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- Mathematics In Europe - Mathematics in Serbia

University of Novi Pazar http www np ac rs Faculty of Sciences University of Priština www pmfkm info Astronomical Society Rudjer Boskovic Public Observatory Planetarium http adrb org Astronomical Observatory Belgrade www aob rs Astronomical Society Novi Sad Public Observatory Planetarium www adnos org opserv aspx Petnica Science Center http www petnica rs Electrical Institute Nikola Tesla http www ieent org Institute for Microwave Technology and Electronics IMTEL Communications http www insimtel com Lola Institute http www lola ins co rs Institute Mihajlo Pupin http www imp bg ac rs IRITEL http www iritel com Exhibitions Math Month May M3 May 2012 Popular web pages Center for the Promotion of Science http www cpn rs National Center for Digitization http www ncd org rs index html Centre Dynamical Systems Geometry and Combinatorics http www mi sanu ac rs dsgc dsgc htm Center for Advanced Mathematical Methods in Information Technologies CAMMIT http www mi sanu ac rs CAMMIT CAMMIT htm Mechanics Colloquium http www mi sanu ac rs colloquiums mechcoll htm The Mathematics Colloquium http www mi sanu ac rs colloquiums mathcoll htm Ministry of Education and Science http www mpn gov rs sajt Raising public awareness journals Electronic editions of Serbian mathematical journals http elib mi sanu ac rs Publications de l Institut Mathématique http publications mi sanu ac rs home Visual Mathematics http www mi sanu ac rs vismath Bulletin Classe des Sciences Mathématiques et Naturelles Sciences Mathématiques http elib mi sanu ac rs pages browse publication php db bltn Kragujevac Journal of Mathematics http elib mi sanu ac rs pages browse publication php db kjm Matematički vesnik http elib mi sanu ac rs pages browse publication php db mv Nastava matematike http elib mi sanu ac rs pages browse publication php db nm Review of the National Center

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/avrupa-da-matematik/46-information/math-in-europe/647-mathematics-in-serbia (2013-11-18)

Open archived version from archive - Mathematics In Europe - Mathematics in Spain

www crm cat Instituto de Ciencias Matemáticas CSIC UAM UC3M UCM www icmat es Exhibitions Exposiciones virtuales de divulgamat arte fotografía historia libros y otras www divulgamat net El Rostro Humano de las Matemáticas http divulgamat2 ehu es divulgamat15 index php option com content view article id 11596 enero 2008 el rostro humano de las matematicas catid 62 exposiciones con historia directory 67 Anda con Ojo Pilar Moreno http divulgamat2 ehu es divulgamat15 index php option com content task view id 3993 Itemid 72 Momentos Matemáticos de la AMS http divulgamat2 ehu es divulgamat15 index php option com content view article id 11227 abril 2009 momentos matematicos catid 59 exposicie Itemid 45 Arte Fractal Belleza y Matemáticas http divulgamat ehu es weborriak Exposiciones artemate FractalesICM index asp La mujer Innovadora de la Ciencia http www rsme es comis mujmat mujer ciencia index htm RSME IMAGINARY www imaginary exhibition com Exposiciones de Matemática Vital Martemáticas Geometría Divina Las mates de tu vida Suertes http matematicavital com El legado de las matemáticas De Euclides a Newton Los genios a través de sus libros http euler us es libros Mujeres Matemáticas http www cienciayagua org exposiciones index php id 158 Matemáticas de cerca http www grupoalquerque es mate cerca expo html Popular web pages Divulgamat Centro Virtual de Divulgación de las Matemáticas RSME www divulgamat net Matematicalia revista digital de divulgación matemática www matematicalia es Matemáticas en tu mundo http www catedu es matematicas mundo Raising public awareness journals La Gaceta de la RSME www rsme es gacetadigital Revista SIGMA http www hezkuntza ejgv euskadi net r43 573 es contenidos informacion dia6 sigma es sigma sigma aldizkaria html Revista SUMA www revistasuma es UNION http www fisem org web2 union index html Más información de revistas en http divulgamat2 ehu es divulgamat15 index

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/avrupa-da-matematik/46-information/math-in-europe/108-mathematics-in-spain (2013-11-18)

Open archived version from archive - Mathematics In Europe - Mathematics in Turkey

institution professionally representing and bringing together mathematicians in Turkey It has 818 members from all over the country Turkish Mathematical Society has been a full member of the International Mathematical Union since 1960 Also Turkish Mathematical Society has been a member of European Mathematical Society since 2008 The Society is located in Istanbul and has also a branch in Ankara http www tmd org tr The Association of Mathematicians was founded in 1995 and is located in Ankara Those who are part as student or faculty at some university Mathematics Mathematics Engineering Mathematics Education Departments can apply for membership cf link in Turkish http www matder org tr Mathematics Foundation publishes mathematics teaching books organizes the yearly Cahit Arf Lectures and gives every year the Masatoshi Gündüz İkeda Research award cf link in Turkish http www matematikvakfi org tr Research institutions The Istanbul Center for Mathematical Sciences http www imbm org tr The Boğaziçi University TÜBİTAK Feza Gürsey Institute http www gursey gov tr http www3 iam metu edu tr iam index php Main Page Institute for Applied Mathematics METU http www3 iam metu edu tr Other regular research and education activities Antalya Algebra Days http www aad metu edu tr Gökova Geometry Topology Conference http gokovagt org Nesin Mathematics Village http matematikkoyu org en node Activities web pages http www turkmath org beta index php Exhibitions Popular web pages http www matematiktutkusu com Raising public awareness journals Matematik Dünyası the World of Mathematics MD is a quarterly journal aiming to convey abstract mathematics to young people Although its focus is high school and university students thanks to the universality of mathematics it has reached a larger scope of readers The journal is owned by the Turkish Mathematics Society and is run by professional mathematicians http www matematikdunyasi org Raising

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/avrupa-da-matematik/46-information/math-in-europe/148-mathematics-in-turkey (2013-11-18)

Open archived version from archive - Mathematics In Europe - Mathematics in the United Kingdom

pages journals NRICH Monthly published on line mathematics puzzles for children children can submit their answers http nrich maths org by the Millennium Mathematics Project http nrich maths org Symmetry Plus published three times a year for 10 18 year olds http www m a org uk jsp index jsp lnk 670 by the Mathematical Association PLUS Monthly published on line magazine for 16 25 year olds by the Millennium Mathematics Project www plus maths org cs4fn computer science for fun with the mathematics behind magic tricks www cs4fn org magic by Queen Mary College University of London Tarquin Publications www tarquin books demon co uk specialises in hands on maths books Raising public awareness further activities Mathematics Walks www mathsinthecity com created by Prof Marcus du Sautoy OBE Some activities that tour the UK Hands on Maths Roadshow http www mmp maths org roadshow by Millenium Mathematics Project Fun Maths Road Show http www maths liv ac uk lms funmaths Magic Mathworks Travelling Circus Experiencing Mathematics through Sight Sound Touch and Movement http www magicmathworks org Maths Busking http www mathsbusking com Stand up Mathematician http www standupmaths com Maths In A Suitcase http www mathsinasuitcase co uk Royal Institution Mathematics Masterclasses http www rigb org maths A UK wide directory of Science Technology Engineering and Mathematics STEM experiences for schools http www stemdirectories org uk Mathstastic http www life org uk education workshops mathstastic 202 item 2150 Raising public awareness clubs The Ask a mathematician service http nrich maths org discus messages board topics html by the Millennium Mathematics Project Monthly published Mathematics Puzzles for children children can submit their answers http nrich maths org by the Millennium Mathematics Project The Royal Institution Mathematics Masterclasses for Primary 9 10 year olds and Secondary 13 16 year olds school

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/avrupa-da-matematik/46-information/math-in-europe/105-mathematics-in-the-united-kingdom (2013-11-18)

Open archived version from archive - Mathematics In Europe - test_rg

to utilize the functionality of this Website Skip to main content Press Enter Menu languages Articles in Turkish can be found here Home Anasayfa Uncategorised test rg 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 Society Our Sponsor Munich RE test rg Ayrıntılar Kategori Uncategorised test rg Copyright 2013 Mathematics In Europe

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Open archived version from archive - Mathematics In Europe - Mathematics in Czech Republic

Avrupa da matematik Halka ulaşma faaliyetleri Yarışmalar Matematik Yardım Meslek olarak matematik Karışık Misyon Hoşgeldin Mesajları EMS Destekçiler Diller Iletişim Yasal Bilgi arama The European Mathematical Society Our Sponsor Munich RE Mathematics in Czech Republic Ayrıntılar Kategori math in europe We have asked the colleagues in Czech Republic to provide material It will be presented here as soon as we have got it Societies Research institutions Exhibitions Popular web pages

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/avrupa-da-matematik?id=121 (2013-11-18)

Open archived version from archive - Mathematics In Europe - Countable vs. uncountable

the second set in such a way that no two elements of the first set are mapped to the same element of the second set and such that every element of the second set is the image of some element of the first set For example a function that maps every integer n to its additive inverse n is a bijection of the set of integers to itself For example 3 is mapped to 3 and 14 is mapped to 14 No matter which integer you consider it has precisely one negative and so the conditions of a bijection are satisfied We note that 0 is mapped to itself since 0 0 Now let us attempt to prove that the set of natural numbers 0 1 2 is infinite To do so we must find a proper subset of the natural numbers that we can map bijectively onto the full set of natural numbers We choose as our proper subset the even natural numbers 0 2 4 We now choose the function that maps every natural number to its double This is easily seen to be a bijection between the two sets and we have shown that the set of natural numbers is infinite Now that we know what it means for a set to be infinite we come to the next step 2 Comparing the Sizes of Different Sets We begin here as well with a definition in order to clarify what it means for two sets to be of the same size Two sets are said to be of the same size if there exists a bijection between them Since we have just defined the notion of bijection above this definition should give us no trouble We have also shown above that the set of even natural numbers is of the same size as the complete set of natural numbers even though intuitively one might suppose that there are many more natural numbers than just the even ones A further interesting result is that the set of natural numbers is the same size as the set of integers all positive and negative whole numbers plus zero To prove this we define a mapping in the following way zero is mapped to itself 1 to 1 2 to 1 3 to 2 4 to 2 and so on It should be clear that this mapping is a bijection Now we can approach the definitions of countable and uncountable 3 Countable Sets Definition A set M is said to be countable if there exists a bijection between M and the natural numbers Thus the countable sets are precisely those that are of the same size as the natural numbers What about the set of rational numbers all the fractions Is it countable We must look for a bijection from the natural numbers to the rational numbers Such a bijection indeed exists and it most easily demonstrated as follows We map the natural numbers to the rational numbers by following the

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/avrupa-da-matematik?id=77 (2013-11-18)

Open archived version from archive - Mathematics In Europe - How far?

going from Maciejowice to Ryczywól I have to cross the Vistula so I need to find a bridge The closest bridge is in Deblin and the road there is about 60 kilometres So by distance we need do not necessarily mean the shortest segment joining two points By the way we regularly think about distances in different ways sometimes not even realising what we are doing How do we answer the question about the distance between Berlin and Sydney Considering a straight line Not at all We would travel through the centre of the planet We investigate instead the length of an arc on the surface of the Earth These examples show that there are distances of various kinds No wonder then that we may decide consider a general definition of distance Such a procedure in which a number of examples provide the foundation for a general definition is quite frequent in mathematics We may introduce the notion of distance in any nonempty set We require that the distance between every two points contained in our set should be defined the distance between the point and itself should be equal to 0 the distance between two different points should be greater than 0 the distance is symmetric i e the distance between A and B is the same as the distance between B and A the triangle inequality holds i e the sum of distances between A and C and between C and B is greater or equal to the distance between A and B that is if we go from A to B and want visit C in our way then we cannot shorten the route by visiting C on the way Mathematicians call a distance with these properties a metric on the set and the set is called

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/avrupa-da-matematik?id=78 (2013-11-18)

Open archived version from archive