html#q4

"4. What are the UCAS deadlines for applying?

Completed applications should be at UCAS by the following dates.

15 October 2004 (for 2005 entry) for Dentistry, Medicine, Veterinary
Science and Veterinary Medicine. It is the same date for applications to
the University of Oxford and Cambridge University.

15 January 2005 for all other courses except Route B Art & Design
courses, for which 24 March is the deadline, though we advise applying
by 7 March.

The deadline for applications from outside the UK or EU is 30 June."

[Adam Atkinson]

Post by Samsonknight
A-level Maths is going well, making good progress with the tutor from
imperial college - well I guess its going 20 times better then 2 years
ago....Anyway! I have a question , and would anyone be kind enough to
y = 4/3(pie)r^3

Well, (i) I think you mean "pi", (ii) it's not _entirely_ clear
whether you mean [4 pi r^3]/3 or 4/[3 pi r^3]. I'll assume the former.

Post by Samsonknight
What would happen to the fraction as there is no power as normally the
rule would be dy/dx=nx^n-1 - would the fraction just disappear when
differentiated like a single whole number?

What? If you multiply f by a constant c, its derivative is also
multiplied by c. You can show this directly from the definition of
derivative. (Or use the product rule and check that it gives that
answer too, if you like.)

Post by Samsonknight
dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".

Please don't say "to times". I'm sure Robert de Vincy will have things
to say about "standard English" vs "do what thou wilt shall be the
whole of the law" but "to times" is hideous, so please don't say it.
Of course, I only think it's "hideous" because I'm a right-wing
reactionary prescriptivist.

But I digress.

Your formula is of the form y = cx^n, so yes the derivative is
ncx^(n-1). c, in this case, is 4pi/3 and n is 3. Your answer would
appear to be correct, but I'm not convinced you understand why.
Getting the basics right here is important, because you'll be
differentiating much harder things than this soon enough.

[Robert de Vincy]

Adam Atkinson did write:

[snips]

Post by Adam Atkinson

Post by Samsonknight
dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".

Please don't say "to times". I'm sure Robert de Vincy will have things
to say about "standard English" vs "do what thou wilt shall be the
whole of the law" but "to times" is hideous, so please don't say it.
Of course, I only think it's "hideous" because I'm a right-wing
reactionary prescriptivist.

If you say it's "hideous" and leave it at that, then you -- quite rightly --
deserve heaploads of scorn for being baselessly prescriptivist.

But in this instance, I can see where your feeling of "hideous"ness is
coming from, since it is, in effect, kicking out the standard jargon
[note: not a derogatory use of "jargon"] required for that subject. We
could easily have ended up with "to times" as the 'respected' and standard
term, but fate and the stars have coincided against such a situation, and
we (or, rather, people in mathematical discourse) have ended up with...
what?... "to multiply"?
Someone who uses "to times" is an 'outsider' and hasn't learnt the lingo
of that subject, even for something as elementary as multiplication.

It's when an appeal to some inherent sense of wrongness or an attempt to
rationalize an arbitrary choice by logic is used that I would scowl.

"Six times of one; multiplied by half a dozen of the other," as you might
want to say.

[Toby]

Post by Robert de Vincy
[snips]

Post by Adam Atkinson

Post by Samsonknight
dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".

Please don't say "to times". I'm sure Robert de Vincy will have things
to say about "standard English" vs "do what thou wilt shall be the
whole of the law" but "to times" is hideous, so please don't say it.
Of course, I only think it's "hideous" because I'm a right-wing
reactionary prescriptivist.

If you say it's "hideous" and leave it at that, then you -- quite rightly --
deserve heaploads of scorn for being baselessly prescriptivist.
But in this instance, I can see where your feeling of "hideous"ness is
coming from, since it is, in effect, kicking out the standard jargon
[note: not a derogatory use of "jargon"] required for that subject. We
could easily have ended up with "to times" as the 'respected' and standard
term, but fate and the stars have coincided against such a situation, and
we (or, rather, people in mathematical discourse) have ended up with...
what?... "to multiply"?
Someone who uses "to times" is an 'outsider' and hasn't learnt the lingo
of that subject, even for something as elementary as multiplication.
It's when an appeal to some inherent sense of wrongness or an attempt to
rationalize an arbitrary choice by logic is used that I would scowl.
"Six times of one; multiplied by half a dozen of the other," as you might
want to say.

hehe irrelevant fingy: in my day, it was 'lots of'...Which actually
helped, 'cause it meant I associated 'of' with the 'x' symbol, and so
verbalising maths and learning formulae went much more smoothly...

[Samsonknight]

Post by Robert de Vincy
[snips]

Post by Adam Atkinson

Post by Samsonknight
dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".

Please don't say "to times". I'm sure Robert de Vincy will have things
to say about "standard English" vs "do what thou wilt shall be the
whole of the law" but "to times" is hideous, so please don't say it.
Of course, I only think it's "hideous" because I'm a right-wing
reactionary prescriptivist.

If you say it's "hideous" and leave it at that, then you -- quite rightly --
deserve heaploads of scorn for being baselessly prescriptivist.
But in this instance, I can see where your feeling of "hideous"ness is
coming from, since it is, in effect, kicking out the standard jargon
[note: not a derogatory use of "jargon"] required for that subject. We
could easily have ended up with "to times" as the 'respected' and standard
term, but fate and the stars have coincided against such a situation, and
we (or, rather, people in mathematical discourse) have ended up with...
what?... "to multiply"?
Someone who uses "to times" is an 'outsider' and hasn't learnt the lingo
of that subject, even for something as elementary as multiplication.

Yeah, which is not a very good sign, I will probably fail as a result! :)

Post by Robert de Vincy
It's when an appeal to some inherent sense of wrongness or an attempt to
rationalize an arbitrary choice by logic is used that I would scowl.
"Six times of one; multiplied by half a dozen of the other," as you might
want to say.

Nah, I assure you I would never use the term "six times of one" - when
describing that form of equation, but instead "six times one" like every
other normal person that has learnt the "lingo".

Post by Robert de Vincy
--
BdeV

[Adam Atkinson]

Post by Robert de Vincy
But in this instance, I can see where your feeling of "hideous"ness is
coming from, since it is, in effect, kicking out the standard jargon
[note: not a derogatory use of "jargon"] required for that subject. We
could easily have ended up with "to times" as the 'respected' and standard
term

Could have done. Didn't.

Post by Robert de Vincy
, but fate and the stars have coincided against such a situation, and
we (or, rather, people in mathematical discourse) have ended up with...
what?... "to multiply"?

Just so.

Post by Robert de Vincy
Someone who uses "to times" is an 'outsider' and hasn't learnt the lingo
of that subject, even for something as elementary as multiplication.

Indeed. Though it may not be his fault. I've seen teachers who
deliberately say "to times" instead of "to multiply" and (eurgh) "share"
instead of "divided by", perhaps out of concern that expecting
people to learn a couple of new words in 5 years of secondary school
is just too much. At least "to times" can be defended on the grounds
that real non-mathematicians do actually say it. "What is ten share
five?" doesn't even reflect non-mathematical real world usage as far
as I know. (I've asked younger colleagues about this and they say "Oh,
yes, that's something maths teachers say.") Of course, I don't wish to
suggest that all maths teachers use or approve of this usage, as I'm
sure plenty don't.

I think that anyone doing A-level maths should certainly learn standard
usages. Saying "to times" in a university interview isn't something
I'd want to happen to anyone, though I'm sure interviewers have heard
worse. No doubt if you were generally very good you'd get in whether
or not you said "to times", but ... shudder.

A-level (and beyond) mathematicians are about the only people left who
still say "a die" instead of "a dice", of course. I was a little
pained to see Ian Stewart use "a dice" in an article in New Scientist
(or was it Scientific American?) recently: my guess is that it was a
deliberate attempt at slumming it.

[Samsonknight]

Post by Adam Atkinson

Post by Samsonknight
A-level Maths is going well, making good progress with the tutor from
imperial college - well I guess its going 20 times better then 2 years
ago....Anyway! I have a question , and would anyone be kind enough to
y = 4/3(pie)r^3

Well, (i) I think you mean "pi", (ii) it's not _entirely_ clear
whether you mean [4 pi r^3]/3 or 4/[3 pi r^3]. I'll assume the former.

This one - 4/[3 pi r^3] - or in english, 4 divided by 3 times pi times r to
the power of 3.

Post by Adam Atkinson

Post by Samsonknight
What would happen to the fraction as there is no power as normally the
rule would be dy/dx=nx^n-1 - would the fraction just disappear when
differentiated like a single whole number?

What? If you multiply f by a constant c, its derivative is also
multiplied by c. You can show this directly from the definition of
derivative. (Or use the product rule and check that it gives that
answer too, if you like.)

Post by Samsonknight
dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".

Please don't say "to times". I'm sure Robert de Vincy will have things
to say about "standard English" vs "do what thou wilt shall be the
whole of the law" but "to times" is hideous, so please don't say it.
Of course, I only think it's "hideous" because I'm a right-wing
reactionary prescriptivist.

Ok, I will bear that in mind in the near future.

Post by Adam Atkinson
But I digress.
Your formula is of the form y = cx^n, so yes the derivative is
ncx^(n-1). c, in this case, is 4pi/3 and n is 3. Your answer would
appear to be correct, but I'm not convinced you understand why.
Getting the basics right here is important, because you'll be
differentiating much harder things than this soon enough.

I agree, which is why I have posted this thread. I will see my tutor on
wednesday, so I will probably ask him this question to see what he has to
say in response of it.

Post by Adam Atkinson
--

[Adam Atkinson]

Post by Samsonknight

Post by Adam Atkinson
Well, (i) I think you mean "pi", (ii) it's not _entirely_ clear
whether you mean [4 pi r^3]/3 or 4/[3 pi r^3]. I'll assume the former.

This one - 4/[3 pi r^3] - or in english, 4 divided by 3 times pi times r to
the power of 3.

This has left me very confused. The "[]" were brackets. What you've
just said is not consistent with the answer you gave to the problem in
your earlier message. Your "in English" version doesn't help as it
doesn't have brackets in it either.

Do you mean (use a non-proportional font to view this message, please):

4 pi r^3
--------
3

or

4
--------
3 pi r^3

?

I was assuming the former, but you've just said it's the latter.

Post by Samsonknight

Post by Adam Atkinson
Getting the basics right here is important, because you'll be
differentiating much harder things than this soon enough.

I agree, which is why I have posted this thread. I will see my tutor on
wednesday, so I will probably ask him this question to see what he has to
say in response of it.

How were derivatives defined in your course?

Can you differentiate, e.g., f(x)=x^2 or f(x)=1/x from first
principles, i.e. using the defintion and not using any results you may
have been taught for products, quotients, function of a function, or
whatever?

[Samsonknight]

Post by Adam Atkinson

Post by Samsonknight

Post by Adam Atkinson
Well, (i) I think you mean "pi", (ii) it's not _entirely_ clear
whether you mean [4 pi r^3]/3 or 4/[3 pi r^3]. I'll assume the former.

This one - 4/[3 pi r^3] - or in english, 4 divided by 3 times pi times r to
the power of 3.

This has left me very confused. The "[]" were brackets. What you've
just said is not consistent with the answer you gave to the problem in
your earlier message. Your "in English" version doesn't help as it
doesn't have brackets in it either.
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4. I hate typing equations on the computer.

Post by Adam Atkinson
I was assuming the former, but you've just said it's the latter.

Post by Samsonknight

Post by Adam Atkinson
Getting the basics right here is important, because you'll be
differentiating much harder things than this soon enough.

I agree, which is why I have posted this thread. I will see my tutor on
wednesday, so I will probably ask him this question to see what he has to
say in response of it.

How were derivatives defined in your course?
Can you differentiate, e.g., f(x)=x^2 or f(x)=1/x from first
principles, i.e. using the defintion and not using any results you may
have been taught for products, quotients, function of a function, or
whatever?

To be honest , we have only recently started calculus, my tutor did cover it
and yes I understand what differentiation is for and how it can be applied.
We did go over first principles, like he made me draw a graph and find the
slopes , draw chords (which I understand) etc etc. However, the problem
arises when trying to solve equations using that method like X^3. I can
solve that equation via using the formula to get dy/dx= 3x^2 , but from
first prnciples on its own I am still rather shakey. I think I may go over
this again with my tutor next time I see him. If however, you are able to
help me pollish up on it , by showing me an example and then I can see how
you did it via that method , that would be nice. Alternatively, if you have
any linsk to any good web sites, I would be grateful.

Post by Adam Atkinson
--
Never attribute to malice that which is adequately explained by
incompetence.

[Alex Warren]

Post by Samsonknight

Post by Adam Atkinson
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4.

Oh dear.

Surely to pass GCSE you have to realise how dumb that sounds.


Alex

[Samsonknight]

Post by Alex Warren

Post by Samsonknight

Post by Adam Atkinson
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4.

Oh dear.
Surely to pass GCSE you have to realise how dumb that sounds.
Alex

Well don't worry then, if I am going to get sarcastically patronised or
flamed for using "to times"! I will in future not bother posting any
equations on here. I have gone through this same question with my ex peers
and first time round they understood what I was on about , and answered my
fairly simple question. I am now able to progress forwards and not
backwards.

[Ken Pledger]

Post by Samsonknight
....
Well don't worry then, if I am going to get sarcastically patronised or
flamed for using "to times"! I will in future not bother posting any
equations on here....

You may not have chosen the best news group for your original
question. There are mathematical groups which handle things like that,
and are usually quite polite. ;-)

The biggest is sci.math but you might prefer to try
alt.algebra.help (which takes "algebra" to include calculus) or even
alt.math.undergrad (as plenty of undergraduates ask questions like
yours).

Good luck!

Ken Pledger.

[Adam Atkinson]

Post by Samsonknight
Well don't worry then, if I am going to get sarcastically patronised or
flamed for using "to times"! I will in future not bother posting any
equations on here.

I wasn't flaming you. As an A-level mathematician you should
(probably) be saying "to multiply", "a die", "a pair of compasses" and
"protractor" rather than "to times", "a dice", "a compass" and
"angle-measurer".

Post by Samsonknight
I have gone through this same question with my ex peers
and first time round they understood what I was on about , and answered my
fairly simple question.

Well, I _guessed_ that you meant the first interpretation of what you
said, and I was right. I just wasn't _sure_. When talking to your ex
peers, you probably didn't need to type it. Even if you _said_ the
formula to them, the location of the pause probably told them what was
being divided by what.

[K. Edgcombe]

Post by Adam Atkinson

Post by Samsonknight
Well don't worry then, if I am going to get sarcastically patronised or
flamed for using "to times"! I will in future not bother posting any
equations on here.

I wasn't flaming you. As an A-level mathematician you should
(probably) be saying "to multiply", "a die", "a pair of compasses" and
"protractor" rather than "to times", "a dice", "a compass" and
"angle-measurer".

I must say I think there are more important things to worry about. Plenty of
my colleagues are happy to talk about "a dice", though I'm not. And although I
might wince at "to times" in an interview, it certainly wouldn't count against
you. I'm as pedantic as they come, but I try to keep it in its place.

Katy

[Adam Atkinson]

Post by K. Edgcombe

Post by Adam Atkinson
I wasn't flaming you. As an A-level mathematician you should
(probably) be saying "to multiply", "a die", "a pair of compasses" and
"protractor" rather than "to times", "a dice", "a compass" and
"angle-measurer".

I must say I think there are more important things to worry about.

Well of course there are. I thought it was worth mentioning, though.
If no-one ever tells him to say "multiply", how's he ever going to
find out?

Post by K. Edgcombe
And although
I might wince at "to times" in an interview, it certainly wouldn't count
against you.

I wouldn't expect it to. But I thought it was worth the small
investment of his and my time to nip the problem in the bud.

[Samsonknight]

Post by Adam Atkinson

Post by Samsonknight
Well don't worry then, if I am going to get sarcastically patronised or
flamed for using "to times"! I will in future not bother posting any
equations on here.

I wasn't flaming you. As an A-level mathematician you should
(probably) be saying "to multiply", "a die", "a pair of compasses" and
"protractor" rather than "to times", "a dice", "a compass" and
"angle-measurer".

Post by Samsonknight
I have gone through this same question with my ex peers
and first time round they understood what I was on about , and answered my
fairly simple question.

Well, I _guessed_ that you meant the first interpretation of what you
said, and I was right. I just wasn't _sure_. When talking to your ex
peers, you probably didn't need to type it. Even if you _said_ the
formula to them, the location of the pause probably told them what was
being divided by what.

As in ex-college friends that did do the A-level Maths course last year, and
yes I did have to type it as I had asked them over MSN.

Post by Adam Atkinson
--
If you're not part of the solution, you're part of the precipitate.

[Adam Atkinson]

Post by Samsonknight
As in ex-college friends that did do the A-level Maths course last year, and
yes I did have to type it as I had asked them over MSN.

Ah, whoops. Sorry.

[H Bergeron]

Post by Adam Atkinson

Post by Samsonknight
Well don't worry then, if I am going to get sarcastically patronised or
flamed for using "to times"! I will in future not bother posting any
equations on here.

I wasn't flaming you. As an A-level mathematician you should
(probably) be saying "to multiply", "a die", "a pair of compasses" and
"protractor" rather than "to times", "a dice", "a compass" and
"angle-measurer".

On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

And as a new A-level student the last thing he needs to be nagged
about is words.

Almost certainly, he needs to be nagged about the use of brackets,
about descriminating between variables and constants, about refraining
from the assumption that all unary operations distribute across
addition, about the need to learn how to deal with fractions, about
how to do basic algebraic manipulation accurately and about
structurings solutions clearly, fully and logically.

Unless he is very different from most students, he does *not* need -
at this stage of his studies - any traffic warden to plaster layers of
irrelevant rebuke over the windscreen of his self-esteem.

BTW, if your dictionary does not recognise "dice" as a synonym for
"die", you should buy a better dictionary.

[Adam Atkinson]

Post by H Bergeron

Post by Adam Atkinson
I wasn't flaming you. As an A-level mathematician you should
(probably) be saying "to multiply", "a die", "a pair of compasses" and
"protractor" rather than "to times", "a dice", "a compass" and
"angle-measurer".

On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

"constraint on mathematical thinking"? Oh, please.

Post by H Bergeron
And as a new A-level student the last thing he needs to be nagged
about is words.

I don't know that I was "nagging". In any event, he might as well
learn to say "to multiply" now rather than later. When would you
suggest? I'd have thought earlier, actually, but never mind.

Post by H Bergeron
Almost certainly, he needs to be nagged about the use of brackets,
about descriminating between variables and constants, about refraining
from the assumption that all unary operations distribute across
addition, about the need to learn how to deal with fractions, about
how to do basic algebraic manipulation accurately and about
structurings solutions clearly, fully and logically.

Still not sure about "nagging", but yes.

Post by H Bergeron
Unless he is very different from most students, he does *not* need -
at this stage of his studies - any traffic warden to plaster layers of
irrelevant rebuke over the windscreen of his self-esteem.

I remember people claiming to me years ago that correcting students'
spelling would crush the delicate flower that was their instinct for
self-expression, even if it lost them no marks. I thought that was
nonsense too.

Post by H Bergeron
BTW, if your dictionary does not recognise "dice" as a synonym for
"die", you should buy a better dictionary.

I don't agree. "a dice" has pretty well conquered in non-mathematical
contexts, but "a die" is still standard in mathematics.

[H Bergeron]

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson
I wasn't flaming you. As an A-level mathematician you should
(probably) be saying "to multiply", "a die", "a pair of compasses" and
"protractor" rather than "to times", "a dice", "a compass" and
"angle-measurer".

On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

"constraint on mathematical thinking"? Oh, please.

The proof of the pudding is in the eating. Judging by
cj7r68$9e$***@titan.btinternet.com you (with a little outside help)
appear to have annoyed the OP. Pissing off the student is one of the
best ways I know of hampering the development of their thinking.

Post by Adam Atkinson

Post by H Bergeron
And as a new A-level student the last thing he needs to be nagged
about is words.

I don't know that I was "nagging".

Then I humbly suggest that you don't know enough about usenet. The
large number of people who hang around simply to score points (and I
forgive you if you feel the urge to place me in that category), the
fact that the discourse is public, and the lack of behavioural cues
moderating the content of bald text mean, taken together, that
anything tending towards nitpicking is always likely to be taken
badly. Hence the conventions about not pointing out typos, etc.

Post by Adam Atkinson
In any event, he might as well
learn to say "to multiply" now rather than later. When would you
suggest?

I really don't care if he never does, and am amazed that you do. If he
ever does find that people whose opinion he values care whether he
says "multiply" rather than "times", he will presumably alter his
behaviour. But that is entirely up to him.

For myself, I think that punchy, if non-standard, verbalisations of
mathematical notation are great. I'd far prefer to talk about
"dotting" or "crossing" than to embark on some cumbersome
circumlocution about forming a certain kind of product. And I
shamelessy use the verbs "to log" and "to e".

That is not to say I don't make sure my students also understand the
poncy, "correct" ways of expressing such things. But I consider the
rites of passage into the mathematical community are about being able
to do the maths, not about saying "die" instead of "dice".

Post by Adam Atkinson
I'd have thought earlier, actually, but never mind.

Post by H Bergeron
Almost certainly, he needs to be nagged about the use of brackets,
about descriminating between variables and constants, about refraining
from the assumption that all unary operations distribute across
addition, about the need to learn how to deal with fractions, about
how to do basic algebraic manipulation accurately and about
structurings solutions clearly, fully and logically.

Still not sure about "nagging", but yes.

Post by H Bergeron
Unless he is very different from most students, he does *not* need -
at this stage of his studies - any traffic warden to plaster layers of
irrelevant rebuke over the windscreen of his self-esteem.

I remember people claiming to me years ago that correcting students'
spelling would crush the delicate flower that was their instinct for
self-expression, even if it lost them no marks. I thought that was
nonsense too.

Of course it is nonsense. The point is that you need to correct the
spelling in such a way that you don't completely alienate the student,
a feat that is entirely possible.

Do you not recognise that you may be in danger of losing the student
if you elicit the response, "if I am going to get sarcastically
patronised or flamed for using "to times"! I will in future not bother
posting any equations on here."?

Post by Adam Atkinson

Post by H Bergeron
BTW, if your dictionary does not recognise "dice" as a synonym for
"die", you should buy a better dictionary.

I don't agree. "a dice" has pretty well conquered in non-mathematical
contexts, but "a die" is still standard in mathematics.

If you claim that "die" tends to be favoured by authors, I will accept
your claim. If you assert that any significant proportion of their
readers care (or that the minority who don't conform are "wrong"), I
beg to differ.

[Adam Atkinson]

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

"constraint on mathematical thinking"? Oh, please.

The proof of the pudding is in the eating. Judging by
appear to have annoyed the OP. Pissing off the student is one of the
best ways I know of hampering the development of their thinking.

"he should be developing a growing disregard..."? I'd have thought
part of learning any subject is learning the lingo. cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
And as a new A-level student the last thing he needs to be nagged
about is words.

I don't know that I was "nagging".

Then I humbly suggest that you don't know enough about usenet.

I mentioned the issue to him once (and again in replies to messages
such as yours). I'd be "nagging" if I did it repeatedly, which I had
no intention of doing. I'd say "Oh, please say 'multiply' instead" or
similar in real life too... after a first offence (just in case) and
infrequently thereafter.

Post by H Bergeron
The
large number of people who hang around simply to score points (and I
forgive you if you feel the urge to place me in that category),

At least one person who's witnessed this exchange thinks from your
choice of pseudonym and the content of your earlier message that
you're trolling me. I wasn't quite sure one way or the other, and I'm
still not.

Post by H Bergeron
the
fact that the discourse is public, and the lack of behavioural cues
moderating the content of bald text mean, taken together, that
anything tending towards nitpicking is always likely to be taken
badly. Hence the conventions about not pointing out typos, etc.

On the whole I'd only point out typos if I saw the same ones
repeatedly, in which case I'd imagine that perhaps they weren't typos.
I wouldn't want someone to go through life getting "parallel" wrong
every time just because no-one had ever bothered to correct it. For
all I know, no-one had ever bothered to say to Samsonknight "'to
times' is a _very_good_ way to say that, but I think there's an _even_
better one, don't you?". I generally correct _everything_ on
it.cultura.linguistica.inglese, but that's a special case. If I know
the poster, I usually say "typo?" if I suspect it might be one because
it's not a mistake I'd expect him/her to make.

Post by H Bergeron

Post by Adam Atkinson
In any event, he might as well
learn to say "to multiply" now rather than later. When would you
suggest?

I really don't care if he never does, and am amazed that you do. If he
ever does find that people whose opinion he values care whether he
says "multiply" rather than "times", he will presumably alter his
behaviour. But that is entirely up to him.

Well of course it's up to him. I didn't know whether anyone had ever
mentioned it to him or not. I guessed not, which could be wrong.
I don't think I/you/anyone would be doing A-level students any favours
if we failed to at least mention in passing that "to times" and "100
share 5" might make listeners wince. My O-level teachers made a bit of
a joke out of dutifully saying "a pair of compasses" whenever anyone
called the instrument in question "a compass". I don't recall "to times"
being a problem, but I'm sure they'd have made the same sort of joke out
of dutifully saying "multiply" as and when.

Post by H Bergeron
For myself, I think that punchy, if non-standard, verbalisations of
mathematical notation are great. I'd far prefer to talk about
"dotting" or "crossing" than to embark on some cumbersome
circumlocution about forming a certain kind of product. And I
shamelessy use the verbs "to log" and "to e".

I'd prefer to use standard terminology because if they don't pick it
up from me, where will they pick it up from? "100 share 5" is well
beyond the pale as far as I'm concerned and I would refuse to use it
in any circumstances I can reasonably imagine. (I'm not suggesting you'd
defend it) For me to say "to times" would take serious effort, and I'd
feel as though I was being seriously patronizing, just as I would if I
attempted to talk jive or express an insincere appreciation for hiphop,
"Top of the Pops" or similar.

Post by H Bergeron
That is not to say I don't make sure my students also understand the
poncy, "correct" ways of expressing such things.

Well, fair enough then.

Post by H Bergeron
But I consider the
rites of passage into the mathematical community are about being able
to do the maths, not about saying "die" instead of "dice".

In the particular case of "die" I'd mostly stick with using it myself and
hoping they'd eventually notice, I think. I note that rulebooks for
role-playing games and wargames mostly use "a die" as far as I can see.

Post by H Bergeron

Post by Adam Atkinson
I remember people claiming to me years ago that correcting students'
spelling would crush the delicate flower that was their instinct for
self-expression, even if it lost them no marks. I thought that was
nonsense too.

Of course it is nonsense. The point is that you need to correct the
spelling in such a way that you don't completely alienate the student,
a feat that is entirely possible.

Oh, we were told this very... dogmatically. We were also told that you
should never set anything that _anyone_ can get less than 50% on. I'd
like to believe I misheard that, since some of the people at my school
made it a point of honour to get the lowest possible mark on anything.

Post by H Bergeron
Do you not recognise that you may be in danger of losing the student
if you elicit the response, "if I am going to get sarcastically
patronised or flamed for using "to times"! I will in future not bother
posting any equations on here."?

Yes. Though he said that to the person who said "You realise how dumb
that sounds?", not to me. Also, please notice that I attempted to
answer his questions.

Post by H Bergeron

Post by Adam Atkinson
I don't agree. "a dice" has pretty well conquered in non-mathematical
contexts, but "a die" is still standard in mathematics.

If you claim that "die" tends to be favoured by authors, I will accept
your claim. If you assert that any significant proportion of their
readers care (or that the minority who don't conform are "wrong"), I
beg to differ.

I checked with a bunch'o'people yesterday and they all preferred "a
die" to "a dice", though not all said they'd bother to correct it.
Some went so far as to say "'a dice' is illiterate", but they were
American and maybe "a dice" is less common in the US. They all felt
that "to times" was painful.

[Samsonknight]

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

"constraint on mathematical thinking"? Oh, please.

The proof of the pudding is in the eating. Judging by
appear to have annoyed the OP. Pissing off the student is one of the
best ways I know of hampering the development of their thinking.

"he should be developing a growing disregard..."? I'd have thought
part of learning any subject is learning the lingo. cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
And as a new A-level student the last thing he needs to be nagged
about is words.

I don't know that I was "nagging".

Then I humbly suggest that you don't know enough about usenet.

I mentioned the issue to him once (and again in replies to messages
such as yours). I'd be "nagging" if I did it repeatedly, which I had
no intention of doing. I'd say "Oh, please say 'multiply' instead" or
similar in real life too... after a first offence (just in case) and
infrequently thereafter.

<snip>

Ok my opinion : Initially when I read Adams reply I felt that he was being a
bit snobbish by picking out my words like that - especially as Maths is
based around symbols. If it was an english examination I would have not felt
that way. Secondly, yes I was taught about the term "to multiply" and I
guess the reason why I used "to times" is because it is a bad habbit of
mine. Thirdly concerning the terms "a die" and " a dice" - why does it
matter? The mathmatics teachers mainly used "a dice" in my school and I have
only really heard posh people use the terms "a die". It all just seems so
very petty and snobbish to discriminate people according to their use of
language in this context.

At the end of the day , I don't think that when it comes to me taking my
examinations in January and June, that the examiners will care about my use
of language, but the ability of me solving the equation set. - which will be
in symbols anyway not verbally.

I guess it was good for Adam to correct me, because if that is the petty
mentality people carry by scrutanizing every word you say and how you say it
then I guess its best that I learn the *correct* way in future. I must also
admit that I am now very nervous about applying to more "pristigious"
universities where there are many public school boys , as I have a bad
feeling that as many of the individuals speak "correctly" there will be much
more prejudice of this sort.

Adam is also right to say that I did get pissed off with the person that
said "You realise how dumb that sounds?", because firstly by him saying what
he said did not by the slightest bit help my confidence in mathematics , but
instead made me much more reserved in asking questions - and as I am making
an effort to learn I found that very disrespectful. This also leads me to my
next point, I think is the reason why many students find maths hard, because
in my experience a lot of students including myself were reluctant to ask
the teacher questions because they were scared that they would be patronised
as a result. This in turn will therefore stop them making progress, and yes
wreck confidence.

[Dr A. N. Walker]

Post by Samsonknight
At the end of the day , I don't think that when it comes to me taking my
examinations in January and June, that the examiners will care about my use
of language, but the ability of me solving the equation set. - which will be
in symbols anyway not verbally.

Sadly, you are probably right. But my experience is that
90% of the problems that our students *really* have with maths
stem from misuse of language. Not 90% of the errors -- those are
signs and factors of 2 gone astray, brackets left off, and other
trivia that are obvious as soon as you point them out -- but the
underlying difficulties.

When students are *made* to punctuate their equations
properly, to make sure that "it" has a proper antecedent, to
write words around their equations, to use "=" to denote
equality rather than "and hence it follows that", to use "=>"
only for "implies" rather than "and the next step in the
argument is", when their scripts look like proper maths and not
just a magic jumble of symbols -- then suddenly they start to
*do* proper maths, and not just guess at it. As a consequence,
the trivial errors become much less frequent, and the real,
conceptual errors stand out in isolation, making them much
easier to analyse and cure.

Post by Samsonknight
I guess it was good for Adam to correct me, because if that is the petty
mentality people carry by scrutanizing every word you say and how you say it
then I guess its best that I learn the *correct* way in future.

It is indeed "best" that you learn the "correct" way.
But not because scrutineers are being petty [which sometimes
they are]; rather because it is not possible to do good
science by being sloppy. FWIW, this has absolutely nothing
at all to do with being "posh" or "public school", or with
your accent or local dialect.

Post by Samsonknight
I must also
admit that I am now very nervous about applying to more "pristigious"
universities where there are many public school boys , as I have a bad
feeling that as many of the individuals speak "correctly" there will be much
more prejudice of this sort.

I see a great many students, from all walks of life, from
public schools, private schools, leafy suburb 6FCs, inner city
comps, the lot. I have absolutely no idea which are which, except
by looking up their UCAS forms. The public school ones do not go
around with neon signs that say "I was at Eton, you need to speak
correctly in my presence". They are normal people, with the same
interests in football, drinking, clubbing, sex, films, politics,
etc., etc as everyone else. Inverse snobbery is just as bad as
the direct form; and a university *ought* to be [and largely is]
a place where all those prejudices disappear, and people judge you
by what you are and what you do, not your social background.

There are rude, sneering, bigoted people at every university,
people who think they are superior and miss no opportunity to let you
know that. You meet them in every walk of life, too. You are a fool
if you let them ruin, or even affect, your own life and attitudes.
The vast, overwhelming majority of students are not like that. They
are not like it here, they are not like it at Cambridge, they are not
like it at any university I know.

FGS, decide what course *you* want to do, and what univ(s)
you want to do it at, on the basis of your interests and abilities,
not on some imaginary fear of what some of your fellow students may
be like.

Post by Samsonknight
[...] I think is the reason why many students find maths hard, because
in my experience a lot of students including myself were reluctant to ask
the teacher questions because they were scared that they would be patronised
as a result.

A patronising response from a teacher (a) is a sign of a bad
teacher [or, at best, a good teacher having a bad day], and (b) is a
sign of a teacher who does not fully understand the subject -- which,
sadly, is all too common in maths, given the desperate shortage of
qualified mathematicians and the way that those that exist are sought
out by the best and most congenial schools. You should not feel
scared by either of these.

[Adam Atkinson]

Post by Samsonknight
At the end of the day , I don't think that when it comes to me taking my
examinations in January and June, that the examiners will care about my use
of language, but the ability of me solving the equation set. - which will be
in symbols anyway not verbally.

As with showing your working (which I hated to do: my maths homework
was often "yes, no, 56, it goes up"), saying what you mean clearly and
correctly is a good idea if it helps the examiner understand what you
are trying to do. If your answer goes wrong, there is more hope of
getting marks for the correct bits if the examiner is able to identify
them. (I freely admit that I am guessing here. I don't actually know
how examiners work.) Having readable handwriting will also obviously
help, even though that's nothing to do with maths either.

For instance if, in a mechanics question, you write down a bunch of
equations and then some things apparently derived from them which go
nowhere, the examiner might struggle to justify giving you many marks.
If your argument, as far as it goes, is explained, things might go a
bit better for you. Certainly if there are any questions which ask you
to prove anything, use of language will be important. I don't know if
you need to prove anything on single maths A-level, though.

My own experience doing an MSc with the OU at the moment is that
the language element is no less important than the maths element when
it comes to me asking questions. "I don't get the proof of theorem 14"
doesn't tell him what my problem is anything like as clearly as "I
don't see how step 3 of the proof of Theorem 14 is supposed to work.
Is he trying to say that the 90% of the infinite sum (blah)
actually comes from the kth term? If so, why didn't he say
(alternative version)." My tutor then replies e.g. "No, he's using the
reverse thingybob inequality, but using the results of theorem 9.4
without even saying so. This is, admittedly, not obvious at first
sight. Your proposed alternative doesn't work because after (step) and
(other step) it gets stuck and doesn't take you anywhere"

Also, most of my homeworks look a lot chattier than you might expect
in the circumstances. "Calculate (whatever)" tends to be chat-free,
but "Prove that..." often consists more of text than formulae.

Incidentally, beware maths books that say "It can be shown that...".
This often means that if you spend 3 hours and 5 sheets of paper
working on it, you can go from one line to the next in the argument
presented.

Post by Samsonknight
I must also
admit that I am now very nervous about applying to more "pristigious"
universities where there are many public school boys , as I have a bad
feeling that as many of the individuals speak "correctly" there will be much
more prejudice of this sort.

Please, please do NOT feel that you should be nervous about applying
to "prestigious" universities. If you're good at your subject, they'll
be glad to have you. And I'm pretty sure that one of the reasons
Oxbridge has a relatively low number of people from state schools is
that too few apply in the first place. For the most part, people I
knew at university didn't know or care who went to public school
and who didn't. I don't know what interviewers will or won't choose to
care about. As Matthew and others say here frequently, there isn't a
national interviewers' cabal which decides these things. More than one
(Cambridge) interviewer has told me they like to see applicants show a
bit of backbone, so if an interviewer appears to be being unreasonable
it could be to see if you will stand up for yourself. The "You're from
Essex, so I don't expect you'll know what these squiggles are" case
from a few years ago is an absurdly over-the-top example of this,
perhaps.

Post by Samsonknight
but
instead made me much more reserved in asking questions

Ask all the questions you like. FWIW, I'm happy enough to deal with
moderate numbers of questions via private email if you prefer.

You might find Tom Ko"rner's "The Pleasures of Counting" interesting
if you want to see A-level-ish maths actually being used to accomplish
things. The target audience is, according to the author, "bright 14
year olds". I think the 14 year olds in question must be IMO team
members, and a more realistic audience for the book would, imho, be
A-level students. If you're very (Spivak-type level) ambitious, you might
also want to try Dr Korner's "A Companion to Analysis", whose target
audience is most likely undergraduates and people like me. If you are
insanely ambitious, you might want to try his "Fourier Analysis",
which is way over my head, and probably aimed at postgrads, or at
least at people who are/were much better at undergrad maths than I
ever was or expect to be.

[Toby]

Post by Adam Atkinson

Post by Samsonknight
At the end of the day , I don't think that when it comes to me taking my
examinations in January and June, that the examiners will care about my use
of language, but the ability of me solving the equation set. - which will be
in symbols anyway not verbally.

As with showing your working (which I hated to do: my maths homework
was often "yes, no, 56, it goes up"), saying what you mean clearly and
correctly is a good idea if it helps the examiner understand what you
are trying to do. If your answer goes wrong, there is more hope of
getting marks for the correct bits if the examiner is able to identify
them. (I freely admit that I am guessing here. I don't actually know
how examiners work.) Having readable handwriting will also obviously
help, even though that's nothing to do with maths either.

If, for simple instance, ummm, you had to state f^-1(X) and the range,
and got the calculation or whatever for the range wrong, but stated in
words that the range of the inverse is the domain of the function,
you'd get marks...Not sure how many though!

[Robert de Vincy]

Post by Samsonknight
At the end of the day , I don't think that when it comes to me taking
my examinations in January and June, that the examiners will care
about my use of language, but the ability of me solving the equation
set. - which will be in symbols anyway not verbally.

Words are symbols. What is there in the sequence of letters D, O, and
G that is essentially canine? Nothing. It's arbitrary. Just a bunch
of sounds and/or shapes that stand in for something. If that's not
symbols, then nothing is.

But I'm not blaming you for not knowing this. It's just not taught or
even hinted at in so-called English lessons. People here complain about
the total shitness of mathematics teaching in pre-A-level education.
But what about the basics of communication? I don't mean the stupid,
petty rules about how to use "hopefully" or what the singular of "dice"
is. I mean the actual, get-down-to-basics, what-it's-all-about bare-bones
of how we communicate with our fellow human beings.

There are laws against sexual discrimination, against discrimination because
of religion, sexuality, colour of skin, whatever. But we still have... no,
we still ENCOURAGE discrimination on another basic fact of who we are:
our language. We've got at least one extreme example of this sort of
hate-mongerer in this group, and most of us still respond to him. Imagine
if someone here started picking on another poster just because of his
name (inferring a link to some 'foreign' country). Quite rightly, we'd
give him/her as much outrage and indignation as society has instilled in
us to give such abusers. But why do we not have a similar reaction to
abuse-based-on-language criminals? It can't be justified at all. Whatever
reason we can find for its origins (social class, xenophobia, whatever),
that reason will be -- in its barest form -- unacceptable to today's
mores. And yet, it STILL filters through in the form of Language Fascism.

In a culture where our idiolect had as much sanctity as our skin colour,
our religion, and our sexuality have today, the following paragraph would

Post by Samsonknight
I guess it was good for Adam to correct me, because if that is the
petty mentality people carry by scrutanizing every word you say and
how you say it then I guess its best that I learn the *correct* way in
future. I must also admit that I am now very nervous about applying to
more "pristigious" universities where there are many public school
boys , as I have a bad feeling that as many of the individuals speak
"correctly" there will be much more prejudice of this sort.

I just feel so... what's the word? Ashamed? Exasperated? No, more like
just screaming "WHY?" when I read what Samsonknight has written above and
then realize that we have still got a long, long way to go to even start
thinking about calling ourselves a moral and even-handed species.

[Stuart Williams]

Post by Robert de Vincy

Post by Samsonknight
At the end of the day , I don't think that when it comes to me taking
my examinations in January and June, that the examiners will care
about my use of language, but the ability of me solving the equation
set. - which will be in symbols anyway not verbally.

Words are symbols. What is there in the sequence of letters D, O, and
G that is essentially canine? Nothing. It's arbitrary. Just a bunch
of sounds and/or shapes that stand in for something. If that's not
symbols, then nothing is.

Saussure would be proud of you. And of course, you're right. But see
under.

Post by Robert de Vincy
But I'm not blaming you for not knowing this. It's just not taught or
even hinted at in so-called English lessons. People here complain about
the total shitness of mathematics teaching in pre-A-level education.
But what about the basics of communication? I don't mean the stupid,
petty rules about how to use "hopefully" or what the singular of "dice"
is. I mean the actual, get-down-to-basics, what-it's-all-about bare-bones
of how we communicate with our fellow human beings.
There are laws against sexual discrimination, against discrimination because
of religion, sexuality, colour of skin, whatever. But we still have... no,
our language. We've got at least one extreme example of this sort of
hate-mongerer in this group, and most of us still respond to him. Imagine
if someone here started picking on another poster just because of his
name (inferring a link to some 'foreign' country). Quite rightly, we'd
give him/her as much outrage and indignation as society has instilled in
us to give such abusers. But why do we not have a similar reaction to
abuse-based-on-language criminals? It can't be justified at all. Whatever
reason we can find for its origins (social class, xenophobia, whatever),
that reason will be -- in its barest form -- unacceptable to today's
mores. And yet, it STILL filters through in the form of Language Fascism.

This is Utopian: you know as well as anyone that "race", skin colour,
sexual orientation are not chosen. Language register is. I wouldn't point
out to a 50-year-old friend that green nylon shirts, pink socks and a
beard down to the knees was a mistake, but I might venture that view to
an 18-year-old, in the nicest possible way, of course.

Post by Robert de Vincy
In a culture where our idiolect had as much sanctity as our skin colour,
our religion, and our sexuality have today, the following paragraph would

Post by Samsonknight
I guess it was good for Adam to correct me, because if that is the
petty mentality people carry by scrutanizing every word you say and
how you say it then I guess its best that I learn the *correct* way in
future. I must also admit that I am now very nervous about applying to
more "pristigious" universities where there are many public school
boys , as I have a bad feeling that as many of the individuals speak
"correctly" there will be much more prejudice of this sort.

I just feel so... what's the word? Ashamed? Exasperated? No, more like
just screaming "WHY?" when I read what Samsonknight has written above and
then realize that we have still got a long, long way to go to even start
thinking about calling ourselves a moral and even-handed species.

Don't be so po-faced: only when society consists of purely spiritual
beings with no visible, audible or olfactory distinctions will we enter
into this happy state you appear to want. I agree that Samson is adopting
a particularly abject position, but I think it's futile to suggest that
our different idiolects will ever have the same status as sexual
preference etc, precisely because it isn't involuntary. "To imagine a
language is to imagine a way of life" - and there will always be many
"ways of life" - so, many idiolects. Diversity is a sign of complexity,
complexity which enriches rather than divides. People like Samson who are
still learning the ropes might well welcome some hints.

SW

[H Bergeron]

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

"constraint on mathematical thinking"? Oh, please.

The proof of the pudding is in the eating. Judging by
appear to have annoyed the OP. Pissing off the student is one of the
best ways I know of hampering the development of their thinking.

"he should be developing a growing disregard..."? I'd have thought
part of learning any subject is learning the lingo.

Agreed, and in maths the relevant "lingo" is the notation. Correctness
in notation *matters* and needs relentless reinforcement. To become
good mathematicians the students need to feel at home with the
notation and the less they have to translate it back into "proper
English" in order to understand it, the better.

I want my students to realise that writing cos^-1(x) when they mean
1/cos(x) is an infinitely more serious crime than saying "to times"
instead of "to multiply".

Post by Adam Atkinson
cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

I read the book once, but the allusion doesn't click. I'm guessing
that Feynman ran into communication problems when people didn't
understand him.

If so, well sure. But I don't think you are claiming either that you
didn't understand what the OP meant by "to times" or that anyone else
would be likely to fail to understand him.

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
And as a new A-level student the last thing he needs to be nagged
about is words.

I don't know that I was "nagging".

Then I humbly suggest that you don't know enough about usenet.

I mentioned the issue to him once (and again in replies to messages
such as yours). I'd be "nagging" if I did it repeatedly, which I had
no intention of doing.

You said it to him, then later when he made it clear he hadn't found
that helpful, you said it to him again. The context was a
justification of your earlier message, but so what?

Post by Adam Atkinson
I'd say "Oh, please say 'multiply' instead" or
similar in real life too... after a first offence (just in case) and
infrequently thereafter.

Post by H Bergeron
The
large number of people who hang around simply to score points (and I
forgive you if you feel the urge to place me in that category),

At least one person who's witnessed this exchange thinks from your
choice of pseudonym and the content of your earlier message that
you're trolling me. I wasn't quite sure one way or the other, and I'm
still not.

Post by H Bergeron
the
fact that the discourse is public, and the lack of behavioural cues
moderating the content of bald text mean, taken together, that
anything tending towards nitpicking is always likely to be taken
badly. Hence the conventions about not pointing out typos, etc.

On the whole I'd only point out typos if I saw the same ones
repeatedly, in which case I'd imagine that perhaps they weren't typos.
I wouldn't want someone to go through life getting "parallel" wrong
every time just because no-one had ever bothered to correct it.

Fair enough, but I still wouldn't correct a misspelling of "parallel"
on usenet in my first communication with a stranger, unless I had a
separate reason for wanting to annoy them.

Post by Adam Atkinson
For
all I know, no-one had ever bothered to say to Samsonknight "'to
times' is a _very_good_ way to say that, but I think there's an _even_
better one, don't you?".

But I don't agree that "to multiply" is *better* than "to times".
Either will do, and the latter has fewer syllables. Likewise, I see no
point in using "numerator" and "denominator" when "top" and "bottom"
are transparent and unambiguous. YMMV. De gustibus and all that.

The argument in favour of "to multiply" is not that it's better, but
that it's standard. But unlike the meaning of cos^-1, it is not a
convention that is mathematically important.

Post by Adam Atkinson
I generally correct _everything_ on
it.cultura.linguistica.inglese, but that's a special case. If I know
the poster, I usually say "typo?" if I suspect it might be one because
it's not a mistake I'd expect him/her to make.

Post by H Bergeron

Post by Adam Atkinson
In any event, he might as well
learn to say "to multiply" now rather than later. When would you
suggest?

I really don't care if he never does, and am amazed that you do. If he
ever does find that people whose opinion he values care whether he
says "multiply" rather than "times", he will presumably alter his
behaviour. But that is entirely up to him.

Well of course it's up to him. I didn't know whether anyone had ever
mentioned it to him or not. I guessed not, which could be wrong.
I don't think I/you/anyone would be doing A-level students any favours
if we failed to at least mention in passing that "to times" and "100
share 5" might make listeners wince. My O-level teachers made a bit of
a joke out of dutifully saying "a pair of compasses" whenever anyone
called the instrument in question "a compass". I don't recall "to times"
being a problem, but I'm sure they'd have made the same sort of joke out
of dutifully saying "multiply" as and when.

Which is all fine and dandy. I poke gentle fun at my students when
they ask to "lend" something when they really want to borrow it, and
so on. But I only start this once I know them and they know that
mutual friendly piss-taking is expected. If I tried this with a
stranger I'd expect a black eye.

Post by Adam Atkinson

Post by H Bergeron
For myself, I think that punchy, if non-standard, verbalisations of
mathematical notation are great. I'd far prefer to talk about
"dotting" or "crossing" than to embark on some cumbersome
circumlocution about forming a certain kind of product. And I
shamelessy use the verbs "to log" and "to e".

I'd prefer to use standard terminology because if they don't pick it
up from me, where will they pick it up from? "100 share 5" is well
beyond the pale as far as I'm concerned and

I can't remember hearing "share".

What *does* come up with division is problems with "divide into". I'd
guess that the majority of students, when they start AS, think that 10
divided into 2 is 5. This time, it *does* matter, and although I think
the standard usage is the less logical, I obviously insist they
conform to it - when it cannot be avoided.

Post by Adam Atkinson
I would refuse to use it
in any circumstances I can reasonably imagine. (I'm not suggesting you'd
defend it) For me to say "to times" would take serious effort, and I'd
feel as though I was being seriously patronizing, just as I would if I
attempted to talk jive or express an insincere appreciation for hiphop,
"Top of the Pops" or similar.

Post by H Bergeron
That is not to say I don't make sure my students also understand the
poncy, "correct" ways of expressing such things.

Well, fair enough then.

Post by H Bergeron
But I consider the
rites of passage into the mathematical community are about being able
to do the maths, not about saying "die" instead of "dice".

In the particular case of "die" I'd mostly stick with using it myself and
hoping they'd eventually notice, I think. I note that rulebooks for
role-playing games and wargames mostly use "a die" as far as I can see.

Post by H Bergeron

Post by Adam Atkinson
I remember people claiming to me years ago that correcting students'
spelling would crush the delicate flower that was their instinct for
self-expression, even if it lost them no marks. I thought that was
nonsense too.

Of course it is nonsense. The point is that you need to correct the
spelling in such a way that you don't completely alienate the student,
a feat that is entirely possible.

Oh, we were told this very... dogmatically. We were also told that you
should never set anything that _anyone_ can get less than 50% on. I'd
like to believe I misheard that, since some of the people at my school
made it a point of honour to get the lowest possible mark on anything.

Post by H Bergeron
Do you not recognise that you may be in danger of losing the student
if you elicit the response, "if I am going to get sarcastically
patronised or flamed for using "to times"! I will in future not bother
posting any equations on here."?

Yes. Though he said that to the person who said "You realise how dumb
that sounds?", not to me. Also, please notice that I attempted to
answer his questions.

Indeed, and I'm not attempting a wholesale assassination of your
character or impeachment of your conduct.

I just happen to think that you weakened the helpfulness of your
advice by taking a potshot at his usage. And I forgive you if you
don't care what I think.

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson
I don't agree. "a dice" has pretty well conquered in non-mathematical
contexts, but "a die" is still standard in mathematics.

If you claim that "die" tends to be favoured by authors, I will accept
your claim. If you assert that any significant proportion of their
readers care (or that the minority who don't conform are "wrong"), I
beg to differ.

I checked with a bunch'o'people yesterday and they all preferred "a
die" to "a dice", though not all said they'd bother to correct it.
Some went so far as to say "'a dice' is illiterate", but they were
American and maybe "a dice" is less common in the US. They all felt
that "to times" was painful.

[Toby]

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

"constraint on mathematical thinking"? Oh, please.

The proof of the pudding is in the eating. Judging by
appear to have annoyed the OP. Pissing off the student is one of the
best ways I know of hampering the development of their thinking.

"he should be developing a growing disregard..."? I'd have thought
part of learning any subject is learning the lingo.

Agreed, and in maths the relevant "lingo" is the notation. Correctness
in notation *matters* and needs relentless reinforcement. To become
good mathematicians the students need to feel at home with the
notation and the less they have to translate it back into "proper
English" in order to understand it, the better.
I want my students to realise that writing cos^-1(x) when they mean
1/cos(x) is an infinitely more serious crime than saying "to times"
instead of "to multiply".

Post by Adam Atkinson
cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

I read the book once, but the allusion doesn't click. I'm guessing
that Feynman ran into communication problems when people didn't
understand him.
If so, well sure. But I don't think you are claiming either that you
didn't understand what the OP meant by "to times" or that anyone else
would be likely to fail to understand him.

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
And as a new A-level student the last thing he needs to be nagged
about is words.

I don't know that I was "nagging".

Then I humbly suggest that you don't know enough about usenet.

I mentioned the issue to him once (and again in replies to messages
such as yours). I'd be "nagging" if I did it repeatedly, which I had
no intention of doing.

You said it to him, then later when he made it clear he hadn't found
that helpful, you said it to him again. The context was a
justification of your earlier message, but so what?

Post by Adam Atkinson
I'd say "Oh, please say 'multiply' instead" or
similar in real life too... after a first offence (just in case) and
infrequently thereafter.

Post by H Bergeron
The
large number of people who hang around simply to score points (and I
forgive you if you feel the urge to place me in that category),

At least one person who's witnessed this exchange thinks from your
choice of pseudonym and the content of your earlier message that
you're trolling me. I wasn't quite sure one way or the other, and I'm
still not.

Post by H Bergeron
the
fact that the discourse is public, and the lack of behavioural cues
moderating the content of bald text mean, taken together, that
anything tending towards nitpicking is always likely to be taken
badly. Hence the conventions about not pointing out typos, etc.

On the whole I'd only point out typos if I saw the same ones
repeatedly, in which case I'd imagine that perhaps they weren't typos.
I wouldn't want someone to go through life getting "parallel" wrong
every time just because no-one had ever bothered to correct it.

Fair enough, but I still wouldn't correct a misspelling of "parallel"
on usenet in my first communication with a stranger, unless I had a
separate reason for wanting to annoy them.

Post by Adam Atkinson
For
all I know, no-one had ever bothered to say to Samsonknight "'to
times' is a _very_good_ way to say that, but I think there's an _even_
better one, don't you?".

But I don't agree that "to multiply" is *better* than "to times".
Either will do, and the latter has fewer syllables. Likewise, I see no
point in using "numerator" and "denominator" when "top" and "bottom"
are transparent and unambiguous. YMMV. De gustibus and all that.

All the books for A Level maths I've seen would say denominator and
numerator, and exam papers too - surely it's better to teach students
the words that will be in the exam for which they are studying? If you
teach them both, why confuse the issue? It would be rather terrible if
someone couldn't answer a question purely because they didn't
associate whole number with integer etc. etc..

[H Bergeron]

On Wed, 29 Sep 2004 22:47:32 +0100, Toby

Post by Toby

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
On the contrary, as a developing mathematician he should be developing
a growing disregard for the niceties of English usage insofar as they
act as a constraint on his mathematical thinking.

"constraint on mathematical thinking"? Oh, please.

The proof of the pudding is in the eating. Judging by
appear to have annoyed the OP. Pissing off the student is one of the
best ways I know of hampering the development of their thinking.

"he should be developing a growing disregard..."? I'd have thought
part of learning any subject is learning the lingo.

Agreed, and in maths the relevant "lingo" is the notation. Correctness
in notation *matters* and needs relentless reinforcement. To become
good mathematicians the students need to feel at home with the
notation and the less they have to translate it back into "proper
English" in order to understand it, the better.
I want my students to realise that writing cos^-1(x) when they mean
1/cos(x) is an infinitely more serious crime than saying "to times"
instead of "to multiply".

Post by Adam Atkinson
cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

I read the book once, but the allusion doesn't click. I'm guessing
that Feynman ran into communication problems when people didn't
understand him.
If so, well sure. But I don't think you are claiming either that you
didn't understand what the OP meant by "to times" or that anyone else
would be likely to fail to understand him.

Post by Adam Atkinson

Post by H Bergeron

Post by Adam Atkinson

Post by H Bergeron
And as a new A-level student the last thing he needs to be nagged
about is words.

I don't know that I was "nagging".

Then I humbly suggest that you don't know enough about usenet.

I mentioned the issue to him once (and again in replies to messages
such as yours). I'd be "nagging" if I did it repeatedly, which I had
no intention of doing.

You said it to him, then later when he made it clear he hadn't found
that helpful, you said it to him again. The context was a
justification of your earlier message, but so what?

Post by Adam Atkinson
I'd say "Oh, please say 'multiply' instead" or
similar in real life too... after a first offence (just in case) and
infrequently thereafter.

Post by H Bergeron
The
large number of people who hang around simply to score points (and I
forgive you if you feel the urge to place me in that category),

At least one person who's witnessed this exchange thinks from your
choice of pseudonym and the content of your earlier message that
you're trolling me. I wasn't quite sure one way or the other, and I'm
still not.

Post by H Bergeron
the
fact that the discourse is public, and the lack of behavioural cues
moderating the content of bald text mean, taken together, that
anything tending towards nitpicking is always likely to be taken
badly. Hence the conventions about not pointing out typos, etc.

On the whole I'd only point out typos if I saw the same ones
repeatedly, in which case I'd imagine that perhaps they weren't typos.
I wouldn't want someone to go through life getting "parallel" wrong
every time just because no-one had ever bothered to correct it.

Fair enough, but I still wouldn't correct a misspelling of "parallel"
on usenet in my first communication with a stranger, unless I had a
separate reason for wanting to annoy them.

Post by Adam Atkinson
For
all I know, no-one had ever bothered to say to Samsonknight "'to
times' is a _very_good_ way to say that, but I think there's an _even_
better one, don't you?".

But I don't agree that "to multiply" is *better* than "to times".
Either will do, and the latter has fewer syllables. Likewise, I see no
point in using "numerator" and "denominator" when "top" and "bottom"
are transparent and unambiguous. YMMV. De gustibus and all that.

All the books for A Level maths I've seen would say denominator and
numerator, and exam papers too - surely it's better to teach students
the words that will be in the exam for which they are studying?

As it happens, I can't remember those particular words being used in
any exam my students have taken, but you have a fair point. Or you
would have, if I were saying that students shouldn't *know* the
standard words. Whilst they remain standard, of course they would.

To know a term is is not necessary that you use it daily. If you know
several equivalent terms, you will tend to use the one you like best.
I think there are good reasons for liking the shorter, easier words
for parts of fractions.

Post by Toby
If you
teach them both, why confuse the issue?

I don't teach them both. For the most part they already know both when
they come to me. The occasional student needs to have the longer words
explained, or re-explained. I do make sure they are aware of
"numerator" and "denominator", but that is a totally different matter
from insisting they use those terms or pretending they are "better".

I asked some students today how x could be changed to 3x. They said
"times it by three". I asked if they would say it that way in a
university interview, and they said, "no, then we'd say 'multiply'
because they'd probably want us to be posh".

Which goes to show (i) that usage of "times" does not imply ignorance
of "multiply" and (ii) that students (those ones anyway) are fully
aware of the need to match language to context.

I somehow rather doubt that the OP didn't know the word "multiply" at
the beginning of this thread. More likely is that he thought he was
posting in an informal context.

Post by Toby
It would be rather terrible if
someone couldn't answer a question purely because they didn't
associate whole number with integer etc. etc..

Of course, but you have to be a bit careful with those two. Some
authors mean different things by "integer" and "whole number".

[Adam Atkinson]

Post by H Bergeron

Post by Adam Atkinson
"he should be developing a growing disregard..."? I'd have thought
part of learning any subject is learning the lingo.

Agreed, and in maths the relevant "lingo" is the notation.

Not just that. "inverse", "subtends", "symmetrical", "similar",
"congruent", "perpendicular" and such like are part of it too.

Post by H Bergeron
I want my students to realise that writing cos^-1(x) when they mean
1/cos(x) is an infinitely more serious crime than saying "to times"
instead of "to multiply".

I would agree with you. And of course the bad news is that in some
contexts "f^2(x)" means f(x)*f(x) and in others it means f(f(x)).
Not sure if this happens at A-level, but I dimly recall iterative
processes being on mine. Not sure if there was a notation for them.

Post by H Bergeron

Post by Adam Atkinson
cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

I read the book once, but the allusion doesn't click. I'm guessing
that Feynman ran into communication problems when people didn't
understand him.

He'd done a lot of stuff from books and didn't know how to pronounce
a lot of it. Actually, this can matter more than you might think:
as well as teaching people the notation, you do need to tell them
how to read it aloud ("The integral from blah to blah of thingummy
dx"). In a classroom, I would guess this would be automatic
but it isn't if you do stuff from books. Non-native English speakers
whose everyday English is wonderful sometimes discover they have
no idea how to read formulae, even as simple as "x/y", aloud. It's
something I'm probably not great at in Italian. For whatever reason,
most language courses don't spend much time on differential
and integral equations.

Post by H Bergeron
If so, well sure. But I don't think you are claiming either that you
didn't understand what the OP meant by "to times"

no

Post by H Bergeron
or that anyone else
would be likely to fail to understand him.

Non-native English speakers, I'm not so sure. Though he's not
likely to have this problem at the moment, of course. I'll
ask about this on it.cultura.linguistica.inglese this evening.

Post by H Bergeron

Post by Adam Atkinson
On the whole I'd only point out typos if I saw the same ones
repeatedly, in which case I'd imagine that perhaps they weren't typos.
I wouldn't want someone to go through life getting "parallel" wrong
every time just because no-one had ever bothered to correct it.

Fair enough, but I still wouldn't correct a misspelling of "parallel"
on usenet in my first communication with a stranger, unless I had a
separate reason for wanting to annoy them.

I have seen some typos in Samson's messages, but so far I've not
had the impression that any of them were anything other than typos
so I've not said anything about them. If he said "derirative" more
than about once I'd probably ask about it, though.

Post by H Bergeron

Post by Adam Atkinson
For
all I know, no-one had ever bothered to say to Samsonknight "'to
times' is a _very_good_ way to say that, but I think there's an _even_
better one, don't you?".

But I don't agree that "to multiply" is *better* than "to times".

It's probably better in some contexts.

Post by H Bergeron
Either will do, and the latter has fewer syllables. Likewise, I see no
point in using "numerator" and "denominator" when "top" and "bottom"
are transparent and unambiguous. YMMV. De gustibus and all that.

There's even a somewhat famous formula with "top" and "bottom" in it.
Derivative of f/g. Or at least I learned it as "bottom times derivative of top
minus top times derivative of bottom, over bottom squared"

Post by H Bergeron

Post by Adam Atkinson
I'd prefer to use standard terminology because if they don't pick it
up from me, where will they pick it up from? "100 share 5" is well
beyond the pale as far as I'm concerned and

I can't remember hearing "share".

I've only encountered this a few times, but they were all within
a few miles and weeks of each other, which I found very disturbing.
It could be that it's died out by now. In a school I visited
a teacher asked someone in a (fifth form) class "What is 100 share 5,
(name)?". I had never heard this before and wasn't sure what it meant.
I asked, and was told it meant "divided by". I was told that "divided
by" was too hard for (at least some) 16 year olds so this school,
at least, preferred to use "100 share 5" instead. I later saw or heard
this in a couple of other places nearby. I am not aware of "share"
being used like this anywhere in real life. I have asked various
people if they know what "100 share 5" means and most say they wouldn't
understand it. I myself would prefer never say "to times" because I didn't
grow up saying it and it would seem pretty artificial to start
using it now. This business with "share" seems different, though.
As far as I can see, it's not even a question of using a non-standard,
but common, usage in a classroom: it's a made-up term that doesn't
come from anywhere. It seems pretty insulting to suggest that "to divide"
is too difficult, and I can't see the point of giving students the
impression that "100 share 5" is something people say. I would like
to hope that this is no longer being used. Of course, if maths teachers
did this for a few decades perhaps they could arrange for "100 share
5" to become standard usage. My current impression is that this
is not remotely close to happening. I would have to describe this
"share" idea as some combination of misguided, stupid, irresponsible,
risible and criminal.

Post by H Bergeron
What *does* come up with division is problems with "divide into". I'd
guess that the majority of students, when they start AS, think that 10
divided into 2 is 5. This time, it *does* matter, and although I think
the standard usage is the less logical, I obviously insist they
conform to it - when it cannot be avoided.

Hmm. How often does this one come up? Off the top of my head
I'd have thought "Does a divide into b?" is a more likely
question than "What is a divided into b?" but maybe I'm picturing
the wrong context.

Post by H Bergeron
I just happen to think that you weakened the helpfulness of your
advice by taking a potshot at his usage. And I forgive you if you
don't care what I think.

It was probably silly of me to imagine/suspect/worry he didn't know about
"multiply". Presumably it's ok if I continue to use "multiply", "die"
and the like myself? I find it pretty creepy when people attempt
to ingratiate themselves with "the kids" by wearing baseball caps
backwards, saying "respect!" and so on, if this is not the sort
of thing they would do in other situations. My mother was an infant
school head teacher, and watching the total personality transformation
she underwent when talking to the students was pretty surreal.

[Dr A. N. Walker]

Post by Adam Atkinson

Post by Adam Atkinson
cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

Presumably you intended "*not* very approximate"?

Post by Adam Atkinson
He'd done a lot of stuff from books and didn't know how to pronounce
a lot of it.

It's a long time since I read SYJMF, but this sounds more
like an Erdos story, he having learned English entirely from books
and thus pronouncing everything as spelled. Feynman was at least
a native speaker of English; OTOH, as an *American* native speaker,
one might expect him to mispronounce foreign names -- the story is
well known that Niklaus Wirth is "called by name in Europe and by
value in America".

[Adam Atkinson]

Post by Dr A. N. Walker

Post by Adam Atkinson

Post by Adam Atkinson
cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

Presumably you intended "*not* very approximate"?

Hmm. Maybe I have this backwards. I was thinking that the opposite of
"approximate" was "precise" so "very approximate" would be "not at all
precise". Maybe that doesn't work.

Post by Dr A. N. Walker

Post by Adam Atkinson
He'd done a lot of stuff from books and didn't know how to pronounce
a lot of it.

It's a long time since I read SYJMF, but this sounds more
like an Erdos story, he having learned English entirely from books
and thus pronouncing everything as spelled.

It's too long since I read it too, I fear, but I think he didn't know
how to read formulae aloud, or perhaps used his own notation. Hmm.
Notation yes. Less sure about the rest... should check.

Post by Dr A. N. Walker
Feynman was at least
a native speaker of English; OTOH, as an *American* native speaker,
one might expect him to mispronounce foreign names -- the story is
well known that Niklaus Wirth is "called by name in Europe and by
value in America".

Feynman said "Baronally" and no-one knew what he meant, apparently.

[Dr A. N. Walker]

Post by Adam Atkinson
Hmm. Maybe I have this backwards. I was thinking that the opposite of
"approximate" was "precise"

No, no! "Approximate" means "close". The opposite would
be something like "rough" or "distant", so ...

Post by Adam Atkinson
so "very approximate" would be "not at all
precise".

... "very approximate" means "very close", not "very rough".
Of course, far too many people think "your" way, so careful writers
have to avoid the phrase altogether.

Post by Adam Atkinson
Feynman said "Baronally" and no-one knew what he meant, apparently.

What *did* he mean? [Or should one not ask, as no-one knows?]

[Adam Atkinson]

Post by Dr A. N. Walker

Post by Adam Atkinson
Hmm. Maybe I have this backwards. I was thinking that the opposite of
"approximate" was "precise"

No, no! "Approximate" means "close". The opposite would
be something like "rough" or "distant", so ...

Well, of course I can see that "proximate" means close so that
"approximate" ought to mean close. However, I'm pretty sure I've seen
"very approximate" used like this. Not a usage I should imitate,
perhaps.

Post by Dr A. N. Walker
... "very approximate" means "very close", not "very rough".
Of course, far too many people think "your" way, so careful writers
have to avoid the phrase altogether.

I can see that, yes.

Post by Dr A. N. Walker

Post by Adam Atkinson
Feynman said "Baronally" and no-one knew what he meant, apparently.

What *did* he mean? [Or should one not ask, as no-one knows?]

Bernoulli.

[Adam Atkinson]

Post by H Bergeron

Post by Adam Atkinson
"he should be developing a growing disregard..."? I'd have thought
part of learning any subject is learning the lingo.

Agreed, and in maths the relevant "lingo" is the notation.

Not just that. "inverse", "subtends", "symmetrical", "similar",
"congruent", "perpendicular" and such like are part of it too.

Post by H Bergeron
I want my students to realise that writing cos^-1(x) when they mean
1/cos(x) is an infinitely more serious crime than saying "to times"
instead of "to multiply".

I would agree with you. And of course the bad news is that in some
contexts "f^2(x)" means f(x)*f(x) and in others it means f(f(x)).
Not sure if this happens at A-level, but I dimly recall iterative
processes being on mine. Not sure if there was a notation for them.

Post by H Bergeron

Post by Adam Atkinson
cf. "Surely you're
joking, Mr Feynman" and Dick Feynman's personal terms for things and
very approximate ways of pronoucing e.g. "Bernoulli".

I read the book once, but the allusion doesn't click. I'm guessing
that Feynman ran into communication problems when people didn't
understand him.

He'd done a lot of stuff from books and didn't know how to pronounce
a lot of it. Actually, this can matter more than you might think:
as well as teaching people the notation, you do need to tell them
how to read it aloud ("The integral from blah to blah of thingummy
dx"). In a classroom, I would guess this would be automatic
but it isn't if you do stuff from books. Non-native English speakers
whose everyday English is wonderful sometimes discover they have
no idea how to read formulae, even as simple as "x/y", aloud. It's
something I'm probably not great at in Italian. For whatever reason,
most language courses don't spend much time on differential
and integral equations.

Post by H Bergeron
If so, well sure. But I don't think you are claiming either that you
didn't understand what the OP meant by "to times"

no

Post by H Bergeron
or that anyone else
would be likely to fail to understand him.

Non-native English speakers, I'm not so sure. Though he's not
likely to have this problem at the moment, of course. I'll
ask about this on it.cultura.linguistica.inglese this evening.

Post by H Bergeron

Post by Adam Atkinson
On the whole I'd only point out typos if I saw the same ones
repeatedly, in which case I'd imagine that perhaps they weren't typos.
I wouldn't want someone to go through life getting "parallel" wrong
every time just because no-one had ever bothered to correct it.

Fair enough, but I still wouldn't correct a misspelling of "parallel"
on usenet in my first communication with a stranger, unless I had a
separate reason for wanting to annoy them.

I have seen some typos in Samson's messages, but so far I've not
had the impression that any of them were anything other than typos
so I've not said anything about them. If he said "derirative" more
than about once I'd probably ask about it, though.

Post by H Bergeron

Post by Adam Atkinson
For
all I know, no-one had ever bothered to say to Samsonknight "'to
times' is a _very_good_ way to say that, but I think there's an _even_
better one, don't you?".

But I don't agree that "to multiply" is *better* than "to times".

It's probably better in some contexts.

Post by H Bergeron
Either will do, and the latter has fewer syllables. Likewise, I see no
point in using "numerator" and "denominator" when "top" and "bottom"
are transparent and unambiguous. YMMV. De gustibus and all that.

There's even a somewhat famous formula with "top" and "bottom" in it.
Derivative of f/g. Or at least I learned it as "bottom times derivative of top
minus top times derivative of bottom, over bottom squared"

Post by H Bergeron

Post by Adam Atkinson
I'd prefer to use standard terminology because if they don't pick it
up from me, where will they pick it up from? "100 share 5" is well
beyond the pale as far as I'm concerned and

I can't remember hearing "share".

I've only encountered this a few times, but they were all within
a few miles and weeks of each other, which I found very disturbing.
It could be that it's died out by now. In a school I visited
a teacher asked someone in a (fifth form) class "What is 100 share 5,
(name)?". I had never heard this before and wasn't sure what it meant.
I asked, and was told it meant "divided by". I was told that "divided
by" was too hard for (at least some) 16 year olds so this school,
at least, preferred to use "100 share 5" instead. I later saw or heard
this in a couple of other places nearby. I am not aware of "share"
being used like this anywhere in real life. I have asked various
people if they know what "100 share 5" means and most say they wouldn't
understand it. I myself would prefer never say "to times" because I didn't
grow up saying it and it would seem pretty artificial to start
using it now. This business with "share" seems different, though.
As far as I can see, it's not even a question of using a non-standard,
but common, usage in a classroom: it's a made-up term that doesn't
come from anywhere. It seems pretty insulting to suggest that "to divide"
is too difficult, and I can't see the point of giving students the
impression that "100 share 5" is something people say. I would like
to hope that this is no longer being used. Of course, if maths teachers
did this for a few decades perhaps they could arrange for "100 share
5" to become standard usage. My current impression is that this
is not remotely close to happening. I would have to describe this
"share" idea as some combination of misguided, stupid, irresponsible,
risible and criminal.

Post by H Bergeron
What *does* come up with division is problems with "divide into". I'd
guess that the majority of students, when they start AS, think that 10
divided into 2 is 5. This time, it *does* matter, and although I think
the standard usage is the less logical, I obviously insist they
conform to it - when it cannot be avoided.

Hmm. How often does this one come up? Off the top of my head
I'd have thought "Does a divide into b?" is a more likely
question than "What is a divided into b?" but maybe I'm picturing
the wrong context.

Post by H Bergeron
I just happen to think that you weakened the helpfulness of your
advice by taking a potshot at his usage. And I forgive you if you
don't care what I think.

It was probably silly of me to imagine/suspect/worry he didn't know about
"multiply". Presumably it's ok if I continue to use "multiply", "die"
and the like myself? I find it pretty creepy when people attempt
to ingratiate themselves with "the kids" by wearing baseball caps
backwards, saying "respect!" and so on, if this is not the sort
of thing they would do in other situations. My mother was an infant
school head teacher, and watching the total personality transformation
she underwent when talking to the students was pretty surreal.

[H Bergeron]

On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren

Post by Samsonknight

Post by Adam Atkinson
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4.

Oh dear.
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to be
ignorant of what students typically struggle with when they move on
from GCSE to AS/A level.

[Alex Warren]

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to be
ignorant of what students typically struggle with when they move on
from GCSE to AS/A level.

Clearly.

But surely before commencing A-level study, students ought to have a firm grasp
of basic algebra? Or can one pass a GCSE these days without even that?


Alex

[Samsonknight]

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to be
ignorant of what students typically struggle with when they move on
from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to have a firm grasp
of basic algebra? Or can one pass a GCSE these days without even that?
Alex

If you had payed close attention to the thread, the communication between
Adam and I over this equation got messier and messier, hence why I came out
with the reply to be as accurate as possible - as that is how the question
wass exactly layed out in the book that I am currently working from.

[Adam Atkinson]

Post by Samsonknight
If you had payed close attention to the thread, the communication between
Adam and I over this equation got messier and messier, hence why I came out
with the reply to be as accurate as possible - as that is how the question
wass exactly layed out in the book that I am currently working from.

Was my answer any use? (The bit where I answered your question, not
the bit where I told you not to say "to times")

[Samsonknight]

Post by Adam Atkinson

Post by Samsonknight
If you had payed close attention to the thread, the communication between
Adam and I over this equation got messier and messier, hence why I came out
with the reply to be as accurate as possible - as that is how the question
wass exactly layed out in the book that I am currently working from.

Was my answer any use? (The bit where I answered your question, not
the bit where I told you not to say "to times")
--
alt.folklore.computers FAQ: http://www.best.com/~wilson/faq/

Yeah cheers mate, your answer was helpful . I also went over first
principles with my tutor yesterday for the sake of it. Thanks again.

[Adam Atkinson]

Post by Samsonknight
Yeah cheers mate, your answer was helpful . I also went over first
principles with my tutor yesterday for the sake of it. Thanks again.

Differentiating from first principles isn't something you're likely to
have to do very often. Once you know how to differentiate constants
and the function "f(x)=x", and you know how to differentiate sums
and products of things you already know, that's enough to handle
all polynomials. Add the chain rule and you can do a lot more. Add
"f(x)=1/x" (from first principles, I suppose) and you can do a lot more.
Knowing how to differentiate the inverse of something you've already done
helps matters again. (I'd hope that your textbook will show that sums,
products, chain rule and inverses all work by doing them from first
principles, but that might be optimistic)

At that point, there will still be things you can't do, like e^x and sin(x),
so first principles will be necessary a few more times. But those added to
the sum/product/etc. rules will enable you to differentiate great swathes
of absurd-looking things. sin(x^3/(sin(x^3/sin(x^3)))), sort of thing (
that's an example from Spivak, IIRC).

[Toby]

Post by Adam Atkinson

Post by Samsonknight
Yeah cheers mate, your answer was helpful . I also went over first
principles with my tutor yesterday for the sake of it. Thanks again.

Differentiating from first principles isn't something you're likely to
have to do very often. Once you know how to differentiate constants
and the function "f(x)=x", and you know how to differentiate sums
and products of things you already know, that's enough to handle
all polynomials. Add the chain rule and you can do a lot more. Add
"f(x)=1/x" (from first principles, I suppose) and you can do a lot more.
Knowing how to differentiate the inverse of something you've already done
helps matters again. (I'd hope that your textbook will show that sums,
products, chain rule and inverses all work by doing them from first
principles, but that might be optimistic)
At that point, there will still be things you can't do, like e^x and sin(x),
so first principles will be necessary a few more times. But those added to
the sum/product/etc. rules will enable you to differentiate great swathes
of absurd-looking things. sin(x^3/(sin(x^3/sin(x^3)))), sort of thing (
that's an example from Spivak, IIRC).

Sadly not available new on Amazon, as far as I can tell :(

[Adam Atkinson]

Post by Toby

Post by Adam Atkinson
At that point, there will still be things you can't do, like e^x and sin(x),
so first principles will be necessary a few more times. But those added to
the sum/product/etc. rules will enable you to differentiate great swathes of
absurd-looking things. sin(x^3/(sin(x^3/sin(x^3)))), sort of thing ( that's
an example from Spivak, IIRC).

Sadly not available new on Amazon, as far as I can tell :(

I have an awful feeling I had to order my copy of the third edition
from amazon.com rather than amazon.co.uk. If you can find _any_
edition of Spivak second hand I'd say go for it. It's very very
expensive new even if you can find it - over 50 pounds? I don't know
quite why I bothered: perhaps because it had been a long, long time
since the previous edition(s) and I wanted to see what, if anything,
had changed. ISTR feeling that the third edition was less austere than
earlier ones: it had surprisingly concrete things like volumes of
revolution in it.

As I mention in another message, a possible substitute might be
Korner's "A Companion to Analysis". The first chapter is called
something like "Why do we bother?" and includes things that might
surprise even people who had done a university analysis course.
Consider what (i) continuous and (ii) differentiable functions from Q to
Q look like, for example.

[Toby]

Post by Adam Atkinson

Post by Toby

Post by Adam Atkinson
At that point, there will still be things you can't do, like e^x and sin(x),
so first principles will be necessary a few more times. But those added to
the sum/product/etc. rules will enable you to differentiate great swathes of
absurd-looking things. sin(x^3/(sin(x^3/sin(x^3)))), sort of thing ( that's
an example from Spivak, IIRC).

Sadly not available new on Amazon, as far as I can tell :(

I have an awful feeling I had to order my copy of the third edition
from amazon.com rather than amazon.co.uk. If you can find _any_
edition of Spivak second hand I'd say go for it. It's very very
expensive new even if you can find it - over 50 pounds? I don't know
quite why I bothered: perhaps because it had been a long, long time
since the previous edition(s) and I wanted to see what, if anything,
had changed. ISTR feeling that the third edition was less austere than
earlier ones: it had surprisingly concrete things like volumes of
revolution in it.
As I mention in another message, a possible substitute might be
Korner's "A Companion to Analysis". The first chapter is called
something like "Why do we bother?" and includes things that might
surprise even people who had done a university analysis course.
Consider what (i) continuous and (ii) differentiable functions from Q to
Q look like, for example.

Cool, thanks for the tips; keep the recommendations coming (that
applies to you, too, Andy of Notts!). I'm getting quite a lot of maths
books, I'm really quite sad!

[Adam Atkinson]

Post by Toby
Cool, thanks for the tips; keep the recommendations coming (that
applies to you, too, Andy of Notts!). I'm getting quite a lot of maths
books, I'm really quite sad!

Korner's "The Pleasures of Counting" is pretty good value, and has a
very good bibliography at the end. Get TPOC and read/buy anything in
the bibliography that sounds like your sort of thing. About the only
thing missing from it is "The Flying Circus of Physics" by Jearl
Walker, which is of course not really a maths book anyway.

[Toby]

Post by Adam Atkinson

Post by Toby
Cool, thanks for the tips; keep the recommendations coming (that
applies to you, too, Andy of Notts!). I'm getting quite a lot of maths
books, I'm really quite sad!

Korner's "The Pleasures of Counting" is pretty good value, and has a
very good bibliography at the end. Get TPOC and read/buy anything in
the bibliography that sounds like your sort of thing. About the only
thing missing from it is "The Flying Circus of Physics" by Jearl
Walker, which is of course not really a maths book anyway.

hehe I bought that book when you recommended it ages ago!

[Adam Atkinson]

Post by Toby
Cool, thanks for the tips; keep the recommendations coming (that
applies to you, too, Andy of Notts!). I'm getting quite a lot of maths
books, I'm really quite sad!

I'm finding it quite hard to think of things to recommend which aren't
in the bibliography of "The Pleasures of Counting". "Winning Ways" is
in there. It costs a fortune, but I must (naturally) agree with TK
when he says that if you understand anything in it at all it will be
money well spent. It's recently been reprinted in 4 volumes rather
than two, so you could start with just volume 1 and see what you
think.

Another item from TK's bibliography is "The Visual Display of
Quantitative Information" (or something very similar to that) by
Edward Tufte. It's about how to draw graphs and other such things
_well_. "How to Lie with Statistics" by Darell (sp?) Huff is lots of
fun too and would probably accompany Tufte's book quite well. There
are two other Tufte books you might want to get if you like the first
one. "Envisioning Information" and "Visual Explanations", I think.
The Tufte books are more graphic design than mathematics, perhaps, but
I remember on O-level statistics we got SOME advice about how to draw
graphs, histograms, etc.

I'm not sure if TK mentions "Concrete Mathematics" by Graham, Knuth
and... Potashnik? Patashnik? It's not an easy read by any stretch of
the imagination, but if you want to become shockingly good as
simplifying sums and products of expressions full of factorials and
similar, it might be worth a look.

Also "generatingfunctionology" by Wilf, which is downloadable as a
PDF. I haven't read it myself, but multiple people have recommended it
to me.

What else? Hmm.. "Innumeracy" by Paulos, "Numerical Methods that
(usually) Work" by Forman S Acton, maybe "An Introduction to the
Theory of Number" by Hardy and Wright, maybe "Game Theory and
Strategy" by Straffin, "Forever Undecided" by Smullyan (if you can
find it - a lot of his stuff seems to be out of print). "Probability
and Random Processes" by Grimmett and Stirzaker is nice if you like
probability a lot.

[Dr A. N. Walker]

Post by Adam Atkinson
I'm finding it quite hard to think of things to recommend which aren't
in the bibliography of "The Pleasures of Counting". "Winning Ways" is
in there. It costs a fortune, but I must (naturally) agree with TK
when he says that if you understand anything in it at all it will be
money well spent.

Not sure I really agree. The implication seems to be that
"WW" is v difficult, but chock-full of Really Useful stuff. The
reality is that its standard veers alarmingly, sometimes within a
page, from material that any bright 12yo should be able to follow
to results that PhD mathematicians find hard. The distribution of
RU stuff is just as weird, and not at all correlated, AFAICT, with
the difficulty. Ideally, it needs re-organising into a coherent
book on game theory at u/g maths level, without losing the flavour.
I need to write my book .... There are also great [and important]
swathes of game theory that are just not in "WW".

Post by Adam Atkinson
I'm not sure if TK mentions "Concrete Mathematics" [...].

I tried to read this once or twice, and fell asleep. I
expect that's my fault; I'm sure it's excellent, but these days
we use Maple to do all the grunt work.

[Adam Atkinson]

Post by Dr A. N. Walker

Post by Adam Atkinson
"Winning Ways" is
in there. It costs a fortune, but I must (naturally) agree with TK
when he says that if you understand anything in it at all it will be
money well spent.

Not sure I really agree. The implication seems to be that
"WW" is v difficult, but chock-full of Really Useful stuff.

Well, there's certainly some Really Useful stuff in there. There's a
lot I don't understand at all. However, warts (or bits I don't get) and
all it's one of the most fun maths books I own.

Post by Dr A. N. Walker
Ideally, it needs re-organising into a coherent
book on game theory at u/g maths level, without losing the flavour.

Well, that would certainly be nice. The second edition hasn't changed
things as much as I'd expected. New bibliography, a few updated
Extras.

Post by Dr A. N. Walker
I need to write my book .... There are also great [and important]
swathes of game theory that are just not in "WW".

What other books should I get? I have "Games of No Chance" and "More
Games of No Chance", but they're fairly clearly from the same stable.
I have Straffin's book, but that's more Game Theory in the sense
economists mostly use it, if I recall correctly.

Post by Dr A. N. Walker

Post by Adam Atkinson
I'm not sure if TK mentions "Concrete Mathematics" [...].

I tried to read this once or twice, and fell asleep. I
expect that's my fault; I'm sure it's excellent, but these days
we use Maple to do all the grunt work.

Yes. Maple is something I need to get hold of and learn how to use one
of these years. Or Mathematica, or something. Fortunately, one of the
modules on my MSc is about using Maple to do... stuff... so I'll be
able to get a cheap copy that way. I hope it runs on Linux or FreeBSD.

[Andy Walker]

Post by Adam Atkinson

Post by Dr A. N. Walker
I need to write my book .... There are also great [and important]
swathes of game theory that are just not in "WW".

What other books should I get? I have "Games of No Chance" and "More
Games of No Chance", but they're fairly clearly from the same stable.
I have Straffin's book, but that's more Game Theory in the sense
economists mostly use it, if I recall correctly.

There is quite a nice book, "The Mathematics of Games", by
John Beasley, which covers a decent range of game theory at a more
consistent [undergrad-ish] level than WW. But it's not a *big*
book, and it's also now quite old. There is probably more recent
stuff out there. I occasionally get flyers from publishers, but
nothing has really caught my eye. For decent coverage in total,
you do need the "economic" stuff, some of which is quite interesting.
You also need to understand the algorithms involved [alpha-beta
and its relatives], and preferably the relation between all that
and NP-completeness; sadly, I don't know of *any* competent book
on it, it's all scattered over conference proceedings, journals,
theses, .... Then there are all the "games of chance"; seems a
shame if we can't discuss backgammon, ludo, ....

Post by Adam Atkinson
Yes. Maple is something I need to get hold of [...].
I hope it runs on Linux or FreeBSD.

Certainly does, else we couldn't use it!

[Adam Atkinson]

Post by Andy Walker

Post by Adam Atkinson

Post by Dr A. N. Walker
I need to write my book .... There are also great [and important]
swathes of game theory that are just not in "WW".

What other books should I get? I have "Games of No Chance" and "More
Games of No Chance", but they're fairly clearly from the same stable.
I have Straffin's book, but that's more Game Theory in the sense
economists mostly use it, if I recall correctly.

There is quite a nice book, "The Mathematics of Games", by
John Beasley, which covers a decent range of game theory at a more
consistent [undergrad-ish] level than WW. But it's not a *big*
book, and it's also now quite old.

Hm. I don't think I have that one. I look at the game theory books
when I'm in the Waterstones in Gower Street or in Foyles, and so far
nothing much has grabbed me. Straffin seems to cover the
game-theory-as-done-by-economists stuff. I thought you meant WW was
missing great swathes of combinatorial game theory. It may well be, of
course.

Post by Andy Walker
For decent coverage in total,
you do need the "economic" stuff, some of which is quite interesting.
You also need to understand the algorithms involved [alpha-beta
and its relatives], and preferably the relation between all that
and NP-completeness; sadly, I don't know of *any* competent book
on it, it's all scattered over conference proceedings, journals,
theses, .... Then there are all the "games of chance"; seems a
shame if we can't discuss backgammon, ludo, ...

I have some stuff on the "economic" flavour of game theory. I also
have some of the "computers and games" collections of articles and
quite a lot of books on probability, some of which cover games.

Thanks for the tips, though. I'll probably be in Gower Street tomorrow
so will have a bit of a rummage.

Post by Andy Walker

Post by Adam Atkinson
Yes. Maple is something I need to get hold of [...].
I hope it runs on Linux or FreeBSD.

Certainly does, else we couldn't use it!

(Monty Burns accent) Excellent!

[Toby]

On 1 Oct 2004 5:48:47 +0100, "Adam Atkinson" <***@mistral.co.uk>
wrote:


<kind recommendations by Adam>

Thanks again, I'm looking into them!

[Adam Atkinson]

Post by Toby
<kind recommendations by Adam>
Thanks again, I'm looking into them!

Well, don't go mad. The comments in TK's bibliography should probably
let you know whether something is worth looking at or not.

I ought to recommend something on group theory, but it's something I
don't understand at all so I'm not best placed to do this. Fraleigh?
Herstein?

Almost everything I've mentioned is pure or applicable maths. I don't
know much about applied maths but I'm sure other people here do.

[Toby]

Post by Adam Atkinson

Post by Toby
<kind recommendations by Adam>
Thanks again, I'm looking into them!

Well, don't go mad. The comments in TK's bibliography should probably
let you know whether something is worth looking at or not.
I ought to recommend something on group theory, but it's something I
don't understand at all so I'm not best placed to do this. Fraleigh?
Herstein?
Almost everything I've mentioned is pure or applicable maths. I don't
know much about applied maths but I'm sure other people here do.

hehe well problem is I'm not always discerning and I have about £1000
worth of book tokens to use up...(don't ask)....I'm just looking for a
core selection of maths books that everyone 'in the know' has, then
I'll take it from there when I find particular areas that fascinate
me, unless there's a better way...

[Adam Atkinson]

I have about £1000 worth of book tokens to use up...

!!

(don't ask)

Curses!

....I'm just looking for a
core selection of maths books that everyone 'in the know' has, then
I'll take it from there when I find particular areas that fascinate
me, unless there's a better way...

Well, it could be argued that using the tokens to get stuff you need
for whatever course you're actually doing might not be a bad idea.
However, I'm sure you could spare some for a few real corkers. With a
budget like that, perhaps you should plan a trip to London to visit
Foyles or Waterstones, or some other city with a large university
bookshop in it, to have a _good_ look at the candidates.

There's probably very little that "everyone in the know" has. I bought
very few textbooks at university because they didn't appear to be
necessary - for all I know, this could have been a mistake, but I
don't THINK most people bought the recommended books for most courses
as lectures seemed to cover most/all of it. I probably bought more
books for third year courses than I did for earlier ones.

However lovely I think Spivak might be, it has to be said that it's
"just" a (very good) first book on analysis. In the long term, will you
really want one? I know various group theorists, applied
mathematicians, etc. who would probably regard things like Spivak as
worthy but dull. I have a copy of "The Atlas of Finite Groups" because
various group theory friends assured me it was wonderful. It's so
large you could probably use it _as_ a coffee table. I have _no_ idea
what it's about and strongly suspect I'm never going to know enough
group theory to get any benefit out of it at all.

[Toby]

Post by Adam Atkinson

I have about £1000 worth of book tokens to use up...

!!

(don't ask)

Curses!

lol sorry ;D

Post by Adam Atkinson

....I'm just looking for a
core selection of maths books that everyone 'in the know' has, then
I'll take it from there when I find particular areas that fascinate
me, unless there's a better way...

Well, it could be argued that using the tokens to get stuff you need
for whatever course you're actually doing might not be a bad idea.
However, I'm sure you could spare some for a few real corkers. With a
budget like that, perhaps you should plan a trip to London to visit
Foyles or Waterstones, or some other city with a large university
bookshop in it, to have a _good_ look at the candidates.

Oooh that sounds like a cool idea.

Post by Adam Atkinson
There's probably very little that "everyone in the know" has. I bought
very few textbooks at university because they didn't appear to be
necessary - for all I know, this could have been a mistake, but I
don't THINK most people bought the recommended books for most courses
as lectures seemed to cover most/all of it. I probably bought more
books for third year courses than I did for earlier ones.
However lovely I think Spivak might be, it has to be said that it's
"just" a (very good) first book on analysis. In the long term, will you
really want one? I know various group theorists, applied
mathematicians, etc. who would probably regard things like Spivak as
worthy but dull. I have a copy of "The Atlas of Finite Groups" because
various group theory friends assured me it was wonderful. It's so
large you could probably use it _as_ a coffee table. I have _no_ idea
what it's about and strongly suspect I'm never going to know enough
group theory to get any benefit out of it at all.

Yes, it seems like I'm actually going to have to become at least a
little discerning...Why couldn't there have been some kind of maths
bible!

Cheers again.

[Adam Atkinson]

Post by Toby
Yes, it seems like I'm actually going to have to become at least a
little discerning...Why couldn't there have been some kind of maths
bible!

Looking around my big pile'o'books, I noticed "Proofs from the Book".
It's a collection of especially lovely proofs of various things. That
might be a candidate. "All the Math You Missed (but now need to know
for graduate school" is a rather curious, but inexpensive,
whistle-stop tour of more or less everything on a maths degree. I
could imagine that looking through that, finding out which bits
interest you, and investigating them further might be worth a try.

Another book that various people including TK think is a lot of fun is
the very odd "Mathematics Made Difficult". It's supposed to be some
kind of a spoof. TK claims that to get the joke you need to have done
at least a couple of years of mathematics at university. It's out of
print and very very hard to find, but if you do happen to stumble
across a copy in a second-hand shop, you might want to have a leaf
through it to see if you find it amusing.

[Toby]

Post by Adam Atkinson

Post by Toby
Yes, it seems like I'm actually going to have to become at least a
little discerning...Why couldn't there have been some kind of maths
bible!

Looking around my big pile'o'books, I noticed "Proofs from the Book".
It's a collection of especially lovely proofs of various things. That
might be a candidate. "All the Math You Missed (but now need to know
for graduate school" is a rather curious, but inexpensive,
whistle-stop tour of more or less everything on a maths degree. I
could imagine that looking through that, finding out which bits
interest you, and investigating them further might be worth a try.
Another book that various people including TK think is a lot of fun is
the very odd "Mathematics Made Difficult". It's supposed to be some
kind of a spoof. TK claims that to get the joke you need to have done
at least a couple of years of mathematics at university. It's out of
print and very very hard to find, but if you do happen to stumble
across a copy in a second-hand shop, you might want to have a leaf
through it to see if you find it amusing.

Cheers. I wonder if I could find a first edition of that bloke
Newton's book on maths...Hmm, it's probably in Latin though...

[Adam Atkinson]

Post by Toby
Cheers. I wonder if I could find a first edition of that bloke
Newton's book on maths...Hmm, it's probably in Latin though...

I'm not sure you can use book tokens for antiques or even in most
second-hand bookshops. Also, I suspect 1000 pounds wouldn't be
enough.

I've thought of an anti-recommendation: don't get "Go"del, Escher,
Bach: An Eternal Golden Braid". It used to be very popular as a
present for 17 year olds who wanted to do maths at university.
(A few years later "Chaos" by Gleick (sp?) took over this role.
These days, I don't know.) I think "Forever Undecided" by Smullyan
explains Go"del better, as do various more normal books about Go"del,
there are various splendid books of Escher stuff if you want that, and
no doubt there's stuff on Bach too.

[Toby]

Post by Adam Atkinson

Post by Toby
Cheers. I wonder if I could find a first edition of that bloke
Newton's book on maths...Hmm, it's probably in Latin though...

I'm not sure you can use book tokens for antiques or even in most
second-hand bookshops. Also, I suspect 1000 pounds wouldn't be
enough.

I can't tell, so: I was joking! :P

Post by Adam Atkinson
I've thought of an anti-recommendation: don't get "Go"del, Escher,
Bach: An Eternal Golden Braid". It used to be very popular as a
present for 17 year olds who wanted to do maths at university.
(A few years later "Chaos" by Gleick (sp?) took over this role.
These days, I don't know.) I think "Forever Undecided" by Smullyan
explains Go"del better, as do various more normal books about Go"del,
there are various splendid books of Escher stuff if you want that, and
no doubt there's stuff on Bach too.

sk tsk, you must try to keep up with the latest fashions a bit more!
:-)

[Malcolm]

If you are still doing A-levels and aim to do Maths/Physics courses at
university you shouldn't start buying boring:-) textbooks. Go for
demanding popular books that show you have an interest in the subject
besides just doing schoolwork. That's what will get interviewers
interested in you. A common question asked at interview is "what are
you reading". A good one to start with is "The Road to Reality" by
Roger Penrose:

http://www.321books.co.uk/reviews/the-road-to-reality-by-roger-penrose.htm

THIS IS THE MATHS BIBLE!

Anything by Ian Stewart (for Maths) or Richard Feynman (for physics)
should also float your boat. Stephen Hawking is fine, but you should
show you've read more than BHT.

Of course any of these authors are also a superb read, and if you
don't enjoy reading them then Maths/Physics may not be for you!

Don't forget to check out the latest releases from Amazon, you can get
40% off. For instance, Penrose is 40% off. Also at a discount is
Dawkins:

http://www.321books.co.uk/reviews/the-ancestors-tale-richard-dawkins.htm

Top universities like to see evidence of reasonably broad reading, so
a mathematician with an interest in Dawkins will be welcomed with a
smile. John Carey the Oxford professor of English has a book on 'easy
to read ' novels, so you could check that out as well and read a few
novels. I would say just read Dickens: David Copperfield, Hard Times &
Great Expectations are short and reveal the height of his powers. They
are also about youngsters moving onto 'higher' pursuits so you might
even learn something. (Try Bleak House if you really want to impress,
save Pickwick Papers for your mid-life crisis:-) There's a great
Oxford series of hardback Dickens whcih isn't expensive & will look
good on any bookshelf.

But if it's maths your REALLY after then two must buys are Martin
Gardner's update of the book by Sylvanus P. Thompson (Who? Everyone
should know him, not many do) that taught Feynman calculus:

http://www.321books.co.uk/reviews/calculus-made-easy-silvanus-p-thomson-martin-gardner.htm

And a superb, unbelievable cheap, quality translation of Euclid from
Dover publications with full commentary from Sir Thomas Heath (Who?
You should know!):

http://www.321books.co.uk/reviews/elements-euclid.htm

Well there's a £100 worth of advice. Tell any Maths interviewer you're
reading or have read all these books he'll beg you to sign up for his
department.

With £1000 you could probably buy Dover's entire list (now that would
impress....)

Reading Penrose & Dawkins & Dickens should get you into Oxford (as
long as you get those A** as well!!)

Penrose has a superb biography & guides to further reading, such as to
G.H. Hardy, Smolin, calculus books, geometry books etc, etc, etc......
and he is in the know :-)

Post by Toby

Post by Adam Atkinson

I have about £1000 worth of book tokens to use up...

!!

(don't ask)

Curses!

lol sorry ;D

Post by Adam Atkinson

....I'm just looking for a
core selection of maths books that everyone 'in the know' has, then
I'll take it from there when I find particular areas that fascinate
me, unless there's a better way...

Well, it could be argued that using the tokens to get stuff you need
for whatever course you're actually doing might not be a bad idea.
However, I'm sure you could spare some for a few real corkers. With a
budget like that, perhaps you should plan a trip to London to visit
Foyles or Waterstones, or some other city with a large university
bookshop in it, to have a _good_ look at the candidates.

Oooh that sounds like a cool idea.

Post by Adam Atkinson
There's probably very little that "everyone in the know" has. I bought
very few textbooks at university because they didn't appear to be
necessary - for all I know, this could have been a mistake, but I
don't THINK most people bought the recommended books for most courses
as lectures seemed to cover most/all of it. I probably bought more
books for third year courses than I did for earlier ones.
However lovely I think Spivak might be, it has to be said that it's
"just" a (very good) first book on analysis. In the long term, will you
really want one? I know various group theorists, applied
mathematicians, etc. who would probably regard things like Spivak as
worthy but dull. I have a copy of "The Atlas of Finite Groups" because
various group theory friends assured me it was wonderful. It's so
large you could probably use it _as_ a coffee table. I have _no_ idea
what it's about and strongly suspect I'm never going to know enough
group theory to get any benefit out of it at all.

Yes, it seems like I'm actually going to have to become at least a
little discerning...Why couldn't there have been some kind of maths
bible!
Cheers again.

[Toby]

On 20 Oct 2004 08:18:48 -0700, ***@dsl.pipex.com (Malcolm) wrote:

<cool stuff>

Thanks very much for that, I appreciate it and will most certainly
look into all of the books/authors you mention. Did you do
maths/physicseee stuff or are you just in-the-know too? :)

Cheers!

[Robert de Vincy]

Malcolm did write:

[snip]

Post by Malcolm
Reading Penrose & Dawkins & Dickens should get you into Oxford (as
long as you get those A** as well!!)

Is it okay to admit to reading them for personal enjoyment?

(Just finished reading "Great Expectations" last night, coincidentally.)

[Toby]

Post by Robert de Vincy
[snip]

Post by Malcolm
Reading Penrose & Dawkins & Dickens should get you into Oxford (as
long as you get those A** as well!!)

Is it okay to admit to reading them for personal enjoyment?
(Just finished reading "Great Expectations" last night, coincidentally.)

Sure it is, though I read them all for English over the years...

[Stuart Williams]

Post by Malcolm
If you are still doing A-levels and aim to do Maths/Physics courses at
university you shouldn't start buying boring:-) textbooks. Go for
demanding popular books that show you have an interest in the subject
besides just doing schoolwork. That's what will get interviewers
interested in you. A common question asked at interview is "what are
you reading". A good one to start with is "The Road to Reality" by
http://www.321books.co.uk/reviews/the-road-to-reality-by-roger-penrose.htm
THIS IS THE MATHS BIBLE!

Maybe I'm underestimating Toby, but The Road To Reality is very difficult
for an A level student. Demanding is one thing: this is some way beyond
demanding.

I agree about the Ian Stewart recommendation: History of Maths is an
underestimated area - Cantor and infinities, Euler and e^[i(pi)]+1=0,
Leibniz/Newton and calculus is all good non-A level stuff that
promising candidates ought to make contact with.

SW

[Toby]

On Wed, 20 Oct 2004 21:09:03 +0100, Stuart Williams

Post by Stuart Williams

Post by Malcolm
If you are still doing A-levels and aim to do Maths/Physics courses at
university you shouldn't start buying boring:-) textbooks. Go for
demanding popular books that show you have an interest in the subject
besides just doing schoolwork. That's what will get interviewers
interested in you. A common question asked at interview is "what are
you reading". A good one to start with is "The Road to Reality" by
http://www.321books.co.uk/reviews/the-road-to-reality-by-roger-penrose.htm
THIS IS THE MATHS BIBLE!

Maybe I'm underestimating Toby, but The Road To Reality is very difficult
for an A level student. Demanding is one thing: this is some way beyond
demanding.
I agree about the Ian Stewart recommendation: History of Maths is an
underestimated area - Cantor and infinities, Euler and e^[i(pi)]+1=0,
Leibniz/Newton and calculus is all good non-A level stuff that
promising candidates ought to make contact with.
SW

You know, you're probably not underestimating me at all :) But I
welcome any and all relevant recommendations and am thankful for them!

[Adam Atkinson]

Post by Toby

Post by Stuart Williams
I agree about the Ian Stewart recommendation: History of Maths is an
underestimated area - Cantor and infinities, Euler and e^[i(pi)]+1=0,
Leibniz/Newton and calculus is all good non-A level stuff that
promising candidates ought to make contact with.
SW

You know, you're probably not underestimating me at all :) But I
welcome any and all relevant recommendations and am thankful for them!

The Eli Maor stuff is quite nice. Um... "e, history of a number",
"trigonometric delights" are two I can remember.


Is "infinity and beyond" Maor or Rudy Rucker? There's a book on
infinity
by Rucker which is quite interesting. Smullyan's logic puzzle books
are worth grabbing if you can find them. and of course "How to lie
with statistics" (Duff) and "Innumeracy" (Paulos).

[Adam Atkinson]

Post by Malcolm
If you are still doing A-levels and aim to do Maths/Physics courses at
university you shouldn't start buying boring:-) textbooks.

Well, Toby has quite a budget. Spending all of it on "popular" books
would be difficult and probably pretty silly. Keeping some of it
to be spent (later) on textbooks as and when wouldn't be a bad idea at all:
though as I've said, for a lot of courses buying the recommended
book could be a waste of time/money.

Toby should probably find out where his tastes lie before spending
significant amounts of money on very hard books. If he turns
out to be an applied sort of mathematician, having lots of stuff
on Galois Theory, Measure Theory and similar wouldn't make much sense.

Anyway, Spivak isn't boring :-)

Post by Malcolm
Go for
demanding popular books that show you have an interest in the subject
besides just doing schoolwork. That's what will get interviewers
interested in you. A common question asked at interview is "what are
you reading". A good one to start with is "The Road to Reality" by
http://www.321books.co.uk/reviews/the-road-to-reality-by-roger-penrose.htm
THIS IS THE MATHS BIBLE!

"A Very Short Introduction to Mathematics" by Gowers or the revised version of
"What is Mathematics" would do. Or Davies and Hersh "The Mathematical
Experience" I suppose.

Post by Malcolm
Anything by Ian Stewart (for Maths)

I find the business with stories and jokes in his recent books rather
annoying, actually.

Post by Malcolm
or Richard Feynman (for physics)

to be sure. Also Jearl Walker's "The Flying Circus of Physics"

Post by Malcolm
Don't forget to check out the latest releases from Amazon, you can get
40% off. For instance, Penrose is 40% off.

Crikey. I've never seen anything above 30 before.

Post by Malcolm
Also at a discount is
http://www.321books.co.uk/reviews/the-ancestors-tale-richard-dawkins.htm

"Selfish Gene" or "Blind Watchmaker" also good fun. Dimininshing returns
set in if you buy River out of Time and Extended Phenotype and
Devil's Chaplain and Unweaving the Rainbow as well.

Post by Malcolm
But if it's maths your REALLY after then two must buys are Martin
Gardner's update of the book by Sylvanus P. Thompson (Who? Everyone

Spivak's jolly good value too, though, really.

Post by Malcolm
With £1000 you could probably buy Dover's entire list (now that would
impress....)

Dover's list is very very long! I think Pierce's book on information
theory is published by Dover. That's pretty readable - though
Shannon's original paper is available in a cheap edition too, and
that's fairly readable too.

Post by Malcolm
Penrose has a superb biography & guides to further reading, such as to
G.H. Hardy, Smolin, calculus books, geometry books etc, etc, etc......
and he is in the know :-)

The bibliography in Korner's "The Pleasures of Counting" is pretty
solid, and we know Toby already has that.

[Toby]

On 21 Oct 2004 05:56:49 -0700, ***@mistral.co.uk (Adam Atkinson)
wrote:

<snip coolness>

teehee my local bookshop loves me now, and knows me by name, even just
by my telephone voice (which is the same as my normal voice, I hasten
to add...Unless I'm being silly).

[Malcolm]

Post by Toby
<snip coolness>
teehee my local bookshop loves me now, and knows me by name, even just
by my telephone voice (which is the same as my normal voice, I hasten
to add...Unless I'm being silly).

I made it to Masters level in Astronomy and have worked in
universities for 20+ years. Sorry if I implied all textbooks are
boring, my comment was slightly tongue in cheek. Spivak is certainly
worth buying. I saw several copies in Blackwell's second hand section
in Oxford recently -- definitely go there on a shopping expedition if
you can. I also agree £1000 on popular books would be a bit much.
Limit your spending to about £200, the remaining £800 may be
sufficient for funding textbook buying for three years. But wait till
you get the lists and ask students & staff what you REALLY need. I
agree that Penrose is hard, but I did point out it was a BIBLE. Don't
expect to read it like Brief History of Time. It's full of equations
that usually only postgrad. theoretical physicists see. It was
reviewed on 'start the week' and Andrew Marr said it was the only book
he had never managed to get through. Give yourself a few years. It
would be great to read it while doing a B.Sc. in
mathematics/physics/astronomy. You can bother all your lecturers by
saying, "But Penrose says..."

For those without £1000 to buy books, you don't really need books.
See:

http://www.phys.uu.nl/~thooft/theorist.html

to learn how to become a nobel prize winning theoretical physicist
from a nobel prize winning theoretical physicist. (This is the most
amazing page I've ever seen). Most university lecturers & text book
writers are second rate hacks so you'll need people like Richard
Feynman, Roger Penrose and Gerard 't Hooft to refer to when you get
upset about not being taught by the best.

Also, wait until January you may find bargains in the sales.

I notice Simon Singh has a new book out: "Big Bang". This is much
easier than Penrose, and he's a professional science writer as well as
a PhD. Well worth a look. He's also doing a book tour so check if he's
speaking at a bookshop near you. I've heard him give a talk and he's
well worth a listen.

I'm reading Murray Gell-Mann's "Quark and the Jaguar" at the moment.
It's definitely worthy reading (another nobel prize winner - he
predicted quarks and came up with the name). I picked it up in the
remainder section of Dillons in London (close to Euston). Great
bargains there!

[Robert de Vincy]

he predicted quarks and came up with the name

What's that sound?

Ah, it's James Joyce trying to lift his hand to raise an objection!

[Toby]

Post by Robert de Vincy

he predicted quarks and came up with the name

What's that sound?
Ah, it's James Joyce trying to lift his hand to raise an objection!

hehe damnit you beat me...I think the real story here is that a
scientist was actually well-read :P <runs>

[Adam Atkinson]

Post by Malcolm
But wait till
you get the lists and ask students & staff what you REALLY need.

Absolutely. Buying everything on reading lists is crazy. Even buying
all the "recommended" stuff is probably unnecessary.

Post by Malcolm
You can bother all your lecturers by
saying, "But Penrose says..."

Trouble is that Penrose says some very odd things elsewhere, e.g. in
"The Emperor's New Brain". People I know who probably outrank Penrose
at least as regards Computer Science tend to say TENB is nonsense
at least when talking about their areas.

Post by Malcolm
Most university lecturers & text book
writers are second rate hacks so you'll need people like Richard
Feynman, Roger Penrose and Gerard 't Hooft to refer to when you get
upset about not being taught by the best.

t'Hooft? Don't recognise that name at all. What of his should I look at?

Post by Malcolm
Also, wait until January you may find bargains in the sales.

Can you use book tokens in sales? You probably can't use them for
second hand books or on Amazon, more's the pity.

[Ian/Cath Ford]

On Thu, 21 Oct 2004 14:27:12 +0100, Toby

Post by Toby
<snip coolness>
teehee my local bookshop loves me now, and knows me by name, even just
by my telephone voice (which is the same as my normal voice, I hasten
to add...Unless I'm being silly).

What sorts of books do you actually want though Tobe? Are we talking
intellectually stimulating (in which case I'm bloody useless for you)
or fun and funky (I recommend Asterix which OS loves at the minute,
although he doesn't get half the gags) or useful (I can suggest a half
dozen cook books that if you don't like you could pass on to me - in
fact, there's an idea: you buy us all 6 books and get rid of the
tokens. How about it?)

Ian
Ian, Cath, Eoin and Calum Ford
Beccles, Suffolk, UK

I loved the word you wrote to me/But that was bloody yesterday

There's no e-mail address. We can talk here and go back to your place later

[Toby]

Post by Ian/Cath Ford
On Thu, 21 Oct 2004 14:27:12 +0100, Toby

Post by Toby
<snip coolness>
teehee my local bookshop loves me now, and knows me by name, even just
by my telephone voice (which is the same as my normal voice, I hasten
to add...Unless I'm being silly).

What sorts of books do you actually want though Tobe? Are we talking
intellectually stimulating (in which case I'm bloody useless for you)
or fun and funky (I recommend Asterix which OS loves at the minute,
although he doesn't get half the gags) or useful (I can suggest a half
dozen cook books that if you don't like you could pass on to me - in
fact, there's an idea: you buy us all 6 books and get rid of the
tokens. How about it?)
Ian
Ian, Cath, Eoin and Calum Ford
Beccles, Suffolk, UK
I loved the word you wrote to me/But that was bloody yesterday
There's no e-mail address. We can talk here and go back to your place later

Well I'll be buying 'normal' books as well hehe (just bought Jonathan
Strange and Mr Norrell and the new Terry Pratchett yay!) But I asked
on here particularly about mathsy books 'cause there seems to be a few
hardcore maths people lurkin' about...My mum and sister have between
them several billion cook books, so if I were ever inclined to cook
something ultra-fancy I'm sure I'd have no problem!!I was very
disappointed not to find any expletives in Gordon Ramsay's books :D

I don't think I'm after any colouring-in books at the mo'! teehee
<runs>

[jess]

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to
be ignorant of what students typically struggle with when they move
on from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to have a
firm grasp of basic algebra? Or can one pass a GCSE these days
without even that?

wasn't it in the news recently that that is indeed true?

[H Bergeron]

Post by jess

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to
be ignorant of what students typically struggle with when they move
on from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to have a
firm grasp of basic algebra? Or can one pass a GCSE these days
without even that?

wasn't it in the news recently that that is indeed true?

What was in the news was that the raw marks corresponding to certain
grade boundaries were (to some people) surprisingly low. A boundary at
A/B of 45% and a C/D boundary of 16% (both on the highest tier paper)
were bandied about.

The one thing that can't be concluded from these figures is that the
exams are easy or that the qualifications are worthless.

However, given that different questions test different parts of the
syllabus, it can be concluded that you can get a good grade without
demonstrating mastery of everything on the syllabus. Canny GCSE
teachers who recognise this and deliberately teach to the exam may
therefore not teach some "hard" topics as thoroughly as I'd like. I'd
prefer they didn't behave this way, but I can't altogether blame them.

[jess]

Post by H Bergeron

Post by jess

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to
be ignorant of what students typically struggle with when they move
on from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to have a
firm grasp of basic algebra? Or can one pass a GCSE these days
without even that?

wasn't it in the news recently that that is indeed true?

What was in the news was that the raw marks corresponding to certain
grade boundaries were (to some people) surprisingly low. A boundary at
A/B of 45% and a C/D boundary of 16% (both on the highest tier paper)
were bandied about.

the news story specifically mentioned that, with edexcel ayway, you could
get an a without knowing any algebra.

[H Bergeron]

Post by jess

Post by H Bergeron

Post by jess

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to
be ignorant of what students typically struggle with when they move
on from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to have a
firm grasp of basic algebra? Or can one pass a GCSE these days
without even that?

wasn't it in the news recently that that is indeed true?

What was in the news was that the raw marks corresponding to certain
grade boundaries were (to some people) surprisingly low. A boundary at
A/B of 45% and a C/D boundary of 16% (both on the highest tier paper)
were bandied about.

the news story specifically mentioned that, with edexcel ayway, you could
get an a without knowing any algebra.

Which means only that the journo found someone prepared to say that,
on the record.

Not that it is necessarily untrue. However, you can write an
intelligible novel without using the letter E. It does not follow that
this is a frequent occurrence.

[jess]

Post by H Bergeron

Post by jess

On Tue, 28 Sep 2004 17:10:56 +0100, "jess"

Post by jess

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have
to be ignorant of what students typically struggle with when
they move on from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to
have a firm grasp of basic algebra? Or can one pass a GCSE these
days without even that?

wasn't it in the news recently that that is indeed true?

What was in the news was that the raw marks corresponding to certain
grade boundaries were (to some people) surprisingly low. A boundary
at A/B of 45% and a C/D boundary of 16% (both on the highest tier
paper) were bandied about.

the news story specifically mentioned that, with edexcel ayway, you
could get an a without knowing any algebra.

Which means only that the journo found someone prepared to say that,
on the record.
Not that it is necessarily untrue. However, you can write an
intelligible novel without using the letter E. It does not follow that
this is a frequent occurrence.

that wasn't what alex asked, though.

[H Bergeron]

Post by jess

Post by H Bergeron

Post by jess

On Tue, 28 Sep 2004 17:10:56 +0100, "jess"

Post by jess

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have
to be ignorant of what students typically struggle with when
they move on from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to
have a firm grasp of basic algebra? Or can one pass a GCSE these
days without even that?

wasn't it in the news recently that that is indeed true?

What was in the news was that the raw marks corresponding to certain
grade boundaries were (to some people) surprisingly low. A boundary
at A/B of 45% and a C/D boundary of 16% (both on the highest tier
paper) were bandied about.

the news story specifically mentioned that, with edexcel ayway, you
could get an a without knowing any algebra.

Which means only that the journo found someone prepared to say that,
on the record.
Not that it is necessarily untrue. However, you can write an
intelligible novel without using the letter E. It does not follow that
this is a frequent occurrence.

that wasn't what alex asked, though.

If you interpret his question to include theoretical but implausible
scenarios for passing, it becomes IMO a silly question. Of course it
is possible to pass GCSE by being a (very lucky) monkey bashing a
typewriter or by the exam board making a clerical error in your
favour. So what?

[jess]

Post by H Bergeron

Post by jess

On Wed, 29 Sep 2004 19:21:32 +0100, "jess"

Post by jess

On Tue, 28 Sep 2004 17:10:56 +0100, "jess"

Post by jess

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you
have to be ignorant of what students typically struggle with
when they move on from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to
have a firm grasp of basic algebra? Or can one pass a GCSE these
days without even that?

wasn't it in the news recently that that is indeed true?

What was in the news was that the raw marks corresponding to
certain grade boundaries were (to some people) surprisingly low.
A boundary at A/B of 45% and a C/D boundary of 16% (both on the
highest tier paper) were bandied about.

the news story specifically mentioned that, with edexcel ayway, you
could get an a without knowing any algebra.

Which means only that the journo found someone prepared to say that,
on the record.
Not that it is necessarily untrue. However, you can write an
intelligible novel without using the letter E. It does not follow
that this is a frequent occurrence.

that wasn't what alex asked, though.

If you interpret his question to include theoretical but implausible
scenarios for passing, it becomes IMO a silly question. Of course it
is possible to pass GCSE by being a (very lucky) monkey bashing a
typewriter

how so?

[Adam Atkinson]

Post by H Bergeron
Of course it
is possible to pass GCSE by being a (very lucky) monkey bashing a
typewriter or by the exam board making a clerical error in your
favour. So what?

Maybe you can clarify something for me. What does it mean to "pass"
GCSE? When GCSEs first came out, I was told that one of the reasons
for their existence was to eliminate the concept of failure. Instead,
they would measure levels of success. A grade G in GCSE represented a
particular level of success. Other grades represented... other...
levels of success. Now, actually, it WAS possible to get less than a
grade G, which meant that GCSE had not really eliminated the concept
of failure. However, to get less than a grade G would appear to
be quite difficult. How lucky would the monkey with the typewriter
need to be?

However, the way "pass GCSE" is used these days does not
appear to mean "at least a grade G". My best guess is that these days
people use it to mean "at least a grade C". What's your take on this?

[Adam Atkinson]

Post by H Bergeron
If you interpret his question to include theoretical but implausible
scenarios for passing, it becomes IMO a silly question. Of course it
is possible to pass GCSE by being a (very lucky) monkey bashing a
typewriter or by the exam board making a clerical error in your
favour. So what?

His original question included "without a firm grasp of basic algebra".

It seems clear from your earliest messages in this thread that people can and
do pass, or even get an A in, GCSE without a firm grasp of basic algebra
and that at least some people find this unremarkable.

"no algebra at all" is presumably a very different proposition,
though I suspect one could pass (get a G in) GCSE without knowing
any algebra: the final (i.e.. end of 5th form) bottom-tier GCSE textbook
I saw quite a few years ago now had chapters on "how to read ',000' aloud",
reading maps, the shapes and words "sphere", "cylinder" and "cone",
percentages. Since grade G presumably represents a fairly modest performance
on the bottom tier paper, being able to get it knowing absolutely
no algebra sounds plausible enough. Of course, bottom tier GCSE now
may be very different from this textbook I saw c. 15 years ago.

[Dr A. N. Walker]

Post by Adam Atkinson
It seems clear from your earliest messages in this thread that people can and
do pass, or even get an A in, GCSE without a firm grasp of basic algebra
and that at least some people find this unremarkable.

I don't think that's really sustainable. The "complaint" was
that a A-grade pass mark of 45% shows dumbing down [whereas, as we all
know here, it could equally show that the exam was rather hard], and
that the implication was that you could get an A while knowing nothing
about half the course. The teachers here will know more about exactly
what that could imply; but there are [at least] two other considerations.

Firstly, that was the "hard" paper; a plausible syllabus should
have tested at least the "firm grasp of the basics" elsewhere. Secondly,
it is probably just as true that you could get first-class honours in
maths without any calculus. But you would need to be *so* brilliant at
all the algebra, discrete, etc., that it just isn't plausible. There
are not, in real life, students who can score 100% on really difficult
material in some parts of maths, yet were absolutely hopeless at the
foundational stuff from two or three years earlier. Yes, we can all
have blind spots; but the students who are superb at number theory
have their blind spots in quantum mechanics or statistical inference,
not in basic calculus [or algebra]. The very occasional exception,
if any, is not telling you anything about the structure or suitability
of the course or its assessment.

[Adam Atkinson]

Post by Dr A. N. Walker

Post by Adam Atkinson
It seems clear from your earliest messages in this thread that people can
and do pass, or even get an A in, GCSE without a firm grasp of basic algebra
and that at least some people find this unremarkable.

I don't think that's really sustainable. The "complaint" was
that a A-grade pass mark of 45% shows dumbing down

I was referring to a message from before the 45%/16% thing came up.
Someone said something about "how can you pass GCSE without knowing
that?" and someone else (HB) seemed less fazed.

Post by Dr A. N. Walker
[whereas, as we all
know here, it could equally show that the exam was rather hard],

Just so.

Post by Dr A. N. Walker
and
that the implication was that you could get an A while knowing nothing
about half the course.

Well, I'm trying to distinguish between "not having a firm grasp of
algebra" and "not knowing any algebra at all". I should think getting
a C without a firm grasp is possible. And maybe getting an A if you
don't have firm grasp but are good at cookbook style solutions.
Knowing no algebra at all... C or better seems harder. But if "passing GCSE"
only means getting a G then I should think passing GCSE knowing no algebra
is realistic.

Post by Dr A. N. Walker
Firstly, that was the "hard" paper; a plausible syllabus should
have tested at least the "firm grasp of the basics" elsewhere.

Do candidates do multiple papers? There'll be less algebra on the
non-hard papers. Getting by without a "firm grasp" might be doable:
I've seen masters of cookbookery perform miracles.

It might be interesting to see what the worst possible grade G paper
looks like. Also some sample worst possible grades C and A.

[H Bergeron]

On Tue, 28 Sep 2004 08:22:15 +0100, Alex Warren

Post by Alex Warren

Post by H Bergeron
On Mon, 27 Sep 2004 00:25:58 +0100, Alex Warren

Post by Alex Warren
Surely to pass GCSE you have to realise how dumb that sounds.

Surely, to deliver such a nasty and unhelpful response, you have to be
ignorant of what students typically struggle with when they move on
from GCSE to AS/A level.

Clearly.
But surely before commencing A-level study, students ought to have a firm grasp
of basic algebra?

What they *ought* to have is perhaps a different question from that of
what they *do* have.

Sixth form teachers (like me) enjoy moaning about GCSE teaching, just
as secondary teachers moan about primary schools and university
lecturers moan about sixth forms (you will find plenty who express
amazement that undergraduates with maths A level still can't do baby
algebra).

Fun though such moaning is, it doesn't alter the necessity to face up
to the inherited deficiencies and do something to tackle them.

Whilst some students starting AS are very well prepared, the majority
are hopeless at fractions and have a very rudimentary understanding of
algebra. Many have been drilled to rearrange formulae using mystic
incantations such as "change the side and change the sign". Many
struggle to write out the stages of any non-trivial calculation with
any clarity and abuse the equals sign with reckless abandon. No sense
in tut-tutting at them - that is where they are starting from and they
need help in sorting these things out.

Post by Alex Warren
Or can one pass a GCSE these days without even that?

Dunno about "these days". My comments above apply to the entire period
since I started teaching (mid 80s). Can't vouch for before then, but
if you go that far back, bear in mind that a *much* smaller proportion
of kids took A levels.

Post by Alex Warren
Alex

[Adam Atkinson]

Post by Samsonknight

Post by Adam Atkinson
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4.

So that would be the first formula, then. (4/3) pi r^3 is the same as
(4 pi r^3)/3. You DO see that, don't you?

Post by Samsonknight
I hate typing equations on the computer.

It's not great, it has to be said. If you really really need to type
complicated formulae/equations on a computer you might want to look at
TeX. If you use windows, http://www.miktex.org/ is the most obvious
place to get it. Otherwise, http://www.tug.org/. It's probably not the
best use of your time at the moment. I use TeX to do the versions of
my maths homework I hand in, though the rough versions are usually
done by hand.

Post by Samsonknight

Post by Adam Atkinson
How were derivatives defined in your course?
Can you differentiate, e.g., f(x)=x^2 or f(x)=1/x from first
principles, i.e. using the defintion and not using any results you may
have been taught for products, quotients, function of a function, or
whatever?

To be honest , we have only recently started calculus, my tutor did cover it
and yes I understand what differentiation is for and how it can be applied.
We did go over first principles, like he made me draw a graph and find the
slopes , draw chords (which I understand) etc etc.

Mm. How is the derivative actually _defined_ on your course, though?

Post by Samsonknight
I think I may go over
this again with my tutor next time I see him. If however, you are able to
help me pollish up on it , by showing me an example and then I can see how
you did it via that method , that would be nice. Alternatively, if you have
any linsk to any good web sites, I would be grateful.

I don't know of any web sites on this, and I'm sure you're as capable
of finding them as I am. I'd recommend the seriously excellent
"Calculus" by Michael Spivak if you plan on doing mathematics at
university.

Anyway, "first principles" to me means doing something like this:

(non-proportional font, please)

f(x+h)-f(x)
----------- = (whatever)
h

Then take the limit as h goes to 0.

So in the case of f(x)=x^3, we have:

f(x+h)-f(x) x^3+3x^2h+3xh^2+h^3 - x^3 3x^2 + 3xh + h^2
----------- = ------------------------- =
h h

and this tends to 3x^2 as h tends to 0. Hence, the derivative of
f(x)=x^3 is f'(x)=3x^2. (This final "limit" step is trivial in this
case, but sometimes isn't).

It should be pretty clear that if you multiply f by a constant c,
f(x+h) and f(x) are both multiplied by c, and so the derivative is
multiplied by c.

How about doing f(x)=1/x from first principles on your own? You
already know what the answer is going to be, which should help.

[Toby]

On 27 Sep 2004 5:23:3 +0100, "Adam Atkinson" <***@mistral.co.uk>
wrote:

<snip>

Post by Adam Atkinson

Post by Samsonknight
I hate typing equations on the computer.

It's not great, it has to be said. If you really really need to type
complicated formulae/equations on a computer you might want to look at
TeX. If you use windows, http://www.miktex.org/ is the most obvious
place to get it. Otherwise, http://www.tug.org/. It's probably not the
best use of your time at the moment. I use TeX to do the versions of
my maths homework I hand in, though the rough versions are usually
done by hand.

Is that with the OU? How's it going?

[Adam Atkinson]

Post by Toby

Post by Adam Atkinson
I use TeX to do the versions of
my maths homework I hand in, though the rough versions are usually
done by hand.

Is that with the OU? How's it going?

Yes. 95, 97, 98 and 97% on the homeworks. Almost all the marks I've
lost have been for stupid mistakes - transcription errors and
suchlike. Quite annoying. However, I've been spending far, far too
long on the homeworks. I've signed up for two courses next year, so
won't be able to do the same. And second-year Japanese won't help
either, of course.

Exam on the 15th of October. We shall see.

[Toby]

Post by Adam Atkinson

Post by Toby

Post by Adam Atkinson
I use TeX to do the versions of
my maths homework I hand in, though the rough versions are usually
done by hand.

Is that with the OU? How's it going?

Yes. 95, 97, 98 and 97% on the homeworks. Almost all the marks I've
lost have been for stupid mistakes - transcription errors and
suchlike. Quite annoying. However, I've been spending far, far too
long on the homeworks. I've signed up for two courses next year, so
won't be able to do the same. And second-year Japanese won't help
either, of course.
Exam on the 15th of October. We shall see.

hehe I am extremely well-acquainted with silly mistakes. I assume with
four assignments it was a 30 credits course? MSc level? Unless it's
different to the beginner's courses, at least you'll have half the
marks in the bag already! I always found homework time expanded to the
time I had available, and vice versa...It was only half done, mind,
but...heh

hehe Second-year Japanese sounds, err, fun :-) That's through
somewhere in London, though, isn't it, not the O.U.?

Good luck for the exam!

[Adam Atkinson]

Post by Toby

Post by Adam Atkinson
Exam on the 15th of October. We shall see.

hehe I am extremely well-acquainted with silly mistakes. I assume with
four assignments it was a 30 credits course? MSc level?

Yes to both. I can see my module choices after next year becoming more
problematic. Nonlinear differential equations? Hmm. Applied Complex
Variables? Hmm...

Post by Toby
Unless it's
different to the beginner's courses, at least you'll have half the
marks in the bag already!

Yes. Of course, even with 100% on the coursework you need to get at
least 40% on the exam.

Post by Toby
I always found homework time expanded to the
time I had available, and vice versa...It was only half done, mind,
but...heh

Well, I was well past the point of diminishing returns on all four.
I suspect I earned few if any marks in the last two weeks each time.

Post by Toby
hehe Second-year Japanese sounds, err, fun :-) That's through
somewhere in London, though, isn't it, not the O.U.?

SOAS. 2 hours a week on Saturdays. So it's a very slow course, really.

Post by Toby
Good luck for the exam!

Ta muchly. Or "Crepi!" as they say in Italy.

[H Bergeron]

Post by Adam Atkinson

Post by Samsonknight

Post by Adam Atkinson
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4.

So that would be the first formula, then. (4/3) pi r^3 is the same as
(4 pi r^3)/3. You DO see that, don't you?

Evidently he does not. One would hardly expect a typical student just
starting AS to be confident of this.

Asserting that he *ought* to see the distinction, when he does not, is
hardly likely to help him.

[JKJK]

Post by Samsonknight

Post by Adam Atkinson
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4. I hate typing equations on the computer.

LOL, your sooo funny

Are you differentiating with respect to x or r? the answer is 0 or 4 pi r^2

[H Bergeron]

Post by JKJK

Post by Samsonknight

Post by Adam Atkinson
4 pi r^3
--------
3
or
4
--------
3 pi r^3
?

Neither , only the 4 is divided by 3 , the rest of the equation is next to
the 4. I hate typing equations on the computer.

LOL, your sooo funny
Are you differentiating with respect to x or r? the answer is 0

Only if you make a large and unwarranted assumption about dx/dr

Post by JKJK
or 4 pi r^2

[H Bergeron]

Post by Samsonknight
Hi,
A-level Maths is going well, making good progress with the tutor from
imperial college - well I guess its going 20 times better then 2 years
ago....Anyway! I have a question , and would anyone be kind enough to
y = 4/3(pie)r^3
What would happen to the fraction as there is no power as normally the
rule would be dy/dx=nx^n-1 - would the fraction just disappear when
differentiated like a single whole number? (because theres no power
next to it) How do you differentiate PIE? does the same rule apply ,
or would it be different because its pie. If I were to take a pot
guess at answering this question I would probably use the rule
dy/dx = 12/3(pie)r^2 then I would probably simplify that by dividing
the fraction to ge this: dy/dx= 4(pie)r^2 ,however I am unsure if this
is the correct answer as I have a feeling that I would have to times
the 4 by "pie".
Thank you all!
P.S.
When is the deadline for the UCAS forms, my tutor said its now moved
from December to April.

Differentiation is all about how things *vary*.

Pi does not vary. The (4/3)pi in your expression is a constant, so
treat as you would 2 or 10.

Although it looks a bit nastier, differentiating (4/3)pi*(r^3) is just
like differentiating 2*(r^3). (I'm using * her to represent
multiplication)

BTW, posting algebraic expressions in ASCII without ambiguity can be a
bit tedious, but it's an *excellent* discipline because it forces you
to use brackets appropriately.

1/2x^2 could mean any of the following:

(1/2)(x^2)
(1/(2x))^2
((1/2)x)^2
1/(2(x^2))
1/((2x)^2)

Only two of these (which?) are the same.

[John Porcella]

Post by Samsonknight
Hi,
A-level Maths is going well, making good progress with the tutor from
imperial college - well I guess its going 20 times better then 2 years
ago....Anyway! I have a question , and would anyone be kind enough to
y = 4/3(pie)r^3

Is the pi next to the 3 or the 4?

Either way, pi is just another constant, like 4/3. There is nothing to
differentiate.