Mathematical minds stir a beauty within

MATHEMATICIAN John Nash was catapulted into the public eye by the film A Beautiful Mind. Now scientists have found that maths activates the same part of the mind that processes beauty.

University College London neurobiologists have discovered that when mathematicians consider aesthetically pleasing formulas it triggers activity in the part of the brain normally stimulated when people contemplate art or music.

more…

In the words of mathematician GH Hardy, “(mathematics) must be justified as art if it can be justified at all”.

I must admit I got that from this contentious opinion piece:

For Britain’s pupils, maths is even more pointless than Latin

http://www.theguardian.com/commentisfree/2014/feb/18/maths-more-pointless-than-latin-british-pupils-china?INTCMP=ILCNETTXT3487

Bubblecar said:

In the words of mathematician GH Hardy, “(mathematics) must be justified as art if it can be justified at all”.

I must admit I got that from this contentious opinion piece:

For Britain’s pupils, maths is even more pointless than Latin

http://www.theguardian.com/commentisfree/2014/feb/18/maths-more-pointless-than-latin-british-pupils-china?INTCMP=ILCNETTXT3487

What a load of self-satisfied garbage.

As he types on his computer in his machine manufactured clothes, sitting on manufactured furniture, inside a concrete or steel office block, having got there on manufactured roads in a manufactured vehicle, does he give a thought to how all these things came into being?

>As he types on his computer in his machine manufactured clothes, sitting on manufactured furniture, inside a concrete or steel office block, having got there on manufactured roads in a manufactured vehicle, does he give a thought to how all these things came into being?

Fair enough, but how much of that actually requires tertiary-level maths?

Bubblecar said:

>As he types on his computer in his machine manufactured clothes, sitting on manufactured furniture, inside a concrete or steel office block, having got there on manufactured roads in a manufactured vehicle, does he give a thought to how all these things came into being?

Fair enough, but how much of that actually requires tertiary-level maths?

Engineering buildings requires maths

computer science, definitely

Bubblecar said:

>As he types on his computer in his machine manufactured clothes, sitting on manufactured furniture, inside a concrete or steel office block, having got there on manufactured roads in a manufactured vehicle, does he give a thought to how all these things came into being?

Fair enough, but how much of that actually requires tertiary-level maths?

For the engineering involved in those things ( which is a significant part of all of them) tertiary-level maths is required for all of them.

And he was talking about school level maths anyway.

Does Britain have a shortage of British-educated engineers?

Bubblecar said:

Does Britain have a shortage of British-educated engineers?

I don’t know, I believe engineering graduate numbers in the UK have fluctuated wildly in recent years.

But if they don’t teach a reasonable level of maths at school they will certainly have a shortage of engineers in 10 years when all of my generation have retired.

I doubt that he’s against a reasonable level of maths teaching, just the Tory’s fixation on maths as an educational panacea.

Tory’s = Tories’

Bubblecar said:

I doubt that he’s against a reasonable level of maths teaching, just the Tory’s fixation on maths as an educational panacea.

Who can say what he really thinks. The article adopted such a scatter-gun approach there was no coherent argument to be found in it.

You might get this in the minds or car lovers, cat lovers or someone simply reading something

The maths thing is just to provide a story

Mind you my old maths teacher told me that there were proofs/ equations that could make him cry

> MATHEMATICIAN John Nash was catapulted into the public eye by the film A Beautiful Mind.

I’ve never though of Nash’s mind as particularly beautiful. He had not even the slightest trace of altruism, and worked to promote the build-up of nuclear bombs, based on his “game theory”.

> In the words of mathematician GH Hardy, “(mathematics) must be justified as art if it can be justified at all”.

I’ve recently developed a great respect for Hardy’s work.
IMHO every high school mathematics teacher should be forced to read a book written by Hardy called:
Orders of infinity: The Infinitarcalcul of Paul du Bois-Reymond

I also love his book “Divergent Sequences”, but that’s more technical.

The one thing this thread has made me do is download a book:

Elementary Calculus: An Infinitesimal Approach

This is a calculus textbook at the college Freshman level based on Abraham Robinson’s infinitesimals, which date from 1960. Robinson’s modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.

The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt. The book is now out of print and the copyright has been returned to me as the author. I have decided (as of September 2002) to make the book available for free in electronic form at this site. These PDF files were made from the printed Second Edition.

http://www.math.wisc.edu/~keisler/calc.html

I’ll give it a look see over the next few weeks.

The Rev Dodgson said:

Bubblecar said:

>As he types on his computer in his machine manufactured clothes, sitting on manufactured furniture, inside a concrete or steel office block, having got there on manufactured roads in a manufactured vehicle, does he give a thought to how all these things came into being?

Fair enough, but how much of that actually requires tertiary-level maths?

For the engineering involved in those things ( which is a significant part of all of them) tertiary-level maths is required for all of them.

And he was talking about school level maths anyway.

Are we classing introductory calculus as secondary or tertiary level? I get the impression that British students are more likely to learn some calculus in high school than many Americans, although that varies from state to state (and even district to district).

I have two nephews in upper secondary school. They both have good maths skills, but only one of them is doing calculus, even though the other is interested in engineering (and being a professional skate-boarder :) ).

I wouldn’t expect most upper secondary students doing maths to be taught calculus, but I would hope that at least they have the option (if they have the necessary aptitude).

I love maths, but I don’t expect a large percentage of the population to share that love. I don’t think much can be done to increase the general population’s appreciation of the beauty of mathematics, but I welcome any attempts to increase mathematical skill & the love of maths in the modern world. But as I’ve said before, I’d be happy if more people left school with an understanding of ratios & how to use them. :)

PM 2Ring said:

The Rev Dodgson said:

Bubblecar said:

>As he types on his computer in his machine manufactured clothes, sitting on manufactured furniture, inside a concrete or steel office block, having got there on manufactured roads in a manufactured vehicle, does he give a thought to how all these things came into being?

Fair enough, but how much of that actually requires tertiary-level maths?

For the engineering involved in those things ( which is a significant part of all of them) tertiary-level maths is required for all of them.

And he was talking about school level maths anyway.

Are we classing introductory calculus as secondary or tertiary level? I get the impression that British students are more likely to learn some calculus in high school than many Americans, although that varies from state to state (and even district to district).

I have two nephews in upper secondary school. They both have good maths skills, but only one of them is doing calculus, even though the other is interested in engineering (and being a professional skate-boarder :) ).

I wouldn’t expect most upper secondary students doing maths to be taught calculus, but I would hope that at least they have the option (if they have the necessary aptitude).

I love maths, but I don’t expect a large percentage of the population to share that love. I don’t think much can be done to increase the general population’s appreciation of the beauty of mathematics, but I welcome any attempts to increase mathematical skill & the love of maths in the modern world. But as I’ve said before, I’d be happy if more people left school with an understanding of ratios & how to use them. :)

I suspect about two thirds, or 50%, of the hoi poli have no idea.

Realistically, from vague memories, I was doing calculus in form 5 (year 11).

suspect about two thirds, or 50%, of the hoi poli have no idea.

at least you didn’t call us plebs.

Boris said:

suspect about two thirds, or 50%, of the hoi poli have no idea.

at least you didn’t call us plebs.

I’m a kind and gentle master.

pats Boris on the head

pfffft you just want to feel what a head with hair is like.

i do wish i had seen the fun maths can be when i was at school. oh well in my next life…

Boris said:

i do wish i had seen the fun maths can be when i was at school. oh well in my next life…

Oh, shit, I hated it at school, couldn’t wait to get away from it. I then hated it 10 years later when I decided to get me some university edumacation. I’ve probably “learnt” basic calculus three or four times in my life. If you don’t continuously use it, it is so easily lost.

I’ve finally grown up (sorta) and appreciate some of the beauty of it. Then again, I’d never be a mathematician, ain’t got the brains, nor the inclination.

Realistically, from vague memories, I was doing calculus in form 5 (year 11).

—-

Me too. I really enjoyed it, too.

Michael V said:

Realistically, from vague memories, I was doing calculus in form 5 (year 11).

—-

Me too. I really enjoyed it, too.

Always said (soto voice) you were a sick bastard.

:)

sibeen said:

Always said (soto voice) you were a sick bastard.

:)

Sotto voce.

sibeen said:

Michael V said:

Realistically, from vague memories, I was doing calculus in form 5 (year 11).

—-

Me too. I really enjoyed it, too.

Always said (soto voice) you were a sick bastard.

:)

Fully sic.

Boris said:

i do wish i had seen the fun maths can be when i was at school. oh well in my next life…

Couldn’t drag yourself out of your acedia?

Witty Rejoinder said:

sibeen said:

Always said (soto voice) you were a sick bastard.

:)

Sotto voce.

ssshhhsss

sibeen said:

The one thing this thread has made me do is download a book:

Elementary Calculus: An Infinitesimal Approach

This is a calculus textbook at the college Freshman level based on Abraham Robinson’s infinitesimals, which date from 1960. Robinson’s modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.

The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt. The book is now out of print and the copyright has been returned to me as the author. I have decided (as of September 2002) to make the book available for free in electronic form at this site. These PDF files were made from the printed Second Edition.

http://www.math.wisc.edu/~keisler/calc.html

I’ll give it a look see over the next few weeks.

OK, been having a quick squiz through. Up to where he gets to quoting the fucking quotient rule.

I hate the fucking quotient rule!

sibeen said:

sibeen said:

The one thing this thread has made me do is download a book:

Elementary Calculus: An Infinitesimal Approach

This is a calculus textbook at the college Freshman level based on Abraham Robinson’s infinitesimals, which date from 1960. Robinson’s modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.

The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt. The book is now out of print and the copyright has been returned to me as the author. I have decided (as of September 2002) to make the book available for free in electronic form at this site. These PDF files were made from the printed Second Edition.

http://www.math.wisc.edu/~keisler/calc.html

I’ll give it a look see over the next few weeks.

OK, been having a quick squiz through. Up to where he gets to quoting the fucking quotient rule.

I hate the fucking quotient rule!

I remember the name, but I forget the rule. Please elaborate.

Michael V said:

sibeen said:

sibeen said:

The one thing this thread has made me do is download a book:

Elementary Calculus: An Infinitesimal Approach

This is a calculus textbook at the college Freshman level based on Abraham Robinson’s infinitesimals, which date from 1960. Robinson’s modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.

The First Edition of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt. The book is now out of print and the copyright has been returned to me as the author. I have decided (as of September 2002) to make the book available for free in electronic form at this site. These PDF files were made from the printed Second Edition.

http://www.math.wisc.edu/~keisler/calc.html

I’ll give it a look see over the next few weeks.

OK, been having a quick squiz through. Up to where he gets to quoting the fucking quotient rule.

I hate the fucking quotient rule!

I remember the name, but I forget the rule. Please elaborate.

Derivative Division. Why teach it? Bring the denominator out, invert it, and apply the product rule. Some other rule you have to memorise when it is not bloody required.

Michael V said:

Realistically, from vague memories, I was doing calculus in form 5 (year 11).

—-

Me too. I really enjoyed it, too.

My best friend at school was a year ahead of me. He decided to learn calculus in 4th form, from “Teach Yourself Calculus”. Then he urged me to give it a go. I certainly wasn’t an expert at calculus in 3rd form, but I got the basics, and I found my “sneak preview” very helpful a couple of years later.

PM 2Ring said:

Michael V said:

Realistically, from vague memories, I was doing calculus in form 5 (year 11).

—-

Me too. I really enjoyed it, too.

My best friend at school was a year ahead of me. He decided to learn calculus in 4th form, from “Teach Yourself Calculus”. Then he urged me to give it a go. I certainly wasn’t an expert at calculus in 3rd form, but I got the basics, and I found my “sneak preview” very helpful a couple of years later.

That stirs memories for me too. I have a little blue covered book on calculus that I was looking at before we got to it in the school curriculum. But I wasn’t calculating cube roots from the hymn numbers in church, like some people :)

sibeen said:

Michael V said:

sibeen said:

OK, been having a quick squiz through. Up to where he gets to quoting the fucking quotient rule.

I hate the fucking quotient rule!

I remember the name, but I forget the rule. Please elaborate.

Derivative Division. Why teach it? Bring the denominator out, invert it, and apply the product rule. Some other rule you have to memorise when it is not bloody required.

Probably why I didn’t remember it. I have a policy of not remembering things that can be worked out from first principles.

sibeen said:

I hate the fucking quotient rule!

Why?
But if it disturbs you that much, rather than using the quotient rule on u/v just use the product rule & the chain rule on uv^-1

sibeen said:

Derivative Division. Why teach it? Bring the denominator out, invert it, and apply the product rule. Some other rule you have to memorise when it is not bloody required.

Please ignore my previous post. :)

PM 2Ring said:

sibeen said:

Derivative Division. Why teach it? Bring the denominator out, invert it, and apply the product rule. Some other rule you have to memorise when it is not bloody required.

Please ignore my previous post. :)

I was drumming my fingers

:)

morrie said:

PM 2Ring said:

My best friend at school was a year ahead of me. He decided to learn calculus in 4th form, from “Teach Yourself Calculus”. Then he urged me to give it a go. I certainly wasn’t an expert at calculus in 3rd form, but I got the basics, and I found my “sneak preview” very helpful a couple of years later.

That stirs memories for me too. I have a little blue covered book on calculus that I was looking at before we got to it in the school curriculum. But I wasn’t calculating cube roots from the hymn numbers in church, like some people :)

Hey, I was only doing square roots. Cube roots are a lot more tedious. :)

I also think we did calculus in Form 5 (now Year 11 in Victoria) at High School. I think most people did General Maths at that stage, but I did something called Maths I and Maths II. And then I did subjects called Pure Maths and Applied Maths for Form 6. I did the science subjects Pure/Applied/Phys/Chem and English and German because I hadn’t decided on a career and those subjects left your options the most open. And I liked them. I got best marks in English and German (but German is, as everyone says, a mathematical language) and I got worst marks in Physics. Which is amusing considering I ended up in an optics career.

It was called Pure and applied maths for me in form 5.