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Wednesday, August 30, 2006


R is a free software environment for statistical computing and graphics and is available as Free Software under the terms of the Free Software Foundation's GNU General Public License in source code form. It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS.

The R distribution contains functionality for a large number of statistical procedures. Among these are: linear and generalized linear models, nonlinear regression models, time series analysis, classical parametric and nonparametric tests, clustering and smoothing. There is also a large set of functions which provide a flexible graphical environment for creating various kinds of data presentations. Additional modules (“add-on packages”) are available for a variety of specific purposes. One of R's strengths is the ease with which well-designed publication-quality plots can be produced, including mathematical symbols and formulae where needed.

R was initially written by Ross Ihaka and Robert Gentleman at the Department of Statistics of the University of Auckland in Auckland, New Zealand. In addition, a large group of individuals has contributed to R by sending code and bug reports.

The latest version 2.3.1 was released on June 1, 2006. For more details and free download visit: R homepage.

Tuesday, August 22, 2006

Fields Medal 2006

(from top to bottom) Terence Tao of Univ California, Los Angeles, Grigory Perelman of Russia, Wendelin Werner of Univ of Paris-Sud, Orsay, Andrei Okounkov of Princeton Univ were awarded the Fields Medal during the International Congress of Mathematicians 2006 in Madrid (photo courtsey: International Congress for Mathematicians)

The Fields Medal is often described as mathematics’ equivalent to the Nobel Prize. The medal was conceived by John Charles Fields, a Canadian mathematician, “in recognition of work already done and as an encouragement for further achievements on the part of the recipient.”
The medal was first awarded in 1936. The award should usually be limited to mathematicians 40 years old or younger and is given every four years, and several can be awarded at once. This year we got 4 recipients:

(i) Grigory Perelman, a reclusive Russian mathematician who solved a key piece in a century-old puzzle known as the Poincaré conjecture. But Dr. Perelman refused to accept the medal, as he has other honors, and he did not attend the ceremonies at the International Congress of Mathematicians in Madrid. He also turned down job offers from Princeton, Stanford and other universities.

(ii) Terence Tao of University of California, Los Angeles. Dr. Tao is a native of Australia and one of the youngest Fields Medal winners ever at age 31, has worked in several different fields, producing significant advances in the understanding of prime numbers, techniques that might lead to simplifying the equations of Einstein’s theory of general relativity and the equations of quantum mechanics that describe how light bounces around in a fiber optic cable.

(iii) Wendelin Werner of the University of Paris-Sud in Orsay. Dr. Werner was born in Germany in 1968. He, like Dr. Tao, has worked at the intersection of mathematics and physics, describing phenomena like percolation and shapes produced by the random paths of Brownian motion.

(iv) Andrei Okounkov of Princeton University. Dr. Okounkov, born in 1969 in Moscow, was recognized for work that tied together different fields of mathematics that had seemed unrelated. Dr. Okounkov’s work has found use in describing the changing surfaces of melting crystals. The boundary between melted and non-melted is created randomly, but the random process inevitably produces a border in the shape of a heart.

To learn more about this award, visit the Field Medal site.

Monday, August 14, 2006

51-year Old Problem of Web Geometry Solved

Wilhelm Blaschke (1885-1962)

In 1955 German mathematician Wilhelm Blaschke, a pioneer in the branch of mathematics known as web geometry, had said that it was nearly impossible to find the conditions under which a web might be transformed into a different kind of web with different numbers of non-intersecting, straight lines. To describe such a transition mathematically would require leaps of logic and multitudes of calculations that were too great, Blaschke said.

Even as economic forecasters and theoretical physicists found uses for web geometry in subsequent decades, Blaschke's riddle remained unsolved. There was, of course, one thing that was not available to Blaschke in the 1950s: a powerful computer. Now, using advanced computer software, Vladislav Goldberg of New Jersey Institute of Technology and Valentin Lychagin of The University of Tromso, Norway have successfully arrived at a solution for the problem. Their paper "On the Blaschke conjecture for 3-webs" was published in the March, 2006 issue of 'The Journal of Geometric Analysis' and have found wide acclaim from mathematicians everywhere. Here is the Abstract of the paper.