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- Mathematics In Europe - Anasayfa

The question seems to be Devamını oku How far Stefan Banach Ayrıntılar Kategori Popular Articles Up to the end of the 19th century Poland was not noted for mathematics The mathematical results Devamını oku Stefan Banach Sewing a football Ayrıntılar Kategori Popular Articles A well known saying by the famous German football coach Sepp Herberger is The ball is round Der Ball ist rund Is it really Devamını oku Sewing a football Mathematical trees growing in chemistry Ayrıntılar Kategori Popular Articles Most of the mathematical disciplines evolved either from physical problems or for pure mathematical reasons Chemistry as a motivator for developing a mathematical theory is at least for more general theories a very rare case Graph theory is an exception Devamını oku Mathematical trees growing in chemistry Football is the most exciting sport Ayrıntılar Kategori Popular Articles Football is the most exciting sport You may or may not agree with the statement in the title and you probably have your own reasons why Devamını oku Football is the most exciting sport A pop quiz paradox Ayrıntılar Kategori Popular Articles A man commits a crime and is sentenced to death The judge Devamını oku A pop quiz paradox The Cake Cutting Problem Ayrıntılar Kategori Popular Articles Are fair divisions possible Devamını oku The Cake Cutting Problem Honeybee cells Ayrıntılar Kategori Popular Articles Three hundred years ago the great Croatian scientist Ruđer Josip Bošković Roger Joseph Boscovich was born see also the entry in the Mathematical Calendar One of the best known of his mathematical results is the description of a honeybee s cell contained in the treatise De apium cellulis Devamını oku Honeybee cells Borromean rings Ayrıntılar Kategori Popular Articles The Borromean rings are the symbol of the famous Borromeo family and of various others Devamını oku Borromean rings The

Original URL path: http://mathematics-in-europe.eu/tr/13-frontpage/popular-articles (2013-11-18)

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The initiative Mathematics of Planet Earth 2013 MPE2013 was launched on December 7 2012 The European MPE activities will start with the MPE2013 day at the UNESCO in Paris on March 5 2013 More information on this event can be found on the MPE2013 homepage and also here on www mathematics in europe eu A compilation of the European MPE2013 activities can be found here Devamını oku MPE2013 Diderot Mathematical

Original URL path: http://mathematics-in-europe.eu/tr/85-frontpage/news-frontpage (2013-11-18)

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content Press Enter Menu languages Articles in Turkish can be found here Home Anasayfa Anasayfa Haberler Bilgiler Halka ulaşma faaliyetleri Yarışmalar Matematik Yardım Meslek olarak matematik Karışık Misyon Hoşgeldin Mesajları EMS Destekçiler Diller Iletişim Yasal Bilgi arama The European Mathematical

Original URL path: http://mathematics-in-europe.eu/tr/17-articles-in-multiple-languages/german (2013-11-18)

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kabul eder http www matder org tr Matematik Vakfı matematik eğitim kitapları yayımlar her yıl bir Cahit Arf Konuşmacısı davet eder ve Masatoshi Gündüz İkeda Araştırma Ödülü nü verir http www matematikvakfi org tr Araştırma Kurumları The Istanbul Center for Mathematical Sciences http www imbm org tr The Boğaziçi University TÜBİTAK Feza Gürsey Institute http www gursey gov tr Institute for Applied Mathematics METU http www3 iam metu edu tr Diğer düzenli araştırma ve eğitim faaliyetleri Antalya Algebra Days http www aad metu edu tr Gökova Geometry Topology Conference http gokovagt org Nesin Mathematics Village http matematikkoyu org tr Sergiler http www turkmath org beta index php Popüler websayfaları http www matematiktutkusu com Matematik Farkındalığını artırma gazete ve dergiler Matematik Dünyası MD soyut matematiği duru bir dille gençlere aktarmayı hedefleyen bir dergidir Daha çok lise ve üniversite gençlerine yöneliktir Ama matematiğin evrenselliği sayesinde herkesin yararlandığı bir dergidir Sahibi Türk Matematik Derneği dir TMD ve profesyonel matematikçiler tarafından hazırlanır http www matematikdunyasi org Matematik Farkındalığını artırma gazeteciler İsmet Berkan Bu e Posta adresi istenmeyen posta engelleyicileri tarafından korunuyor Görüntülemek için JavaScript etkinleştirilmelidir Orhan Bursalı Bu e Posta adresi istenmeyen posta engelleyicileri tarafından korunuyor Görüntülemek için JavaScript etkinleştirilmelidir Nuran Çakmakçı Bu e Posta adresi istenmeyen posta engelleyicileri tarafından korunuyor Görüntülemek için JavaScript etkinleştirilmelidir Pervin Kaplan Bu e Posta adresi istenmeyen posta engelleyicileri tarafından korunuyor Görüntülemek için JavaScript etkinleştirilmelidir Matematik Farkındalığını artırma diğer faaliyetler 10 TL Cahit Arf ın Tosun Terzioğlu tarafından çekilmiş resmi ve Arf Değişmezi formülü 10TL banknotunun arkasındadır Karaköy Seminerleri TMD matematiğin popülerleşmesi amacıyla aylık seminerler düzenlemektedir http www tmd org tr Seminerler Hoşgeldiniz Ayrıntılar Kategori Turkish www mathematics in europe eu sitesine hoşgeldiniz Avrupa Matematik Birliği nin himayesi altında çalışan sitemiz matematiğe meraklı herkese hitap eder Özellikle gazeteciler ortaokul ve lise öğrencileri üniversite öğrencileri öğretmenler profesyonel matematikçiler kamuoyunda matematik bilincini artırmaya çalışan herkes için bilgi sunmaktayız Hoşgeldiniz gazeteciler Ümidimiz bu web sayfasının toplumdaki matematik bilincini artırması Haliyle siz gazeteciler önemli ziyaretçilersiniz Aradıklarınız neler olabilir Genel bilgi Matematik nedir Matematik tarihi felsefesi Yeni gelişmeler Kamu bilinci ile ilgili faaliyetler Lütfen bulamadığınız bir bilgi konusunda bizimle temasa geçin Size yardım edebiliriz Matematikle ilişkisi olan gazetecilerin email adreslerini topluyoruz Lütfen bu listede olmak isteyenler bize haber versin Onayınız olursa ülkenizde gazetecilerle temas kurmak isteyen matematikçilere adresinizi vermek isteriz Saygılarımızla mathematics in europe eu ekibi Hoşgeldiniz ortaöğretim öğrencileri Özellikle hoşgeldiniz Bu websayfasındaki çoğu bilginin ingilizce olduğunu fark edeceksiniz Diğer Avrupa dillerinde de bilgi verebilmeyi hedefliyoruz ama bu bir miktar vakit alacak İngilizceniz yeterli ise şimdiden size ilgilendirecek pek çok şeyle karşılaşacaksınız genel bilgi Matematik nedir Matematiksel harita zamanımızın araştırma problemleri matematik tarihi ve felsefesi matematik ve diğer ilgi alanları müzik sanat hangi yarışmalar ile ilgileniyorsunuz matematik okumayı düşünenler matematikçilerin nerelerde çalıştığını eğitimleri sonrasında neler yaptıklarını öğrenebilirler Bir amacımız da yakında sizlere buradan daha çok matematiksel yardım temin etmek Etrafı kolaçan edin ve hangi ek bilgiler size ilginç gelebilir bize bildirin Saygılarımızla mathematics in europe eu ekibi Hoşgeldiniz üniversite öğrencileri Matematik öğrencileri hoşgeldiniz İngilizce anadiliniz olmasa bile sunduklarımızı anlamak için yeterli ingilizceniz olmalı Yine

Original URL path: http://mathematics-in-europe.eu/tr/38-articles-in-multiple-languages/turkish (2013-11-18)

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which all mathematicians would subscribe We have collected a number of partial answers There is great variation in the ambitions of the authors and the demands placed by them on the reader The mathematical landscape Here is information on the mathematics profession Which areas are of greatest interest What important concepts are at work What of value can be said about particular numbers and formulas Research This is an enormous topic We present an overview of where in Europe outside of the universities special mathematics research institutes have been set up There are also articles on the Millennium Problems each of which carries a million dollar prize for its solution In addition you can learn about the impact of current mathematical problems on our daily lives History and philosophy of mathematics In many instances the development of mathematics was motivated by concrete problems in the natural sciences economics and technology The current state of the mathematical sciences has many historical precedents which we shall illustrate with examples It is by no means clear how well founded the methods of mathematics actually are This issue has been repeatedly addressed by philosophers of mathematics over the course of time At regular intervals

Original URL path: http://mathematics-in-europe.eu/tr/39-information/general (2013-11-18)

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that I guess I forgot the formula but it was something like it wasn t it No the formula is all right But the formula is not the theorem The theorem is If a b and c are the lengths of the sides of a right triangle and if c is the length of the hypotenuse then the equation a 2 b 2 c 2 holds The theorem does not say that the equation is or is not true for any other meanings given to a b and c It does not even say that right triangles exist But if there is a right triangle then the lengths of its sides are sure to be related in the described way Now I am completely confused Geraldine joins in and I think I have a new definition of mathematics it is the art of saying complicated sentences I agree that it is an art But not of formulating complicated sentences An art all three laugh mathematics is as far from art as Earth is from the end of universe if such an end exists Oh you are so wrong How would you define art Art is something created to please my senses or tingle my emotions to uplift my spirit It is essentially creative imaginative If you describe a work of art with what words would you describe it I think in most cases I would say it was beautiful Well mathematicians are motivated in their work mostly by the idea of beauty It is not only the truth of a proof that counts the proof is the more appreciated if it has elegance has beauty An example please Frank turns a new page in his notebook and draws a grid of a chess board see picture right Now imagine you cut out any two white or two black squares of this chess board Don t you think we should first imagine that this is a chess board Joe laughs Good point Frank joins in laughing may I ask you all to imagine that this drawing represents a chess board that the blue approximate squares represent the black squares of the board and that white correspond to white Further imagine that I gave you 31 dominoes and that the sizes of the squares are such that one domino piece fits to cover exactly two squares Now imagine you cut out two squares of the same colour For example two opposite corner squares Geraldine asks Sure lets cross them out to represent that they were cut out Frank crosses two opposite white corner squares But now we cannot play chess anymore Tony puts in but I don t mind that I prefer dominoes anyway Oh we won t play either Frank replies now we have cut out the two squares you are asked to find out if can you cover the board with the dominoes so that every domino covers exactly two squares and no dominoes overlap Uh huh is the sound Frank hears as a response and he continues It is obvious that if you program a computer to check all the possible tilings of the board with the dominoes you could get an answer If the board were smaller say 4x4 there would be not so many possibilities and you could even try all yourselves In any case you would get a negative answer you cannot cover such a board completely with dominoes You could try cutting out some other combination of two squares of the same color but you would end up with the same answer And sooner or later the computer program could check and draw all the possibilities of making such a mutilated chess board and covering it This would be a proof that there is no such tiling of the board with two squares of the same colour removed But it would be a very inelegant proof by exhaustion Geraldine ponders Yes but what else can be done Mathematics Franks mouth begins to stretch into a wide smile beautiful and elegant mathematics It s just about a good idea Is it possible to cover two squares of the same colour with one domino piece Joe immediately joins in Obviously no So each domino piece will cover two squares of different colours This means that any number of dominoes covers the same number of white and black squares of the board But when you removed two squares of the same colour you got a board with different numbers of black and white squares Consequently you cannot cover the board with dominoes in the required fashion no matter which two white or two black squares you remove Proof finished Frank is now wearing a triumphant smile as he sees that all of three are impressed Wow that was nice Geraldine says Beautiful Tony says and Frank asks What makes it beautiful All three are searching for the right words but Frank continues You don t have to answer The mathematician Arthur Cayley once said As for everything else so for a mathematical theory beauty can be perceived but not explained And you need imagination to create mathematics As you can learn to write correctly but this doesn t make you a good writer you can learn to make correct logical conclusions but the ideas for connecting seemingly unrelated concepts in an unexpected or at least not obvious way are what makes a good mathematician The great mathematician David Hilbert once said regarding a former student of his He is a writer now he had not enough imagination Doing mathematics means that you discover new relations new patterns new properties of already known mathematical objects or that you even create new mathematical objects Mathematics is essentially creative I must agree Geraldine says there is something in it Why has nobody told me that in school The better question would be why has nobody showed you that mathematics is creative and imaginative Unfortunately school maths is usually very far from

Original URL path: http://mathematics-in-europe.eu/tr/40-information/what-is-mathematics (2013-11-18)

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in transmission How would you for example send a ten letter text in Morse code so that even if it becomes distorted due to miscoding or an atmospheric disturbance the original ten letters will be guaranteed to arrive intact One idea that may spring to mind is to send the message repeatedly and the recipient should choose the version most frequently received as the correct one That would be much too much work for the CD player and therefore techniques have been developed so that a robust version of the actual transmitted signal is not significantly longer than the original In the meantime the modes of transmission have become so impervious to error that the quality of sound reproduction doesn t suffer even in the face of considerable disturbance For instance even a badly scratched CD can be listened to with no detectable imperfection It is a pity that such techniques were unavailable for vinyl records in the old days one could hear every speck of dust The Sampling Theorem For music or some other acoustic signal to find its way from the original source to your home stereo system the following steps are taken First the sound is digitized that is converted into a very long stream of zeros and ones This transformation from the analog or continuous world to the digital or discrete is a decisive step for it is only after digitization has occurred that the material can be copied and recopied and processed without any loss of quality The success of digitization is possible only because we human beings do not hear perfectly In a world in which we could hear arbitrarily high frequencies there would be no CDs But in fact frequencies above about 20 kilohertz are inaudible to us and so successful digitization can

Original URL path: http://mathematics-in-europe.eu/tr/41-information/research (2013-11-18)

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by a possibility that his hers results will be applied to solve some real world problem Mathematical disciplines evolved through history and some are very old geometry for example while some are fairly young for example set theory Here we present nine disciplines algebra analysis applied mathematics including numerical analysis combinatorics foundations of mathematics mathematical logic and set theory geometry number theory number theory probability and statistics and topology The choice of the described disciplines does not reflect their importance the nine disciplines were chosen because it is possible to give a resonable description of them that is understandable for a general audience The nine disciplines and several of their subdisciplines or typical notions from them are represented graphically by the map of the Land of Middle Math below Please note that this is the author s view of the classification and the sizes of the regions on the map have no implications about the relative importance of the disciplines nor should any other similar conclusions be drawn from the style of the visual representation Still it was on purpose that no clear borders were drawn as many subdisciplines can be considered as jointly governed by two or more of the nine chosen disciplines For example graph theory can be considered as a part of topology as well as of combinatorics so in our map the Sea of graph theory is positioned on the border between Topologiath and Combinatorica If you want to know more about a specific mathematical discipline please click on the corresponding region of our Map of the Land of Middle Math below A much more detailed classification then the one described above is used by professional mathematicians all around the globe It is called the Mathematics Subjects Classification MSC It classifies mathematics in 63 classes and numerous subclasses Many of them have esoteric names such as Transcendental methods of algebraic geometry number 32J25 in MSC But even those sounding relatively harmless like Perfect graphs 05C17 in the MSC are usually not easy to describe An average and many above average research mathematician is usually a specialist in a few subclasses knows what the whole MSC class his subclasses belong to is about and has a general idea what the other classes are about Still the same professional mathematician may and mostly is unable to say what a specific subclass is about This may be compared to the everyday experience of people working in other professions whatever they do especially if they are specialist there are jobs and tasks in their own profession that they do not know much about JavaScript is currently disabled Please enable it for a better experience of Jumi The landscape key concepts Ayrıntılar Kategori Landscape Certain fundamental mathematical notions play an important role in many parts of mathematics Here you can find information on the concepts countable and uncountable which have to do with the size of sets The well known associative commutative and distributive laws are given an extensive treatment here

Original URL path: http://mathematics-in-europe.eu/tr/42-information/landscape (2013-11-18)

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