Plus Blog

May 6, 2008
Tuesday, May 06, 2008

It is common belief among teachers and parents that when teaching mathematical concepts, the best way to illustrate them is with 'real-world' examples. However, researchers at Ohio State University's Center for Cognitive Science have found the exact opposite — that college students taught a new mathematical concept with real-world, concrete examples were less able to apply their knowledge to new situations than students taught with abstract symbols.

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posted by westius @ 4:40 PM

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May 1, 2008
Thursday, May 01, 2008

There are more grains of sand on Earth than there are stars in sky, or so the saying goes.

Mathematician Anne Fey, from Vrije Universiteit Amsterdam, is using sand-pile models as a novel approach to calculate probabilities in fields as diverse as studies of the Earth's crust, stock market fluctuations and the formation of traffic jams.

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posted by Plus @ 9:53 AM

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April 30, 2008
Wednesday, April 30, 2008

We're still safe

NASA mathematicians are maintaining that the world is still safe from asteroids for the time being, despite the calculations of a young German student.

The Near-Earth Object Program Office at NASA's Jet Propulsion Laboratory has not changed its current estimates for the very low probability (1 in 45,000) of an Earth impact by the asteroid Apophis in 2036.

Contrary to recent press reports, NASA offices involved in near-Earth object research were not contacted and have had no correspondence with a young German student, who claims the Apophis impact probability is far higher than the current estimate.

This student's conclusion reportedly is based on the possibility of a collision with an artificial satellite during the asteroid's close approach in April 2029. However, the asteroid will not pass near the main belt of geosynchronous satellites in 2029, and the chance of a collision with a satellite is exceedingly remote.

Therefore, consideration of this satellite collision scenario does not affect the current impact probability estimate for Apophis, which remains at 1 in 45,000.

This information is adapted from a NASA press release.

posted by westius @ 2:44 PM

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April 30, 2008
Wednesday, April 30, 2008

Life is good for only two things, both mathematical

Siméon-Denis Poisson (born 21 June 1781 Pithiviers, France; died 25 April 1840 Sceaux, France) was a French mathematician and physicist who once stated:

"Life is good for only two things, discovering mathematics and teaching mathematics."

Poisson was a student of Laplace and Lagrange and achieved highly at a young age, writing a memoir on finite differences at 18 and graduating at 19 without needing to take the final examination. He then moved immediately to the position of repetiteur at Ecole Polytechnique, which was quite an achievement as most top mathematicians had to serve in the provinces before getting a post in Paris.

In 1802, Poisson was named deputy professor and in 1806 he was appointed to the professorship that had been vacated by none other than Fourier. During this period, he studied ordinary and partial differential equations, and in particular their application to physical problems such as the pendulum and the theory of sound.

In 1808, Poisson became an astronomer at Bureau des Longitudes and in 1809 he added the chair of mechanics in Faculte des Sciences to his impressive list of appointments. In 1808 and 1809 Poisson published three important papers, the first investigating mathematical problems raised by Laplace and Lagrange about perturbations of the planets, and the others incorporating developments in Lagrange's method of variation of arbitrary constants which had been inspired by the first of Poisson's three papers. In addition, he published a new edition of Clairaut's Theorie de la figure de la terre, which had first been published in 1743 and confirmed the Newton-Huygens belief that the Earth was flattened at the poles.

In 1811, Poisson won a "Grand Prix" on electricity studies and in 1813 his results regarding the potential in the interior of attracting masses found application in electrostatics. Papers followed on the velocity of sound in gasses, on the propagation of heat, and on elastic vibrations.

It was in his 1837 work Recherches sur la probabilite des jugements en matière criminelle et matière civile that the Poisson probability distribution first appears. This distribution describes the probability that a random event will occur in a time interval when the probability of the event occurring is very small and the number of trials very large.

He published between 300 and 400 mathematical works and his name is associated to a wide variety of ideas including Poisson's integral, Poisson's equation in potential theory, Poisson brackets in differential equations, Poisson's ratio in elasticity, and Poisson's constant in electricity. However, he was not highly regarded by other French mathematicians, with his reputation much higher among foreign mathematicians than his country-folk.

For more on Poisson, see his MacTutor biography. For more information on Poisson distributions and probability, see the Plus articles Blast it like Beckham, and On the ball.

posted by westius @ 1:36 PM

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April 30, 2008
Wednesday, April 30, 2008

Got what it takes?

The European Space Agency is looking for recruits, and it seems that good mathematical abilities can help you rise to the top of the heap. 50,000 applications are expected for the four positions on offer to be astronauts on the International Space Station.

BBC News Magazine has detailed all the boxes you need to tick to be in the running in their story So what is the right stuff? Apart from being young (between 27 and 37) and having life experience, you need patience, bravery, to work well in a team and in a strange environment, and be psychologically capable of dealing with the stresses (and the loneliness) of the job.

On top of this, you need to be at least degree qualified in engineering, science, medicine or maths. So, if you're a maths grad and this sounds like you, see the ESA careers page.

posted by westius @ 11:50 AM

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April 29, 2008
Tuesday, April 29, 2008

$8m to support mathematical research from quantum physics to biology

An $8 million grant has been awarded to a Cambridge mathematician to support his study of mathematical models relevant to research in the life sciences, engineering and nanotechnology.

Peter Markowich, Professor of Applied Mathematics in the Department of Applied Mathematics and Theoretical Physics, was awarded the funding by Saudi Arabia’s King Abdullah University of Science and Technology (KAUST).

The award was made through KAUST's global research partnership (GRP), which operated for the first time this year. The partnership aims to bring together researchers from across the globe to work on challenging scientific and technological problems which have particular relevance to Saudi Arabia and the region.

KAUST’s funding will help further Professor Markowich's work with the Applied Partial Differential Equations Research Group (APDE), allowing it to take on five new postdoctoral researchers and to expand into a new centre.

Professor Markowich said: "This award is a great honour and it gives a wonderful opportunity to build up my research group and strengthen the field of analysis and numerics of applied partial differential equations at DAMTP."

"I came to Cambridge University not even a year ago, so there is no way I could imagine a better start! It is also very exciting to be part of the endeavour of creating a new high level research institution."

"The biggest part of the funding will go into hiring postdoctoral researchers at DAMTP, working on differential equation models in such diverse areas as quantum physics and biophysical processes."

Their research project, Applied and Computational Differential Equations in Life Sciences, Nanoscience and Engineering, will focus on applications of differential equations, those equations which have functions as solutions, and involve derivatives, or rates of change, of the solution, often in intricate nonlinear ways.

Such equations can be formulated to model situations that arise in a number of disciplines. Whilst physics and engineering yield numerous classical examples, they can also be applied in more unexpected situations. Some of the work currently taking place at APDE involves their use in restoring medieval wall frescoes, for example.

KAUST investigator awards will fund research for five years and have also been made in support of a range of fields other than applied mathematics, including work on immunisation, water desalination, renewable and sustainable energy sources and environmentally friendly construction materials.

Each of the awardees, known as KAUST Investigators, will conduct research at their own institutions and, partly, on the KAUST campus, which will open in September 2009. The university is being built as an international, graduate-level research institute, and intends to become a major contributor to global research.

This article is adapted from material from the University of Cambridge.

posted by westius @ 10:16 AM

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