The Importance Of Maths
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Peripart
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The difference between those two tests is scary.
I'm confident that, given a quiet room, a few pencils to chew, a large flask of coffee and half a day or so, I could make a fair stab at attempting the Chinese problem, though I wouldn't find it straightforward after all these years.
The British "problem", supposedly given to first-year university students, is insulting. It's the kind of thing that GCSE pupils should be able to do in their sleep. The exam setters have chosen the most basic Pythagorean triangle, and asked some pathetically elementary questions about it.
If that illustrates the difference between the maths ability of Chinese and British students, then there's no nice way to put it - we are truly fucked. And as for Gordon Brown laughing at his own mathematical shortcomings - what's so bloody funny, Gordon?
I'm confident that, given a quiet room, a few pencils to chew, a large flask of coffee and half a day or so, I could make a fair stab at attempting the Chinese problem, though I wouldn't find it straightforward after all these years.
The British "problem", supposedly given to first-year university students, is insulting. It's the kind of thing that GCSE pupils should be able to do in their sleep. The exam setters have chosen the most basic Pythagorean triangle, and asked some pathetically elementary questions about it.
If that illustrates the difference between the maths ability of Chinese and British students, then there's no nice way to put it - we are truly fucked. And as for Gordon Brown laughing at his own mathematical shortcomings - what's so bloody funny, Gordon?
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Peripart said:
I remember doing stuff like that for 'O' level maths back in the late 70s (and I confess to having been crap at maths at school).
The Chinese problem is much more like the kind of thing we should be challenging students with in this country, but we've dumbed everything down so anybody can get on a degree course.
We are so in trouble.
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Nobody here has wondered why the RS of Chemistry should be asking this question, but I'll tell you anyway:
It's because 3-D geometry is very important in chemistry when studying the positions of atoms in complex molecules.
(I think I'm correct in saying that different substances can have the same chemical formula, if they differ in the arrangement of their atoms - I think there's some special word for this, which I hope an expert will soon inform us about, to save me trying to google it up!)
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We've had maths and beer - now, maths and football!
The nation’s top ten - no arguments
Our correspondent offers a mathematical conclusion to the Premiership talent contest
Daniel Finkelstein
Five of the best and worst
So here you have it. Every Premiership player’s season, ranked. How did Fink Tank do it? We used a multivariate Poisson log-normal model. I hope you find that information helpful.
Dr Ian Graham and Dr Henry Stott used the model to allow us to identify the relationship between goals scored and every kick of the ball made by every player for every club. Once this was done, they simulated the league season over and over again, removing players one by one and replacing them with an average player in his position.
This allowed them to see whether a player added or subtracted points from his team compared to an average replacement. The best player this season would be the one who added the most points.
But this process did not yield us the player of the year automatically. There were a couple of dilemmas to overcome.
The first was whether to take into account periods out with injury or not being played. Robbie Keane, for instance, is a fabulous player, but for one reason or another he spent only 47 per cent of the season’s playing time on the pitch for Tottenham Hotspur. Should we just ignore this?
We decided not to. Players were penalised for being out of the team. We multiplied the points added in our simulation by the proportion of time on the pitch. This produces one controversial feature of our ranking. If a player adds points compared to the average, they rise up the table the more they play. But if they subtract points, then the more they play the lower they are in the rankings. We take the view that they are making their team worse the more they play.
The other dilemma was more complicated. Gilberto Silva added more points to Arsenal than any player did to any team in England. Should he be the player of the year? The case for him is simply his importance to his team. But the case against him is that he was boosted by the fact that there were fewer impressive Arsenal players during this campaign for him to share the points with. A Manchester United player might have been better but had to split his contribution with four of five other stars.
So we hit on another way of calculating the player of the year. We looked at how many points a player would add to an average team, giving us an even playing field. This is not the perfect solution – Wayne Rooney may score more than a Sheffield United player simply because of the quality of Manchester United’s passing – but we thought that it was fair.
So what was the outcome? Here are a few headline points. Cristiano Ronaldo deserved to be crowned player of the year. The data confirms that judgment.
Also, Frank Lampard is fabulous. The common view is that Steven Gerrard is better than Lampard. Well, we cannot pass comment on basic skills. We are ranking the contributions made by players this season, not ranking abstract talent. Perhaps Liverpool do not let him breathe. Or something. But Fink Tank is absolutely clear that the free-scoring, great-passing Lampard is a towering figure. And Gerrard? He came 80th.
Finally, England and Tottenham have a goalkeeping problem. We rank 403 players and Paul Robinson came 402nd. [No surprise there, then!]
Now feel free to roam our rankings yourself.
HOW IT WORKS
The Fink Tank Predictor provides forecasts and ranking systems for English and European club football, based on a statistical model of matches based on more than five years of football scores.
In looking at player rankings for this season, the phrase “time-adjusted points” means the number of points the player would have added to an average team in the full season, compared with an average replacement. The points are then adjusted to reflect the amount of time spent on the pitch – minimum 400 minutes.
THE TOP 10
KEY: Player, club, position, pitch time, time-adjusted points
1 C Ronaldo Manchester United Midfield 85.12% 19.12
Voted player of the year by his fellow professionals and by football writers, the 22-year-old Portugal winger is our man of the season as well
2 F Lampard Chelsea M 97.31% 16.24
An ordinary season for Lampard? The statistics say otherwise
3 Gilberto Arsenal M 88.14% 16.01 P
Ten league goals was a remarkable return for the midfield man
4 Cech Chelsea G 50.15% 14.41
Chelsea missed their ’keeper desperately when he was injured
5 J Lehmann Arsenal G 97.30% 13.94
He may be 37 but the German is still among the league’s elite
6 P Scholes Man Utd M 79.10% 13.50
Enjoyed spectacular return to form after last season’s eye injury
7 T Howard Everton G 94.59% 12.96
Failed to make the grade at Old Trafford but a Goodison star
8 N Vidic Man Utd D 66.11% 10.48
The centre back was rock-solid in his first full season in England
9 B McCarthy Blackburn F 88.98% 9.91
Eighteen goals in 36 starts proves McCarthy is a lethal predator
10 A Hleb Arsenal M 68.14% 9.87
Not as flashy as some of his teammates, but highly effective
http://www.timesonline.co.uk/tol/sport/ ... 851667.ece
The nation’s top ten - no arguments
Our correspondent offers a mathematical conclusion to the Premiership talent contest
Daniel Finkelstein
Five of the best and worst
So here you have it. Every Premiership player’s season, ranked. How did Fink Tank do it? We used a multivariate Poisson log-normal model. I hope you find that information helpful.
Dr Ian Graham and Dr Henry Stott used the model to allow us to identify the relationship between goals scored and every kick of the ball made by every player for every club. Once this was done, they simulated the league season over and over again, removing players one by one and replacing them with an average player in his position.
This allowed them to see whether a player added or subtracted points from his team compared to an average replacement. The best player this season would be the one who added the most points.
But this process did not yield us the player of the year automatically. There were a couple of dilemmas to overcome.
The first was whether to take into account periods out with injury or not being played. Robbie Keane, for instance, is a fabulous player, but for one reason or another he spent only 47 per cent of the season’s playing time on the pitch for Tottenham Hotspur. Should we just ignore this?
We decided not to. Players were penalised for being out of the team. We multiplied the points added in our simulation by the proportion of time on the pitch. This produces one controversial feature of our ranking. If a player adds points compared to the average, they rise up the table the more they play. But if they subtract points, then the more they play the lower they are in the rankings. We take the view that they are making their team worse the more they play.
The other dilemma was more complicated. Gilberto Silva added more points to Arsenal than any player did to any team in England. Should he be the player of the year? The case for him is simply his importance to his team. But the case against him is that he was boosted by the fact that there were fewer impressive Arsenal players during this campaign for him to share the points with. A Manchester United player might have been better but had to split his contribution with four of five other stars.
So we hit on another way of calculating the player of the year. We looked at how many points a player would add to an average team, giving us an even playing field. This is not the perfect solution – Wayne Rooney may score more than a Sheffield United player simply because of the quality of Manchester United’s passing – but we thought that it was fair.
So what was the outcome? Here are a few headline points. Cristiano Ronaldo deserved to be crowned player of the year. The data confirms that judgment.
Also, Frank Lampard is fabulous. The common view is that Steven Gerrard is better than Lampard. Well, we cannot pass comment on basic skills. We are ranking the contributions made by players this season, not ranking abstract talent. Perhaps Liverpool do not let him breathe. Or something. But Fink Tank is absolutely clear that the free-scoring, great-passing Lampard is a towering figure. And Gerrard? He came 80th.
Finally, England and Tottenham have a goalkeeping problem. We rank 403 players and Paul Robinson came 402nd. [No surprise there, then!]
Now feel free to roam our rankings yourself.
HOW IT WORKS
The Fink Tank Predictor provides forecasts and ranking systems for English and European club football, based on a statistical model of matches based on more than five years of football scores.
In looking at player rankings for this season, the phrase “time-adjusted points” means the number of points the player would have added to an average team in the full season, compared with an average replacement. The points are then adjusted to reflect the amount of time spent on the pitch – minimum 400 minutes.
THE TOP 10
KEY: Player, club, position, pitch time, time-adjusted points
1 C Ronaldo Manchester United Midfield 85.12% 19.12
Voted player of the year by his fellow professionals and by football writers, the 22-year-old Portugal winger is our man of the season as well
2 F Lampard Chelsea M 97.31% 16.24
An ordinary season for Lampard? The statistics say otherwise
3 Gilberto Arsenal M 88.14% 16.01 P
Ten league goals was a remarkable return for the midfield man
4 Cech Chelsea G 50.15% 14.41
Chelsea missed their ’keeper desperately when he was injured
5 J Lehmann Arsenal G 97.30% 13.94
He may be 37 but the German is still among the league’s elite
6 P Scholes Man Utd M 79.10% 13.50
Enjoyed spectacular return to form after last season’s eye injury
7 T Howard Everton G 94.59% 12.96
Failed to make the grade at Old Trafford but a Goodison star
8 N Vidic Man Utd D 66.11% 10.48
The centre back was rock-solid in his first full season in England
9 B McCarthy Blackburn F 88.98% 9.91
Eighteen goals in 36 starts proves McCarthy is a lethal predator
10 A Hleb Arsenal M 68.14% 9.87
Not as flashy as some of his teammates, but highly effective
http://www.timesonline.co.uk/tol/sport/ ... 851667.ece
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Expanding on a theme from another thread:
Mathematicians explore cicada's mysterious link with primes
Numbers: Never mind the zillions of bugs; some experts are intrigued by the 13 and 17 factors.
By Michael Stroh
Sun Staff
Originally published May 10, 2004
It's probably no surprise that periodical cicadas like the clan invading Maryland this month are a big draw for biologists. Less obvious is why someone like Glenn Webb would care.
Webb is a mathematician. Working at Nashville's Vanderbilt University, he spends his days immersed in formulas, not fieldwork. But a backyard encounter with periodical cicadas several years ago led him to a mystery that has seduced more than a few members of his profession over the years: the cicada-prime connection.
Periodical cicadas crawl from their subterranean hideouts en masse every 13 or 17 years, depending on the kind.
For Webb and others, it's a pattern that immediately raises eyebrows: 13 and 17 are prime numbers, integers divisible by only themselves and 1. Primes, like cicadas, have been a source of fascination for centuries. So it didn't take long before scientists wondered: Is it mere coincidence that cicada emergences are timed to primes, or is some deeper mechanism at work?
"To me it's a little puzzle from evolution," says Webb, who has devised a mathematical model of cicada behavior and in 2001 published a tentative conclusion: The prime-number lifecycle is no coincidence but evolved as an effort to avoid predators.
The prime-number conundrum gets to the heart of what most people find beguiling about the bugs in the first place: why an insect would spend most of its life suckling on tree roots and a few short weeks singing and mating in the sunshine.
Adding to the intrigue is that it's difficult to find other examples of cicadalike behavior in nature. In his 1977 essay collection Ever Since Darwin, paleontologist Stephen Jay Gould notes one: Phyllostachys bambusoides, a bamboo native to Japan and China. The plant, writes Gould, flowers and sets seed every 120 years or so.
But as a grass, bamboos can propagate asexually, and typically they do many times before they flower. The 13- and 17-year cicadas have just one brief shot at sex - then they die.
Gould, a polymath who died in 2002, was among the first to propose that the cicada's unusual lifestyle is a strategy it evolved to avoid its predators.
"Some individuals hide, others taste bad, others grow spines or thick shells, still others evolve to look conspicuously like a noxious relative," Gould wrote. Periodical cicadas, he argued, did it by evolving a highly unusual reproductive cycle.
By springing forth from the ground by the millions, cicadas help ensure that no single predator can devour them, a tactic that evolutionary biologists now call the "predator satiation" strategy.
And by emerging every 13 and 17 years, Gould argues in his 1977 book, cicadas minimize the chance that their infrequent invasions will sync with the life cycles of birds and other creatures that dine on them.
For example, imagine bird species that wax and wane on a five-year cycle. If cicadas emerged every 10 years, their arrival might coincide with the peak of this avian predator, setting up a pattern that could drive the cicadas to extinction.
By cycling at a large prime number, cicadas minimize the chance that some bird or other predator can make a living off them. The emergence of a 17-year cicada species, for example, would sync with its five-year predator only every (5 multiplied by 17) 85 years.
That's the theory, anyway.
Intrigued by Gould's explanation, Glenn Webb at Vanderbilt spent several years, off and on, creating a mathematical model of periodical cicadas and hypothetical predators with two- and three-year life cycles. He found that Gould's argument held up: By emerging only every 13 or 17 years, periodical cicadas better ensured their survival.
But other scientists have done the math and concluded it's only coincidence that the insect's lifecycles also happen to be prime numbers.
Still others have argued it's not predators but weather that helped shape the cicada's behavior. The insects are thought to have evolved 1.8 million years ago during the Pleistocene epoch, when glaciers advanced and retreated across North America.
Scientists have created models showing that the more years cicadas remained nestled underground, the less likely they would emerge during a killing summer cold spell.
But that still doesn't explain why periodical cicadas settled on 13 and 17 and not 11, 19 or some other prime number.
"It's pretty controversial," Webb says of the whole cicada/prime business. "I don't know if there will ever be a satisfying scientific resolution."
http://www.baltimoresun.com/features/ba ... 9114.story
I love maths!
Mathematicians explore cicada's mysterious link with primes
Numbers: Never mind the zillions of bugs; some experts are intrigued by the 13 and 17 factors.
By Michael Stroh
Sun Staff
Originally published May 10, 2004
It's probably no surprise that periodical cicadas like the clan invading Maryland this month are a big draw for biologists. Less obvious is why someone like Glenn Webb would care.
Webb is a mathematician. Working at Nashville's Vanderbilt University, he spends his days immersed in formulas, not fieldwork. But a backyard encounter with periodical cicadas several years ago led him to a mystery that has seduced more than a few members of his profession over the years: the cicada-prime connection.
Periodical cicadas crawl from their subterranean hideouts en masse every 13 or 17 years, depending on the kind.
For Webb and others, it's a pattern that immediately raises eyebrows: 13 and 17 are prime numbers, integers divisible by only themselves and 1. Primes, like cicadas, have been a source of fascination for centuries. So it didn't take long before scientists wondered: Is it mere coincidence that cicada emergences are timed to primes, or is some deeper mechanism at work?
"To me it's a little puzzle from evolution," says Webb, who has devised a mathematical model of cicada behavior and in 2001 published a tentative conclusion: The prime-number lifecycle is no coincidence but evolved as an effort to avoid predators.
The prime-number conundrum gets to the heart of what most people find beguiling about the bugs in the first place: why an insect would spend most of its life suckling on tree roots and a few short weeks singing and mating in the sunshine.
Adding to the intrigue is that it's difficult to find other examples of cicadalike behavior in nature. In his 1977 essay collection Ever Since Darwin, paleontologist Stephen Jay Gould notes one: Phyllostachys bambusoides, a bamboo native to Japan and China. The plant, writes Gould, flowers and sets seed every 120 years or so.
But as a grass, bamboos can propagate asexually, and typically they do many times before they flower. The 13- and 17-year cicadas have just one brief shot at sex - then they die.
Gould, a polymath who died in 2002, was among the first to propose that the cicada's unusual lifestyle is a strategy it evolved to avoid its predators.
"Some individuals hide, others taste bad, others grow spines or thick shells, still others evolve to look conspicuously like a noxious relative," Gould wrote. Periodical cicadas, he argued, did it by evolving a highly unusual reproductive cycle.
By springing forth from the ground by the millions, cicadas help ensure that no single predator can devour them, a tactic that evolutionary biologists now call the "predator satiation" strategy.
And by emerging every 13 and 17 years, Gould argues in his 1977 book, cicadas minimize the chance that their infrequent invasions will sync with the life cycles of birds and other creatures that dine on them.
For example, imagine bird species that wax and wane on a five-year cycle. If cicadas emerged every 10 years, their arrival might coincide with the peak of this avian predator, setting up a pattern that could drive the cicadas to extinction.
By cycling at a large prime number, cicadas minimize the chance that some bird or other predator can make a living off them. The emergence of a 17-year cicada species, for example, would sync with its five-year predator only every (5 multiplied by 17) 85 years.
That's the theory, anyway.
Intrigued by Gould's explanation, Glenn Webb at Vanderbilt spent several years, off and on, creating a mathematical model of periodical cicadas and hypothetical predators with two- and three-year life cycles. He found that Gould's argument held up: By emerging only every 13 or 17 years, periodical cicadas better ensured their survival.
But other scientists have done the math and concluded it's only coincidence that the insect's lifecycles also happen to be prime numbers.
Still others have argued it's not predators but weather that helped shape the cicada's behavior. The insects are thought to have evolved 1.8 million years ago during the Pleistocene epoch, when glaciers advanced and retreated across North America.
Scientists have created models showing that the more years cicadas remained nestled underground, the less likely they would emerge during a killing summer cold spell.
But that still doesn't explain why periodical cicadas settled on 13 and 17 and not 11, 19 or some other prime number.
"It's pretty controversial," Webb says of the whole cicada/prime business. "I don't know if there will ever be a satisfying scientific resolution."
http://www.baltimoresun.com/features/ba ... 9114.story
I love maths!
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- 54,631
Vorderman heads maths task force
Carol Vorderman, the former co-host of Channel 4 gameshow Countdown, is to head a maths task force for David Cameron, the Conservatives have said.
She will assess teaching methods in England, how to tackle the "fear" of maths and if tests have got easier.
A package of proposals aimed at improving numeracy is to be unveiled by the Conservative Leader later.
Ms Vorderman said that in the last 10 years 3.5m children had finished school without a basic maths qualification.
The TV presenter, who describes maths as her "passion", will visit schools and hold discussions with experts and parents.
Speaking ahead of the launch, Ms Vorderman said: "Maths is critically important to the future of this country but Britain is falling behind the best performing countries.
"In the last decade, 3.5 million children have left school without a basic qualification in maths, a shocking statistic.
"If they are to get the best jobs in the future and Britain is to emerge stronger from the recession we have little choice but to sort maths out now.
"There are many centres of excellence and many fabulous teachers but help is needed for the children being failed.
"Maths is my passion, and there is no question that Britain has developed a fear of the subject and it is time to break that cycle."
At the launch, Mr Cameron will draw attention to figures that show it is the poorest children who are doing least well at the subject.
Of pupils who received free school meals, about 60% - 44,368 - gained a D grade or below at GCSE maths last year.
By comparison, information from parliamentary questions revealed only 3,312 achieved an A or A*.
http://news.bbc.co.uk/1/hi/education/7864202.stm
I was interested in maths before Ms Vorderman came along, honest!
Carol Vorderman, the former co-host of Channel 4 gameshow Countdown, is to head a maths task force for David Cameron, the Conservatives have said.
She will assess teaching methods in England, how to tackle the "fear" of maths and if tests have got easier.
A package of proposals aimed at improving numeracy is to be unveiled by the Conservative Leader later.
Ms Vorderman said that in the last 10 years 3.5m children had finished school without a basic maths qualification.
The TV presenter, who describes maths as her "passion", will visit schools and hold discussions with experts and parents.
Speaking ahead of the launch, Ms Vorderman said: "Maths is critically important to the future of this country but Britain is falling behind the best performing countries.
"In the last decade, 3.5 million children have left school without a basic qualification in maths, a shocking statistic.
"If they are to get the best jobs in the future and Britain is to emerge stronger from the recession we have little choice but to sort maths out now.
"There are many centres of excellence and many fabulous teachers but help is needed for the children being failed.
"Maths is my passion, and there is no question that Britain has developed a fear of the subject and it is time to break that cycle."
At the launch, Mr Cameron will draw attention to figures that show it is the poorest children who are doing least well at the subject.
Of pupils who received free school meals, about 60% - 44,368 - gained a D grade or below at GCSE maths last year.
By comparison, information from parliamentary questions revealed only 3,312 achieved an A or A*.
http://news.bbc.co.uk/1/hi/education/7864202.stm
I was interested in maths before Ms Vorderman came along, honest!
Mythopoeika
I am a meat popsicle
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rynner2 said:I was interested in maths before Ms Vorderman came along, honest!
Yes, but she makes it so much easier to be interested in maths, doesn't she?
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For more - er - intellectual reasons to be interested in maths, try some of these:
Five of the best mathematics blogs
Posted By: Ian Douglas at Feb 9, 2009 at 15:54:42 [General]
Posted in: Technology
A week or so ago I wrote that while almost every newspaper has an arts section none has one dedicated to mathematics. I was rather hoping that someone would write in pointing out that the Estado de Sao Paolo has a widely-read maths supplement on the first Thursday of every month, but it hasn't so they didn't. There is a large and thriving roster of mathematics blogs though, and I'd like to introduce a few of them.
Gowers's weblog
In at the deep(ish) end, Timothy Gowers is a British mathematician, winner of some very big awards (including the Fields medal in 1998. There is no Nobel prize for mathematics but the Fields medal is as big as they come) and author of Mathematics: a Very Short Introduction. He's running an experiment on his blog at the moment to see if he can find a collaborative, combinatorial approach to solving a mathematical problem. He wants a certain kind of proof of the density Hales-Jewett problem. The Hales-Jewett theorem asserts that for any multi-dimensional cube whose faces are coloured with a set number of colours, there must be a line of faces of all the same colour if the number of dimensions is high enough. That required number of dimensions depends on the number of sides of the cube and number of colours it is painted with. The density version concerns a subset of the cube, giving a stronger version of the problem.
There is now a discussion going on involving mathematicians from several countries all collaborating in a way that normal academic practice would not allow. Some of them are students, some lecturers and some amateurs. Don't worry if you didn't understand the problem to begin with, I'd never heard of it before reading about the experiment, but here's a new kind of enquiry going on that anyone with a handle on the facts of the matter can be involved with.
Secret Blogging Seminar
Written by eight graduate students and recent PhDs at Berkeley the Secret Blogging seminar does contain references to the work of several very bright young people but is mostly attractive for its links to developments across academia.
Shtetl Optimised
Scott Aaronson's blog, ostensibly about quantum computers, is the closest thing here to a personal blog. There are categories entitled 'Rage against doofosity' and 'Embarrassing myself' alongside 'Quantum' and 'Complexity'. Scott is an assistant professor in computer science at MIT so there's a strong emphasis on logic and, in particular, computational complexity (the study of resources required to solve problems in computer science). This is a very good one to start with as it's funny and the posts are as likely to be about films that Scott has been to see as mathematics, and when numbers do come into it they are well explained with little previous knowledge assumed.
Not Even Wrong
More about physics than maths but written from a mathematician's point of view, Peter Woit's site is a model of a good accessible blog. There are posts about the life of a mathematician, mathematics as a profession, news within the academic community and general interest problems. It started as a companion piece to Woit's book of the same name on the inadequacy of string theory as a theory, which is also worth seeking out.
Ars Mathematica
Wonderful general mathematics reporting. Some of it is complex (a series of videos is recommended as 'eminently understandable to someone who's had a course in quantum mechanics'), some is beautifully straightforward stuff that requires no background knowledge at all, and all of it speaks of a love of the subject, clarity of tone and a desire to communicate.
http://blogs.telegraph.co.uk/ian_dougla ... tics_blogs
See page for links. Something there to amuse anyone, I'd say, and it's often most fascinating if you don't understand it!
Five of the best mathematics blogs
Posted By: Ian Douglas at Feb 9, 2009 at 15:54:42 [General]
Posted in: Technology
A week or so ago I wrote that while almost every newspaper has an arts section none has one dedicated to mathematics. I was rather hoping that someone would write in pointing out that the Estado de Sao Paolo has a widely-read maths supplement on the first Thursday of every month, but it hasn't so they didn't. There is a large and thriving roster of mathematics blogs though, and I'd like to introduce a few of them.
Gowers's weblog
In at the deep(ish) end, Timothy Gowers is a British mathematician, winner of some very big awards (including the Fields medal in 1998. There is no Nobel prize for mathematics but the Fields medal is as big as they come) and author of Mathematics: a Very Short Introduction. He's running an experiment on his blog at the moment to see if he can find a collaborative, combinatorial approach to solving a mathematical problem. He wants a certain kind of proof of the density Hales-Jewett problem. The Hales-Jewett theorem asserts that for any multi-dimensional cube whose faces are coloured with a set number of colours, there must be a line of faces of all the same colour if the number of dimensions is high enough. That required number of dimensions depends on the number of sides of the cube and number of colours it is painted with. The density version concerns a subset of the cube, giving a stronger version of the problem.
There is now a discussion going on involving mathematicians from several countries all collaborating in a way that normal academic practice would not allow. Some of them are students, some lecturers and some amateurs. Don't worry if you didn't understand the problem to begin with, I'd never heard of it before reading about the experiment, but here's a new kind of enquiry going on that anyone with a handle on the facts of the matter can be involved with.
Secret Blogging Seminar
Written by eight graduate students and recent PhDs at Berkeley the Secret Blogging seminar does contain references to the work of several very bright young people but is mostly attractive for its links to developments across academia.
Shtetl Optimised
Scott Aaronson's blog, ostensibly about quantum computers, is the closest thing here to a personal blog. There are categories entitled 'Rage against doofosity' and 'Embarrassing myself' alongside 'Quantum' and 'Complexity'. Scott is an assistant professor in computer science at MIT so there's a strong emphasis on logic and, in particular, computational complexity (the study of resources required to solve problems in computer science). This is a very good one to start with as it's funny and the posts are as likely to be about films that Scott has been to see as mathematics, and when numbers do come into it they are well explained with little previous knowledge assumed.
Not Even Wrong
More about physics than maths but written from a mathematician's point of view, Peter Woit's site is a model of a good accessible blog. There are posts about the life of a mathematician, mathematics as a profession, news within the academic community and general interest problems. It started as a companion piece to Woit's book of the same name on the inadequacy of string theory as a theory, which is also worth seeking out.
Ars Mathematica
Wonderful general mathematics reporting. Some of it is complex (a series of videos is recommended as 'eminently understandable to someone who's had a course in quantum mechanics'), some is beautifully straightforward stuff that requires no background knowledge at all, and all of it speaks of a love of the subject, clarity of tone and a desire to communicate.
http://blogs.telegraph.co.uk/ian_dougla ... tics_blogs
See page for links. Something there to amuse anyone, I'd say, and it's often most fascinating if you don't understand it!
- Joined
- Aug 7, 2001
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Just watched the prog - lightweight entertainment rather than heavy science.
However, the bit about prime numbers and the reverberations in a crystal sphere was new to me.
And I was pleased to learn that both Alan and Marcus are Gooners
- what are the chances of that, eh?
However, the bit about prime numbers and the reverberations in a crystal sphere was new to me.
And I was pleased to learn that both Alan and Marcus are Gooners
- what are the chances of that, eh?
The test I was given
Given this as a test at a university beginning with B and ending in ristol.
its quite a famous puzzle and you can find the answer all over the web, there are two ways to solve it, one very easy and one very hard, so here goes.
There are two trains facing each other on a 200 mile length of track, sitting on the front of the first train is a super fly which can fly at 75 miles per hour.
Both trains set off heading for each other at the same time travelling at 50 miles per hour. The fly flies from the first train to the front of the second train, meets the second train, turns round flies back to the first and so on.
The question is how far does the fly fly before the two trains collide?
I hadn't seen the obvious answer until I spent ten minutes trying to solve it the hard way
Given this as a test at a university beginning with B and ending in ristol.
its quite a famous puzzle and you can find the answer all over the web, there are two ways to solve it, one very easy and one very hard, so here goes.
There are two trains facing each other on a 200 mile length of track, sitting on the front of the first train is a super fly which can fly at 75 miles per hour.
Both trains set off heading for each other at the same time travelling at 50 miles per hour. The fly flies from the first train to the front of the second train, meets the second train, turns round flies back to the first and so on.
The question is how far does the fly fly before the two trains collide?
I hadn't seen the obvious answer until I spent ten minutes trying to solve it the hard way
escargot
Disciple of Marduk
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Wolfram Mathworld has a nice explanation, with animated trains.
escargot1 said:I had no clue, then I read the explanation and it went whoosh, over my head.
This sort of thing is what I have a pet physicist for.
well when I first tried to solve it I tried doing it by what they call the brute force method in the illustrated solution, and you do it with calculus and end up with an infinite sum. then you go hold on... the trains will crash after two hours.. fly flies for two hours at 75 MPH which is 150 miles Duh!!!!!
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People tend to get bogged down in the (imaginary) details.escargot1 said:
It's easy to work out how long before the trains crash.
During that time, the fly is doing x mph. So it covers a distance = speed x time .
So the brute-force method is the long way round (even if a genius like John von Neumann can mentally sum a mathematical series!)
escargot
Disciple of Marduk
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It's not the details that get me - i just have little aptitude for maths.
Aidan is explaining it to me now... the fly bounces an infinite number of times in one hour.
Okay, let's say at a time dt before the trains collide the fly hits train A
It then bounces back and hits train B at a time dt2 (dt2<dt)
And then bounces back and hits train A again at a time dt3 etc
If time is continuous then there are an infinite number of collisions, each with their own time dtn and each dt smaller than the last
It stops bouncing after 1 hour
But it bounces an infinite number of times in that hour
Infinity rocks!
Aidan is explaining it to me now... the fly bounces an infinite number of times in one hour.
Okay, let's say at a time dt before the trains collide the fly hits train A
It then bounces back and hits train B at a time dt2 (dt2<dt)
And then bounces back and hits train A again at a time dt3 etc
If time is continuous then there are an infinite number of collisions, each with their own time dtn and each dt smaller than the last
It stops bouncing after 1 hour
But it bounces an infinite number of times in that hour
Infinity rocks!
You'll like this one
another university test question, more of a logic problem than anything else.
You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.
How do you measure exactly 45 minutes by burning the peices of string?
I got this one right woohoo!!!
another university test question, more of a logic problem than anything else.
You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.
How do you measure exactly 45 minutes by burning the peices of string?
I got this one right woohoo!!!
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No!escargot1 said:It's not the details that get me - i just have little aptitude for maths.
Aidan is explaining it to me now... the fly bounces an infinite number of times in one hour.
That's what I mean about getting bogged down in details.
The number of times the fly bounces in a fixed time period is totally irrelevent. We only need to know how far he flies in that period.
Easy peasy!