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- Mathematics In Europe - Set theory and logic

are not white one cannot find out that they are equivalent by means of propositional logic In predicate logic statements P x containing a variable x like the mentioned x is even become propositions if either a value is assigned to the variable e g put x 5 to get 5 is even and now one can determine that it is a false proposition or by using one of the two quantifiers for all universal quantifier and exists existential quantifier where x P x means for all x in the universe P x and x P x means there exists a x in the universe P x In both cases the truth depends on what one takes as the universe For example x such that x is even is true if the universe is that of integers but false if the universe is the set of all odd integers Proof theory is a branch of mathematical logic in which proofs are considered as mathematical objects It is of a syntactic nature meaning that it deals with formal rules without consideration of their interpretation In contrast model theory the study of mathematical structures using the tools of mathematical logic is of a semantic nature it is interested in interpreations Other subdisciplines of mathematical logic include type theory computability and recursion theory algebraic logic Consider two sets of points in the coordinate plane the yellow rectangle A and the red dots B as shown above the third picture in the row above shows the relative position of the two sets The orange region on the left is the intersection and the blue on the right the union of A and B Figure 1 Illustration of two basic operations from algebra of sets intersection and union Many school maths curricula include the description of some topics from naive set thery sets and a few basic operations with sets union intersection difference But rare nonprofessionals know that set theory is not about finding an intersection of a set of groceries with a set of fruits from a market stand or the intersection union and diference of sets shown in figure 1 above Set theory provides an exact way to deal with the infinite as well as answering fundamental questions like what a positive integer is Cantor s proof from 1873 showing that there are various levels of infinity not all infinities are equally infinite is usually taken as the birthmark of set theory Cantor found a way to compare the sizes of infinite sets The idea is simple if you want to know if two finite sets have the same number of elements the cardinality all one has to do is to check if each of the elements of one set can be paired with one element of the other set For example if you want to check if the number of seats in the classroom is enough for all the students you can instead of counting both the seats and the students let

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler?id=91 (2013-11-18)

Open archived version from archive - Mathematics In Europe - A compilation of all links: "Information"

page 1b Landscape top of this page 1c Research The Reuleaux triangle top five October 2012 proposal 5 Jeff Week s Topology and Geometry Software top five July 2012 proposal 5 N body orbits top five July 2012 proposal 4 Niles Johnson explains Hopf fibration top five July 2012 proposal 3 The Institute of Mathematics and its Applications top five June 2012 proposal 2 top of this page 1d History Stamps and the history of mathematics top five October 2012 proposal 4 Various links concerned with the history of mathematics were provided in May 2012 Cartography through history top five December 2010 proposal 1 top of this page 1e Philosophy top of this page 1f Art Superposition An audiovisual performance with a strong soundtrack by Ryoji Ikeda top five June 2013 proposal 4 A video inspired by Escher s work top five April 2013 proposal 1 Quaternions embroidered quilts by Gwen Fisher top five January 2013 proposal 5 A 3D analogue of the Mandelbrot set by Daniel White top five January 2013 proposal 4 Escher and the Droste effect top five January 2013 proposal 3 Mathematical Imagery by Jos Leys top five January 2013 proposal 2 An exhibition created by the Fondation Cartier top five June 2012 proposal 3 Mathematics A beautiful elsewhere An exhibition top five June 2012 proposal 3 Mathematics in art cinema sports history poetry literature society by J M Sorando in Spanish top five April 2012 proposal 5 Maths and art top five November 2011 proposal 4 top of this page 1g Music Mathematics in art cinema sports history poetry literature society by J M Sorando in Spanish top five April 2012 proposal 5 top of this page 1h Mathematicians Martin Gardner and Ian Stewart top five August 2013 proposal 5 TED talk by Benoit Mandelbrot

Original URL path: http://mathematics-in-europe.eu/tr/77-enjoy-maths/topfive/1014-a-compilation-of-all-links-information (2013-11-18)

Open archived version from archive - Mathematics In Europe - A compilation of all links: "Popularization"

top five January 2011 proposal 5 120 cell deconstruction top five November 2010 proposal 1 The number 3 14159265 with the eyes of ISC top five October 2010 proposal 4 Pythagoras theorem proof via animation top five October 2010 proposal 2 The flood of rice a thought experiment made real top five October 2010 proposal 1 top of this page 2c Analysis Functions Mandelbrot set explorer top five October 2011 proposal 4 Floating maths applet top five June 2011 proposal 5 Banchoff s calculus applets top five June 2011 proposal 2 top of this page 2d Geometry Topology Super Fractals by Michael Barnsley top five August 2012 proposal 2 Geometrical shapes by Herwig Hauser top five October 2011 proposal 3 Flexagon Portal top five July 2011 proposal 5 Flexagons top five July 2011 proposal 4 Modular Origami Polyhedra top five July 2011 proposal 3 Paper folding geometry top five July 2011 proposal 2 Poetic Spirals top five June 2011 proposal 1 Adventures of and in a Klein bottle tope five May 2011 proposal 4 Fractals tope five March 2011 proposal 3 Cylinders and Möbius strips top five February 2011 proposal 3 Collaboration How many feet is the radius of this beautiful circle top five January 2011 proposal 4 Star shaped polytopes through low dimensional 3D top five December 2010 proposal 4 Cartography through history top five December 2010 proposal 1 Inversion and division by zero in the plane top five November 2010 proposal 5 120 cell deconstruction top five November 2010 proposal 1 Pythagoras theorem proof via animation top five October 2010 proposal 2 top of this page 2e Applied Mathematics Probability Strategic coalitions top five December 2011 proposal 3 The Shapley value in cooperative game theory top five December 2011 proposal 2 Strategic thinking top five December 2011 proposal

Original URL path: http://mathematics-in-europe.eu/tr/77-enjoy-maths/topfive/1015-a-compilation-of-all-links-popularization (2013-11-18)

Open archived version from archive - Mathematics In Europe - A compilation of all links: "Math Help"

3d Software 3e Learning 3a Mathematics in other languages top of this page 3b Visualization of Mathematics A video with some hypersphere sections top five April 2013 proposal 5 A video about Moebius transformations top five April 2013 proposal 4 A video about a sphere inversion top five April 2013 proposal 3 A video about Magix120Cell a higher dimensional analogue of Rubik s cube top five April 2013 proposal 2 A 3D analogue of the Mandelbrot set by Daniel White top five January 2013 proposal 4 Mathematical Imagery by Jos Leys top five January 2013 proposal 2 Mandelbrot set explorer top five October 2011 proposal 4 Geometrical shapes by Herwig Hauser top five October 2011 proposal 3 Maths in fiction top five October 2011 proposal 1 Statistical data visualized tope five August 2011 proposal 4 Modular Origami Polyhedra top five July 2011 proposal 3 Paper folding geometry top five July 2011 proposal 2 Scaling the Universe top five June 2011 proposal 4 Cylinders and Möbius strips top five February 2011 proposal 3 Collaboration How many feet is the radius of this beautiful circle top five January 2011 proposal 4 Fibonacci numbers and the golden ratio Video top five January 2011 proposal 3 IMAGINARY mathematical sculptures top five January 2011 proposal 2 Star shaped polytopes through low dimensional 3D top five December 2010 proposal 4 Images des Maths top five November 2010 proposal 3 top of this page 3c Teachers Try this for your next chalk on blackboard geometry class tope five July 2013 proposal 1 Paper folding geometry top five July 2011 proposal 2 top of this page 3d Software MathOverflow a question and answer site for professional mathematicians top five July 2012 proposal 1 Evolutionary game theory top five October 2011 proposal 5 Interactive maths top five September 2011

Original URL path: http://mathematics-in-europe.eu/tr/bilgiler/77-enjoy-maths/topfive/1016-a-compilation-of-all-links-math-help (2013-11-18)

Open archived version from archive - Mathematics In Europe - A compilation of all links: "Maths as a profession"

RE A compilation of all links Maths as a profession Ayrıntılar Kategori Topfive 4a Research 4b Education 4c Industry 4a Research Descriptions of professions where mathematics plays a crucial role top five October 2012 proposal 1 Mathematical book reviews top five November 2011 proposal 5 top of this page 4b Education A sketch map of changing education paradigms by Sir Ken Robinson top five July 2012 proposal 2 I will

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Open archived version from archive - Mathematics In Europe - A compilation of all links: "Enjoy Maths"

Magic Tricks and Illusions top five May 2011 proposal 2 top of this page 5c Games SmartGeometry Architectural design with computational tools top five June 2013 proposal 5 Tom Ferguson unpublished on strategic games top five December 2011 proposal 5 How to decide when to stop top five December 2011 proposal 4 Strategic coalitions top five December 2011 proposal 3 The Shapley value in cooperative game theory top five December 2011 proposal 2 Strategic thinking top five December 2011 proposal 1 Evolutionary game theory top five October 2011 proposal 5 Games platform top five February 2011 proposal 1 MMORPG mathematics top five December 2010 proposal 2 top of this page 5d Nature Scaling the Universe top five June 2011 proposal 4 Poetic Spirals top five June 2011 proposal 1 Conchas Geometry in Nature top five November 2010 proposal 2 top of this page 5e Museums Maths and art top five November 2011 proposal 4 Article Eleganz des abstrakten Denkens top five November 2011 proposal 2 Gödel exhibition in Vienna top five October 2011 proposal 2 Mitmach Museum auf der Alten Messe Leipzig top five September 2011 proposal 5 Interactive maths top five September 2011 proposal 4 Maths museum top five September 2011 proposal 3 IMAGINARY mathematical sculptures top five January 2011 proposal 2 top of this page 5f Stamps Stamps and the history of mathematics top five October 2012 proposal 4 top of this page 5g Videos Doodling with stars investigating with patterns top five August 2012 proposal 3 Scaling the Universe top five June 2011 proposal 4 Adventures of and in a Klein bottle tope five May 2011 proposal 4 Dot and line a romance top five May 2011 proposal 3 Benford s Law explained top five April 2011 proposal 4 Fractals tope five March 2011 proposal 3 Multiplication

Original URL path: http://mathematics-in-europe.eu/tr/77-enjoy-maths/topfive/1018-a-compilation-of-all-links-enjoy-maths (2013-11-18)

Open archived version from archive - Mathematics In Europe - A compilation of all links: "Communication"

top five June 2013 proposal 1 Blog of the Chair of Scientific Culture of the University of the Basque Country top five May 2013 proposal 5 Naukas Blog devoted to Science and Scepticism top five May 2013 proposal 4 Blog about optical illusions mathematical problems and literature by Professor Juan Luis Roldan Calzado top five May 2013 proposal 3 Blog by Professor Marta Macho top five May 2013 proposal 2

Original URL path: http://mathematics-in-europe.eu/tr/77-enjoy-maths/topfive/1019-a-compilation-of-all-links-communication (2013-11-18)

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

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 A

Original URL path: http://mathematics-in-europe.eu/tr/halka-ulasma-faaliyetleri/ulusal-faaliyetler/46-information/math-in-europe/103-mathematics-in-croatia (2013-11-18)

Open archived version from archive