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- Mathematics In Europe - Mandelbrot (10/2010)

The fractal dimension of the English coastline is about 1 24 Omnipresent in Nature Once fractals had been discovered and defined it was realized that they are to be found everywhere in nature Clouds cauliflower river systems lightning blood vessels all are examples of fractals Mandelbrot s 1982 book The Fractal Geometry of Nature became an international bestseller and according to the online bookseller Amazon it remains even 28 years after its publication among the 1500 bestselling books in the world And it is not only geometric figures or solids or even dynamical systems that can be fractals Many chaotic processes exhibit fractal behaviour For example the Brownian motion of molecules studied by Albert Einstein is of a fractal nature Mandelbrot discovered fractals when he was studying the upward and downward movements of prices on the stock exchange It occurred to him that graphs of stock prices look the same like the nested dolls of a Russian matryoshka regardless of whether one is looking at weekly daily or minute by minute fluctuations In such a case one speaks of self similar phenomena Self similarity is one of the characteristics of fractals Another though related discovery later named the Mandelbrot set has become one of the icons of modern mathematics It describes a set of points in the complex plane whose boundary is self similar and of a fractal nature Not Taken Seriously Mandelbrot was born in Warsaw in 1924 In 1936 as Jews in Poland began to be persecuted his family moved to Paris His uncle the mathematician Szolem Mandelbrojt professor at the Collège de France was one of the early members of the Bourbaki society in France which was dedicated to developing a pure expression of mathematics This uncle took his nephew under his wing However Mandelbrot s trajectory

Original URL path: http://mathematics-in-europe.eu/tr/haberler/10-frontpage/news/285-mandelbrot-10-2010 (2013-11-18)

Open archived version from archive - Mathematics In Europe - The Óbidos workshop

at YouTube can be followed on Twitter and maintain a web presence as invited guests at the main Portuguese weekly newspaper We have also increased the number of participants in the Math Olympiads by almost 70 and obtained better results at international competitions hosted one such contests and prepared the launching of a second one cooperated with other organizations in Math Games and other mathematical competitions At the same time we have started intervening systematically in the public arena on national problems related to mathematics notably on math education We have taken frontal positions on issues such as curricula exams and textbooks Every year during national exams SPM plays a central role issuing reports and writing tests answers While math popularization is a consensual activity and while we have cooperated positively in many activities such as textbook revision and teachers training education stands have been very controversial Our coherent responsible well founded and courageous stands have complemented the math popularization and achieved a national recognition that reinforces SPM capability for raising youth and public awareness of mathematics To be rigorous when is it appropriate and when is it only pedantry Maria Dedo Universita degli Studi di Milano Italia What does it mean to be rigorous in mathematics and to what extent should this property generally thought as characterizing the subject be transmitted also to informal rpa activities Does this risk to satisfy only mathematicians and bring just confusion to laymen Or on the contrary is this a fundamental point and we cannot give up to pursue it We shall give some examples in order to discuss this problem From some computer games to mathematics Jean Paul Delahaye Université de Lille France Two computer games are presented that may be of interest to raise public awareness in mathematics The first is a game with computer images which can be understood only with some notions about permutations and which can be used for an introduction to group theory The second game is the well known Game of Life of John Conway The observation of the primer configuration a configuration which computes prime numbers and some other surprising configurations is a remarkable tool allowing to introduce a various set of mathematical ideas sieve linear growth quadratic growth pseudo random sequences approximation of Pi computational universality undecidability etc The Game of life as Daniel Dennett has several time mentioned it is also a tool for philosophical reflections about complexity life and freewill Engaging the public in Mathematics in a historical environment Ana M Eiró Universidade de Lisboa Portugal The Museum of Science of the University of Lisbon with a cultural heritage from institutions that occupied the quarters since the 17th century is located in a 19th century building in the historical part of Lisbon The teaching of Mathematics in the era of the Polytechnic School was strongly connected with the teaching of Astronomy one of the most important subjects that justified building an Astronomical Observatory in the campus In this historical context the Museum tries to develop engaging educational activities and exhibitions for all audiences with particular focus on school students In this talk I will describe some of the activities developed in the last years Raising the Public Awareness in Mathematics how Astronomy can be useful João Fernandes Universidade de Coimbra Portugal In 2009 it was celebrated the International Year of Astronomy in more than 140 countries It was a great success involving more than 800 millions participants all over the world For sure Astronomy can help catch the attention for science On that other hand the old and modern Astronomy is full of Mathematics In this talk we briefly present some examples how the Astronomy can be useful on the public awareness in Mathematics Physics and Mathematics outreach do they need to split in science communications Carlos Fiolhais Universidade de Coimbra Portugal The general public has an avid interest in Physics subjects like Cosmology and Astronomy Nanotechnology and Particle Physics But most of this subjects are tightly associated with Mathematics including intricate branches of Mathematics and it is said e g Hawking that the inclusion of a single equation halves the number of readers of a popular science books How is Physics transmitted without Mathematics if the two at least from the perspective of a physicist are inseparable Is Mathematics popularization more difficult than that of Physics And is public awareness of Mathematics facilitated by the inclusion of Physics Playing with mathematics Il Giardino di Archimede Enrico Giusti Universita degli Studi di Firenze Italia Open since 1999 Il Giardino di Archimede Archimede s garden is the first museum completely dedicated to Mathematics and its applications My talk will give a general survey of the philosophy and of the activities of the Museum A particular attention will be reserved to the Laboratori di matematica Math labs Originally designed for students 5 16 and later opened to the general public during the Mathematical Sundays at the museum the labs mix up mathematics with games and history from ancient Egypt to modern times Keeping Mathematical Awareness Alive Vagn Lundsgaard Hansen Technical University of Denmark Caring for development of abstract mathematics is not at first sight useful to people and in modern society the applications of mathematics are more sophisticated and more difficult to grasp than in earlier times This may easily lead to a decline in the emphasis on mathematical knowledge and thought in society in particular in the educational system The increasing pressure from governments for more focus on immediate applications of mathematics in the educational system and in mathematical research at universities makes it a huge task to inform the public about the usefulness and necessity of understanding abstract mathematical thoughts when developing fundamental new applications of mathematics How can we handle it The German website www mathematik de Wolfram Koepf Universität Kassel Germany In this presentation we show how the German website www mathematik de is arranged and with which means we try to raise the public awareness of Mathematics in Germany

Original URL path: http://mathematics-in-europe.eu/tr/haberler/10-frontpage/news/281-the-obidos-workshop (2013-11-18)

Open archived version from archive - Mathematics In Europe - ICM2010

the opening ceremony Here is a picture of the prize winners The recipients of the Fields Medals are Elon Lindenstrass Israel Ngô Báo Châu France Stanislav Smirnov Switzerland and Cédric Villani France And these are the other prizewinners Daniel Spielmann USA Nevanlinna Prize Yves Meyer France Gauß Prize Louis Nirenberg USA Chern Medal Award More details can be found on the homepage of the ICM The next ICM the ICM2014

Original URL path: http://mathematics-in-europe.eu/tr/haberler/10-frontpage/news/74-icm2010 (2013-11-18)

Open archived version from archive - Mathematics In Europe - Matematik nedir?

starting point He also supports his idea of mathematics everywhere with a number of examples pdf 172 kB Franka Brückler Croatia tells a story in which preliminary answers to the question appear in an extensive coffeehouse discussion Krzysztof Ciesielski Poland writes about what mathematics means to him This article can also be read in in Polish pdf 19 kB Ehrhard Behrends Germany emphasizes three important aspects of mathematics It is useful it is fascinating and without mathematics one cannot understand how today s scientists describe the natural world The book of nature is written in the language of mathematics Galileo The following articles appeared originally in the newsletter NL of the European Mathematical Society EMS They are republished here by permission of the EMS and the authors Bourguignon an article from NL36 2000 on the role of mathematics in society pdf 125 kB Davis This article from NL51 2004 is written in the style of Leonhard Euler s letters to a German princess Among other things Davis answers the question what is mathematics pdf 126 kB Brown Porter In two articles several basic questions are given an extensive treatment Is mathematics important What is the object of mathematical research Here

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/matematik-nedir (2013-11-18)

Open archived version from archive - Mathematics In Europe - Manzara

understood that the interdependencies among the various fields cannot be very well represented by the borders of countries on a map in the plane Fundamental concepts Anyone who begins to become involved intensively in mathematics will quickly discover that certain fundamental concepts appear over and over We will discuss some of these here Numbers As everyone knows mathematics deals with numbers Here some of the most important numbers are introduced

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/manzara (2013-11-18)

Open archived version from archive - Mathematics In Europe - Araştırma

Society Our Sponsor Munich RE Research Ayrıntılar Kategori Research Never in the history of mathematics has there been so much research activity as at present A large amount of current research is directed at problems in industry economics science and technology and many mathematicians are working intensively on research into the fundamentals of mathematics And it must further be emphasized that many things that we encounter in our daily lives

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/arast-rma (2013-11-18)

Open archived version from archive - Mathematics In Europe - Tarih/Felsefe

kB Bourguignon Cartan NL70 2008 pdf 45 kB Brüning Euler NL66 2007 pdf kB Baas Selberg NL65 2007 pdf 291207 kB Geiges Huygens NL65 2007 pdf 265 kB Schindler Gödel NL62 2006 pdf 66 kB Reiter Boltzmann NL61 2006 pdf 161 kB Lützen On the Mutual Influence of Mathematics and Physic NL60 2006 pdf 138 kB Samuel Cartan NL53 2004 pdf 263 kB Fokking van Kampen NL52 2004 pdf 1130 kB Rédei von Neumann NL51 2004 pdf 178 kB Gray Legendre NL45 2002 pdf 78 kB Mann Burnside NL 44 2002 pdf 78 kB Bekken Abel NL43 2002 pdf 124 kB Barner Fermat NL42 2001 pdf 293 kB Fauvel Napier NL39 2000 pdf 155 kB Gray Kovalevskaja andBeltrami NL35 2000 pdf 143 kB Barrow Green Celestial mechanics NL34 1999 pdf 193 kB Gray Klein and Krull NL32 1999 pdf 252 kB Philosophy of mathematics The question of the firmness of the foundations of mathematics has various answers depending on one s philosophical perspective The issue was discussed with particular intensity at the beginning of the twentieth century Although it is a question of fundamental importance it is not the focus of interest of most working mathematicians engaged in research or practical applications Here you can find an overview of the most important philosophical viewpoints Introduction Overview of the Philosophy of Mathematics logicism formalism intuitionism these articles are translations of contributions that were written originally for www mathematik de The following articles appeared originally in the Newsletter NL of the European Mathematical Society EMS They are republished here with permission of the EMS and the authors Corfield Nominalism and Realism NL75 2010 pdf 1395 kB Artstein Platonism NL75 2010 pdf 1362 kB Davies Platonism NL72 2009 pdf 108 kB Gardner On the Philosophy of Mathematics NL72 2009 pdf 108 kB Davis

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/tarih-felsefe (2013-11-18)

Open archived version from archive - Mathematics In Europe - Müzik, sanat, ...

relationships with music and art Music One finds information on the relationship between musical intervals and rational numbers Fourier analysis as a construction kit with which all musical tones can be assembled from simple oscillations etc Art Mathematics often reveals an aesthetic side for example when results are displayed graphically A well known example is fractals Other points of contact between mathematics and art can be found under the heading

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/muezik-sanat (2013-11-18)

Open archived version from archive