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  • Mathematics In Europe - Информациjе
    is probably no one answer to 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

    Original URL path: http://mathematics-in-europe.eu/sr/j (2013-11-18)
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  • Mathematics In Europe - 1913: Publication of The Concept of a Riemann Surface, by Hermann Weyl
    in regions where the function was already defined obtaining values however of the function that differ from those originally obtained at the same points There are two apparent ways to deal with the problem Either one gives up on the idea of uniqueness of function values or else one alters the domain of definition in such a way that it covers the complex plane several perhaps infinitely many times the individual layers being joined in a complicated way somewhat analogously to how the floors of a parking garage are linked Before the appearance of Weyl s book this concept was implemented intuitively in simple cases being exemplified by cardboard models with the multiple layers glued one to the next I well remember that the construction of such models was among the problems in complex analysis that I had to solve during my student years back in the 1950s The essence of Weyl s book was to describe such surfaces called Riemann surfaces after the first mathematician to describe them axiomatically as two dimensional manifolds and to study complex valued functions on them without reference to how they were originally constructed and without reference to their embedding in a three dimensional space which ultimately led to the characterization of surfaces by the functions that exist on them Closed surface of genus 3 Nonorientable closed surface Consequently the book consists of two parts called chapters by Weyl In the first part Riemann surfaces are defined and studied using topological concepts and methods where it is to be kept in mind that before 1913 much was not clearly understood in this area with most ideas resting on intuition Thus this chapter is of considerable independent interest even without reference to functions of a complex variable for the development of the topology of surfaces

    Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/47-information/math-calendar/971-1913-publication-of-the-concept-of-a-riemann-surface-by-hermann-weyl (2013-11-18)
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  • Mathematics In Europe - Mathematics in Croatia
    are several national mathematics competitions for primary and secondary school children For more than 50 years the mathematical competitions are held on city regional and state level Croatia participates at International Mathematical Olympiads http web math hr mfl mmo htm http www matematika hr olimpijada http www imo official com and also since 2007 that is from the beginning at the Middle European Mathematical Olympiad International Competitions look for Middle European Mathematical Olympiad at Google http www google com There are also student mathematical competitions and occasional Tournaments of cities Since 2003 Festivals of Science http www festivalznanosti hr 2010 index php are held in various cities in Croatia and the list is expanding In 2010 it was held in the capital city Zagreb and in Lošinj Osijek Rijeka Split Starigrad and Zadar Among other sciences mathematics is always present at these festivals in Rijeka by various activities of the Golden Section Club and in Zagreb chiefly by workshops by Franka Miriam Brueckler and in Osijek by Ljerka Jukić and some other assistants at the Department of Mathematics Local organizers each year also encourage and find local mathematicians to present many popular mathematics themes in lectures and workshops Pictures from Festivals of Science in Zagreb This year 2010 for the first time a Croatian team joined the European Researchers Night http www znanost com clanak noc istrazivaca odrzana u pet hrvatskih gradova and mathematics was also be presented at the manifestation It was be held in five Croatian cities Zagreb Lepoglava Korenica Starigrad Paklenica and Rab on September 24th 2010 Occasionaly popular mathematics books are published by the CMS a series of popular mathematics books since 1998 called Matkina biblioteka so far about twenty popular books were published in this series Školska knjiga http www skolskaknjiga hr hrv and Element http element hr Regional popularisation activities In Zagreb regular 4 6 times per semester popular mathematics lectures under the title CoolMath are organized since 2007 by Franka Miriam Brueckler and held at the Fifth Gymnasium in Zagreb They are announced via the webpage MiddleMath that is run by the same person as a part of the activity in her project Mathematical foundations of the natural and social sciences She also regularly publishes articles on history of mathematics in the journal Osjecki matematicki list and has a regular column on mathematical magic tricks in Matka In springtime the annual University Fair in Zegreb is held and the presentation of the Dept of Mathematics since 1998 has a strong emphasis on popularisation of mathematics via various interactive mathematical presentations the presentations are organized by F M Brueckler earlier in collaboration with Mea Bombardelli Pictures from Zagreb University Fairs In Rijeka the Golden Section Club http www zlatnirez hr is devoted to popularization of science in general particularly mathematics and physics They are involved and organize many projects and activities Science day popular science radio broadcasts BALTAZAR on Radio Rijeka mathematical topics presented at Festivals of science various workshops in the Rijeka region

    Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/46-information/math-in-europe/103-mathematics-in-croatia (2013-11-18)
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  • Mathematics In Europe - Mathematics in France
    de Mathématiques Appliquées et Industrielles SMAI smai emath fr lang fr Research institutions Centre International de Rencontres Mathématiques CIRM www cirm univ mrs fr Institut des Hautes Études Scientifiques IHÉS www ihes fr Institut Henri Poincaré Centre Émile Borel www ihp jussieu fr Exhibitions Salon Culture et Jeux Mathematiques http www cijm org Mathematiques d aujourd hui http smf emath fr content exposition mathematiques daujourdhui For a larger list of mathematical exhbitions see http smf emath fr content maths et travaux expositions sur le theme des mathematiques Popular web pages Images des Mathématiques http images math cnrs fr CultureMATH http www math ens fr culturemath Page Grand Public de la SMF http smf emath fr content grand public CIJM http www cijm org La bibliotheque des mathematiques http www bibmath net Maths et Travaux http smf emath fr content maths et travaux Recueil de problemes de momes net http www momes net education problemes problemes html Carre d as devinettes mathematiques http carredas free fr aMATHeur http www amatheur net maj html Raising public awareness journals Brochure Zoom sur les metiers des mathematiques http smf emath fr content zoom sur les metiers des mathematiques Brochure L Explosion des mathematiques http

    Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/46-information/math-in-europe/119-mathematics-in-france (2013-11-18)
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  • Mathematics In Europe - Mathematics in Italy
    mirrors http specchi mat unimi it Matematica trasparente superfici minime e bolle di sapone Transparent mathematics minimal surfaces and soap bubbles http bolle science unitn it matemilano mathematical paths in the town http matemilano mat unimi it matetrentino mathematical paths in Trento and surrounding http matematita science unitn it matetrentino Un tuffo nella quarta dimensione Diving in 4 th dimension http www matematita it materiale index php p cat sc 919 Uguali Diversi Equal Different http www matematita it materiale index php p cat sc 1014 Besides these ones there have been in Italy other exhibitions about mathematics especially in the last few years mainly these were related to some local events and had just a temporary character Sometimes it happens these activities gave rise to a permanent structure Just to give one example we quote Giocare con le costruzioni la matematica che esiste Playing with constructions mathematics which exists an exhibition of mathematical objects in the maths department of the University of Perugia http www dmi unipg it iniziative mostre We don t give here a list which would be long and could never be complete rather we add two references not so recent but still valuable for anybody willing to know more about the development of mathematics exhibitions in Italy inside and outside science museums in particular you find here also informations about exhibitions like L occhio di Horus hystorically significant but not quoted here because no more available S Di Sieno Matematica al museo Mathematics in museums in Bollettino dell Unione Matematica Italiana A ser 8 vol 6 A 2003 pag 85 103 available online at the adress http www quadernoaquadretti it scuola riflessioni museo pdf S Di Sieno Mostre di matematica soltanto una nuova moda o una strategia interessante Mathematics exhibitions only a new fashion or an interesting strategy in Bollettino dell Unione Matematica Italiana A ser 8 vol 5 A 2002 pag 491 514 available online at the adress http www quadernoaquadretti it scuola riflessioni mostre pdf Popular web pages We prefer to give here a short list and to point out websites which maybe just for a specific reason highlighted in the comment can be particularly interesting either for mathematicians working in rpa activities or for laymen curious about maths The list is obviously and unavoidably incomplete http ulisse sissa it The website of SISSA InternationalSchool for Advanced Studies for general scientific information http ulisse sissa it controluce Inside the Ulisse website this is a page regarding scientific images divided in 3 main groups looking describing and thinking each one further divided in 3 subgroups looking near looking far looking inside describing objects describing places describing changes thinking elements thinking relations thinking spaces Mathematics is mainly in the subgroup thinking spaces http www matematita it materiale index php Inside the website of the Centre matematita this is a page with a large collection of Images for mathematics including some animations some further information for the layman some examples of paths using images for teaching

    Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/46-information/math-in-europe/109-mathematics-in-italy (2013-11-18)
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  • Mathematics In Europe - Mathematics in Turkey
    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 public awareness

    Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/46-information/math-in-europe/148-mathematics-in-turkey (2013-11-18)
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  • Mathematics In Europe - Mathematics in Czech Republic
    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 Raising

    Original URL path: http://mathematics-in-europe.eu/tr/bilgiler?id=121 (2013-11-18)
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  • Mathematics In Europe - Countable vs. uncountable
    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 arrow

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