41. Bibliography kummer, Ernst eduard, 18101893, Collected papers Ernst eduard kummer / editedby Andre Weil, Berlin, Springer-Verlag, 1975 http://www.library.cornell.edu/math/bibliography/display.cgi?start=K&

42. Ernst Eduard Kummer Translate this page Ernst eduard kummer, Matemático alemán recordado por sus trabajos sobre serieshipergeométricas, teoría de números y funciones algebraicas. http://es.geocities.com/fisicas/cientificos/matematicos/kummer.htm

43. Kummer Surfaces kummer surfaces. In 1864 Ernst eduard kummer gave the following real onedimensionalfamily of surfaces of degree four (quartics) http://enriques.mathematik.uni-mainz.de/docs/Ekummer.shtml

Diese Seite auf deutsch Back to the gallery Kummer surfaces In 1864 Ernst Eduard Kummer gave the following real one-dimensional family of surfaces of degree four (quartics): Most of this surfaces admit ordinary nodes, which can of course be complex. By varying one gets the following table: type nodes picture real complex Kummersurface 4 real points double sphere Kummersurface Steiner roman surface Kummersurface four planes Kummersurface =oo Kummersurface All surfaces are invariant under the symmetry group of the tetrahedron S . Moreover, the surface X 4,oo is invariant under the symmetry group of the cube. In the modern classification of surfaces these quartics belong to the family of Kummer surfaces. Kummer surfaces are K3 surfaces containing 16 rational, disjoint -curves. Last update: Thursday, 06-Feb-2003 08:52:25 CET Home Staff Lectures Contact Home: The algebraic geometry group Department of mathematics of the Gutenberg University of Mainz, Germany

44. From Mailer@mailer.siam.org Wed Nov 18 190605 1998 Date Wed, 18 Hensel, K. Gedachtnisrede auf Ernst eduard kummer. Festschr. zur Feier des 100.Geburststages eduard kummers. Leipzig und Berlin 1910, 137. 9. http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/1998.06.fixed

Subject: Minisymposium; Orthogonal polynomials; Theory and Applications A Minisymposium "Orthogonal polynomials; Theory and Applications" will be held during the SIAM Annual Meeting in Atlanta, May 12-15, 1999. The invited speakers are: Percy Deift (New York) Charles Dunkl (Charlottesville, Virginia) Jeff Geronimo (Atlanta) Leonid Golinski (Columbus, Ohio) Sergei Suslov (Tempe, Arizona) Walter Van Assche (Leuven) Gerald Teschl (Vienna) Hugo Woerdeman (Williamsburg, Virginia) Further information will appear in a later issue of OP-SF NET. Topic #5 OP-SF NET 5.6 - November 15, 1998 ~~~~~~~~~~~~~ From: Nico Temme Subject: Subscribing to OP-SF NET There are two ways to subscribe to OP-SF NET: 1. Send a message to poly-request@siam.org with your name and email address in the body of the message. If everything works well, you will be put on the mailing list of OP-SF NET which is maintained by SIAM. 2. Send a message to majordomo@wins.uva.nl and put in the body of the message only the words: subscribe opsfnet This is handled by an automatic list server. You will receive a confirmation, with a list of further commands. You will be put on the opsfnet mailing list of this list server. A new issue of OP-SF NET will be mailed to people on this list immediately after the mailing by SIAM to the people on the list maintained by SIAM. Topic #15 OP-SF NET 5.6 - November 15, 1998 ~~~~~~~~~~~~~ From: OP-SF NET Editors

45. Art-Portal Translate this page Gotthardt Kuehl, Franz Kugler*, Marianna Kürzinger, Robert kummer, Fritz Kunz*,eduard Kurzbauer, Christian Adam Landenberger, Albert Lang, Carl Lange*, http://www.artworld24.com/

das kunstportal h o m e b ü c h e r k u n s t k u l t u r a u k t i o n ... k o n t a k t Das Besondere Angebot: Walther Firle Herzlich willkommen bei artworld24.com - dem Kunstportal Hellmann Fine Art A chenbach, Oswald Achenbach, Albrecht Adam, Eugen Adam, Franz Adam, Heinrich Adam*, Julius Adam*, August Wilhelm Julius Ahlborn, Max Emanuel Ainmiller, Conrad d'Allemand*, Jakob Alt, Rudolf von Alt, Theodor Alt, Oscar von Alvensleben*, Wilhelm Amberg*, Friedrich von Amerling, Alois B ach, Hermann Baisch, Hans Baluschek*, Friedrich Bamberger, Fritz Bamberger*, Carl Bantzer*, Caroline Bardua*, Hans von Bartels*, Paul Baum*, Adolf Baumann*, Peter Becker*, Carl Johann Becker-Gundahl, Carl Friedrich Ferdinand Beckmann, Max Beckmann, Adalbert Begas, Carl Joseph Begas, Oskar Begas, Ferdinand Bellermann*, Eduard Julius Friedrich Bendemann, Wilhelm Ferdinand Bendz, Albert Berg*, Edmund Berninger*, Carl Blechen, Detlev Konrad Blunck, Gregor von Bochmann*, Leopold Bode*, Carl Bodmer*, Arnold Böcklin, Fritz Boehle*, Wilhelm Böttner, Anton Braith, Louis Braun*, Wilhelm Brücke, Samuel Brunner*, Karl Buchholz, Heinrich Bürkel, Hugo Bürkner*, Rudolf Bürkner*, Anton Burger, Peter Burnitz*, Wilhelm Busch, Bernhard Buttersack*, Wilhelm C amphausen*, Gilbert von Canal*, Hans Canon*, Jakob Asmus Carstens*, Carl Gustav Carus, Franz Catel, William Merrit Chase, Adolf Chelius*, Josef Carl Cogels*, Edward Th. Compton*, Maria von Conta-Piloty*, Lovis Corinth, Peter von Cornelius*, Georg Heinrich Crola, Eduard

46. Www.allmath.com/biosearch.php?QMeth=ID ID=18156 Math Library GMT programming languageThis function describes a family of surfaces discovered by Ernst eduard kummerin 1864. There is a family of kummer surfaces admitting the symmetry of the http://www.allmath.com/biosearch.php?QMeth=ID&ID=18156

47. Earliest Known Uses Of Some Of The Words Of Mathematics (I) Ernst eduard kummer (18101893) introduced the term ideale zahl in 1846 in Ber.über die zur Bekanntmachung geeigneten Verh. dK Preuss. Akad. d. http://members.aol.com/jeff570/i.html

Earliest Known Uses of Some of the Words of Mathematics (I) Last revision: July 19, 2005 ICOSAHEDRON is found in English in Sir Henry Billingsley's 1570 translation of Euclid's Elements IDEAL (point or line) was introduced as by J. V. Poncelet in IDEAL (number theory) was introduced by Richard Dedekind (1831-1916) in P. G. L. Dirichlet (ed. 2, 1871) Suppl. x. 452 (OED2). IDEAL NUMBER. Ernst Eduard Kummer (1810-1893) introduced the term ideale zahl in 1846 in IDEMPOTENT and NILPOTENT were used by Benjamin Peirce (1809-1880) in 1870: When an expression raised to the square or any higher power vanishes, it may be called nilpotent; but when, raised to a square or higher power, it gives itself as the result, it may be called idempotent. The defining equation of nilpotent and idempotent expressions are respectively A n = 0, and A n A; but with reference to idempotent expressions, it will always be assumed that they are of the form A A, unless it be otherwise distinctly stated. This citation is excerpted from "Linear Associative Algebra," a memoir read by Benjamin Peirce before the National Academy of Sciences in Washington, 1870, and published by him as a lithograph in 1870. In 1881, Peirce's son, Charles S. Peirce, reprinted it in the American Journal of Mathematics.

48. Ernst Eduard Kummer - Encyklopedia Servis.pl Ernst eduard kummer Encyklopedia Servis.pl. Ernst eduard kummer - matematyk.Urodzil sie 29 stycznia 1810 r. w Zarach, zmarl 14 maja 1893 r. w http://encyklopedia.servis.pl/wiki/Ernst_Eduard_Kummer

49. Timeline Of Fermat's Last Theorem Ernst eduard kummer (18101893), kummer attempted to restore the uniqueness offactorization by introducing ideal numbers. kummer proved that FLT was true http://www.public.iastate.edu/~kchoi/time.htm

Drink to Me (Carolan, sequenced by Barry Taylor) Timeline of Fermat's Last Theorem when who what 1900 BC Babylonians A clay tablet, now in the museum of Columbia University, called Plimpton 322, contains 15 triples of numbers. They show that a square can be written as the sum of two smaller squares, e.g., 5 circa 530 Pythagoras Pythagoras was born in Samos. Later he spent 13 years in Babylon, and probably learned the Babylonian's results, now known as the Pythagorean triples. Pythagoras was also the founder of a secret society that studied among others "perfect" numbers. A perfect number is one that is the sum of its multiplicative factors. For instance, 6 is a perfect number (6 = 1 + 2 + 3). Pythagoreans also recognized that 2 is an irrational number. circa 300 BC Euclid of Alexandria Euclid is best known for his treatise Elements circa 400 BC Eudoxus Eudoxus was born in Cnidos, and became a colleague of Plato. He contributed to the theory of proportions, and invented the "method of exhaustion." This is the same method employed in integral calculus. circa 250 AD Diophantus of Alexandria Diophantus wrote Arithmetica , a collection of 130 problems giving numerical solutions, which included the Diophantine equations , equations which allow only integer solutions (e.g, ax + by = c, x

50. HRUMC XII - April 30, 2005 Williams College Williamstown, MA List eduard Ernst kummer (1810 – 1893) and Richard Dedekind (1831 – 1916). In attempting to solve Fermat’s last theorem, kummer realized that unique http://www.skidmore.edu/wdb/php.cgi/academics/dvella/showpart.2005.htm

HRUMC XII - April 30, 2005 Williams College Williamstown, MA List of Lecture titles/Speaker/Abstracts submitted. TITLE: The Ingredients of Winning Basketball: Do They Differ in College Versus the Pros Adam Ain, Williams College ABSTRACT: Using multi-variable regression, I will show the statistical correlation between basketball stats and winning percentages in the NBA and in men`s Division I basketball. I will also explain why the correlation is not the same in the NBA as compared to the NCAA for some statistics. TITLE: Enigma = TZTTOG Victoria Lu, Todd Ford, Plattsburgh State University ABSTRACT: When Hitler came to power in Germany he instituted the use of the Enigma Machine to encrypt and decrypt secret information. We will discuss how the British used many mathematical and imaginative methods to solve the Enigma. TITLE: The Knapsack on My Back Todd Ford, Victoria Lu, Plattsburgh State University ABSTRACT: Having the encryption public key doesn`t give enough information to decrypt the messages. Or does it? We`re going to explore public key cryptography, namely the knapsack problem. TITLE: The Continued Fraction Revolution Nick Yates, Williams College

51. Enciclopedia :: 100cia.com Translate this page Ernst eduard kummer. (En este momento no hay texto en esta p¡gina. Para iniciarel art­culo, click editar esta p¡gina (http//es.wikipedia. http://100cia.com/enciclopedia/Ernst_Eduard_Kummer

Portada Artículos favoritos Vea sus documentos y artículos favoritos pulsando aquí No hay artículos favoritos todavía. documentos sin leer: Siguiente doc sin leer Borrar los docs leídos Borrar todos los docs ¡Webmaster! ¿Quieres tener los contenidos de 100cia.com en tu página? Pulsa aquí Buscar: en Google en noticias en Enciclopedia Estás en: 100cia.com > Enciclopedia Ernst Eduard Kummer (En este momento no hay texto en esta p¡gina. Para iniciar el art­culo, click editar esta p¡gina http://es.wikipedia.orgErnst_Eduard_Kummer Información de Wikipedia (Licencia de uso GFDL) e Internet ¿Sabías que Ernest Joseph Renan (Filósofo, escritor e historiador francés. 1.823 - 1.892) dijo...? Las verdades que revela la ciencia superan siempre a los sueños que destruye. Acerca de Sync.es Webs amigas: AstroRED CanalGame AweZoom

52. Science News Online - Mystery Box - 3/8/97 Ernst eduard kummer (1810–1893), a German algebraist, was rather poor at arithmetic.Whenever he had occasion to do simple arithmetic in class, http://www.sciencenews.org/pages/sn_arc97/3_8_97/mystbox.htm

Poor Arithmetic "Seven times nine," he began, "Seven times nine is er ah - ah seven times nine is. . . ." "Sixty-one," a student suggested. Kummer wrote 61 on the board. "Sir," said another student, "it should be sixty-nine." "Come, come, gentlemen, it can't be both," Kummer exclaimed. "It must be one or the other." Table of Contents 3/8/97 SEARCH! Science Service

53. Fermat's Last Theorem For example, Polish mathematician Ernst eduard kummer s work in the mid19thcentury arises from connecting the Last Theorem to the theory of cyclotomic http://users.forthnet.gr/ath/kimon/FLT.htm

Fermat's Last Theorem Pierre de Fermat (1601-1665) The story behind Fermat's Last Theorem has exciting elements not usually found in mathematical quests. There is genius, passion, jealousy, money (the Wolfskehl 100,000 DM Prize) and even sex discrimination (in the 19th century, Sophie Germain had to assume a male identity to work on the problem and correspond with other mathematicians). The formulation is deceptively simple: "prove that there are no whole numbers X, Y and Z such that X n +Y n =Z n for n > 2" (contrary to n=2 which is the familiar Pythagorean case). It first appeared in Pierre Fermat's notes published in 1670 and was finally solved by Andrew Wiles in 1995. Fermat claimed to "have a truly marvelous demonstration of this proposition which this margin is too narrow to contain". If it were so, certainly it was not the kind of approach which was finally used by Wiles who had to unify all sorts of modern mathematics - click here to see a diagrammatic representation of the final steps to the proof. This is the reason many people (mostly amateurs) are still trying to find a simpler solution with mathematics of Fermat's times. One argument in favor of the existence of such a solution is that all other Fermat's theorems were shown to be true soon after their publication (hence the name Fermat's "Last" Theorem). Dear ...

54. Kummer - 1878 Translate this page Ernst eduard kummer - 1878. Der Beweis von kummer ist noch einleuchtender alsder von Euklid und so schön kurz und einfach, so daß er unter diesem http://www.mathematic.de/beweise/primenumbers-kummer.html

Ernst Eduard Kummer - 1878 p , p , ..., p r n = p * p * ... * p r . Die Zahl n - 1 hat dann unter der Annahme einer endlichen Primzahlmenge einen gemeinsamen Primteiler p i mit n p i den Term n n - 1) = 1 teilt. Paulo Ribenboim, The Book of Prime Number Records, Springer-Verlag 1989, 2. Auflage www.mathematic.de

55. January 2003 Eliakim Hastings Moore, 27 Charles Dodgson (Lewis Carroll), 28 Louis Joel Mordell,29 Ernst eduard kummer. 30 Michelangelo Ricci, 31 Samuel Loyd http://mathforum.org/~judyann/calendar/January2005.html

January 2005 Can you identify the pictured Mathematicians? Sunday Monday Tuesday Wednesday Thursday Friday Saturday Satyendranath Bose Lev Genrikhovich Shnirelman Louis Poinsot Sir Isaac Newton Camille Jordan Thomas Fincke Emile Borel Richard Courant Nola Haynes Ruth Moufang Guidobaldo del Monte Kurt August Hirsch Gertrude Mary Cox Alfred Tarski Sofia Kovalevskaya William Werner Boone Edward Foyle Collingwood Paul Ehrenfest Garrett Birkhoff Cora B. Hennel Leonard Eugene Dickson David Hilbert Abram Samoilovitch Besicovitch Joseph-Louis Lagrange Eliakim Hastings Moore Charles Dodgson (Lewis Carroll) Louis Joel Mordell Ernst Eduard Kummer Michelangelo Ricci Samuel Loyd A quotation for January: Isaac Newton (1643 - 1727) If I have been able to see further, it was only because I stood on the shoulders of giants. Letter to Robert Hooke This calendar is available in a printable PDF format. Back to calendar page.

56. BibScout - Kummer, Ernst Eduard Translate this page im Südwestdeutschen Bibliotheksverbund (SWB), Neuerscheinungen zuerst. Collectedpapers / Ernst eduard kummer. - Berlin Springer, 19XX Bibliotheken http://titan.bsz-bw.de/bibscout/SA-SP/SF1000-SF9900/SF4670-SF4800/SF.4800

@import url(http://titan.bsz-bw.de/bibscout/ploneColumns.css); @import url(http://titan.bsz-bw.de/bibscout/plone.css); @import url(http://titan.bsz-bw.de/bibscout/ploneCustom.css); Skip to content. BibScout web bibscout Home Mathematik Gesammelte Werke Autoren K Kummer, Ernst Eduard BibScout Home Allgemeines Arch¤ologie Biologie ... Autoren O Kummer, Ernst Eduard Document Actions Regensburger Verbundklassifikation SF.4800 SF 4800 Collected papers / Ernst Eduard Kummer. - Berlin : Springer, 19XX Bibliotheken Erstellt von: BibScout t¤glich aktualisiert Verbund Bayern Thema Kummer, Ernst Eduard Schlagworte Seite drucken Seitenanfang

57. Berühmte Mathematik: Mathematiker > Kummer Translate this page Ernst eduard kummer kummer wurde am 28. Jänner 1810 in Sorau als Sohn eines Arztesgeboren. Der Vater, Carl Gotthelf kummer, starb drei Jahre danach an http://homepages.compuserve.de/thweidenfeller/mathematiker/kummer.html

Ernst Eduard Kummer (1810 bis 1893) Kummer wurde am 28. Jänner 1810 in Sorau als Sohn eines Arztes geboren. Der Vater, Carl Gotthelf Kummer, starb drei Jahre danach an Typhus, so wuchs Kummer eher in ärmlichen Verhältnissen auf, aber seine Mutter ermöglichte ihm dennoch den Besuch des Gymnasiums von Sorau bis zur Reife für die Universität. 1828 inskripierte Kummer in der Universität von Halle Theologe, aber wechselte schon bald wegen seiner philosophischen Studien zur Mathematik. Dort lehrte damals Heinrich Friedrich Scherk, der Kummer während seiner Studienzeit am meisten beeinflußte. Im dritten Studienjahre löste Kummer eine von Scherk gestellte Aufgabe und erhielt dafür Preis, und noch im selben Jahr erhielt er am 10. September sein Doktorat. Nach Abschluß seiner Hochschulstudien wurde er zunächst Gymnasiallehrer in Sorau, seiner Heimatstadt, und lehrte von 1832 bis 1842 am Gymnasium von Liegnitz. Dort verfaßte Kummer mehrere Arbeiten über Funktionentheorie. Eine Arbeit über hypergeometrische Reihen veröffentlichte 1836 er im Crelle's Journal, und sandte ein Kopie an Jacobi . Dieser, und später auch Dirchlet, mit dem Kummer einen Briefwechsel pflegte, erkannten dessen mathematischen Fähigkeiten. So wurde Kummer schon 1939 in Berlin

58. Ernst Eduard Kummer Translate this page Begrifferklärung Ernst eduard kummer. Dieser Artikel basiert auf dem ArtikelErnst eduard kummer (http//de.wikipedia.org/wiki/Ernst_eduard_kummer) aus http://www.netzwelt.de/lexikon/Ernst_Eduard_Kummer.html

Themen Ratgeber Shopping Forum ... PDA Sie sind hier: Home Lexikon Ernst Eduard Kummer Ernst Eduard Kummer 29. Januar in Sorau ( Brandenburg 14. Mai in Berlin ) war ein deutscher Mathematiker Nach seinem Studium in Halle unterrichtete Kummer von 1832 bis 1842 am Gymnasium in Liegnitz , wo unter anderem Leopold Kronecker zu seinen Schülern gehörte. Da er während dieser 10 Jahre durch Forschungsergebnisse auf sich aufmerksam machte, wurde er 1842 zum Professor in Breslau ernannt, bis er 1855 als Nachfolger von Dirichlet nach Berlin berufen wurde. Dort baute er zusammen mit Weierstrass und Kronecker eine bedeutende Mathematikerschule auf, die Berlin für drei Jahrzehnte zu einem der aktivsten Zentren für Mathematik weltweit machte. Kummer arbeitete in mehreren Gebieten der Mathematik, insbesondere Zahlentheorie und Funktionentheorie . Bekannt ist er durch seine Beiträge zur Fermatschen Vermutung , bei der er auf wesentliche Schwierigkeiten in früheren Beweisversuchen hinwies und die er für einige Spezialfälle zeigte. Weitere Forschungsthemen waren hypergeometrische Reihen, reguläre Primzahlen und die Kummer-Fläche, aber auch Ballistik Kummer war in erster Ehe verheiratet mit Ottilie, die Tochter von Nathan Mendelssohn Bartholdy und Henriette Itzig. Ottilie ist die Cousine von

59. Kummer Translate this page kummer, Ernst eduard, deutscher Mathematiker * 29. 1. 1810 Sorau, † 14. 5.1893 Berlin. Arbeitsgebiete Zahlentheorie, Differentialgeometrie http://www.studienseminare-duesseldorf.nrw.de/sekundI/Seminare/Mathe/Kaleidoskop

Zurück zur Übersicht Biografien Kummer , Ernst Eduard, deutscher Mathematiker Arbeitsgebiete: Zahlentheorie, Differentialgeometrie Kummer lehrte in Breslau und (seit 1855) Berlin.

60. References 148149, Leipzig, Germany eduard kummer. Bryant, dA (1982). Phycoerythrocyanin andphycoerythrin properties and occurrence in cyanobacteria. http://www.pasteur.fr/recherche/banques/PCC/Refs.htm

Pasteur Culture Collection of Cyanobacteria References Nostoc muscorum Virology Agardh, C. A. (1824). Systema Algarum . Lund, Sweden: Litteris Berlingianis. Allen, M. B. (1952). The cultivation of Myxophyceae. Archiv für Mikrobiologie Allen, M. M. (1968). Simple conditions for growth of unicellular blue-green algae on plates. Journal of Phycology Journal of General Microbiology Nostoc muscorum. Botanical Gazette Anagnostidis, K. (1989). Geitlerinema , a new genus of oscillatorian cyanophytes. Plant Systematics and Evolution Archiv für Hydrobiologie Suppl. Algological Studies Symploca Kütz. ex Gom. Archiv für Hydrobiologie Suppl. To PCC home page Oscillatoria agardhii from two eutrophic Norwegian lakes. Acta Vet. Scand Microcystis aeruginosa PCC 7941 - isolation and analysis by nuclear magnetic resonance and fast atom bombardment spectroscopy. Journal of Chromatography Microcystis aeruginosa PCC 7806. Archives of Microbiol ogy Bory de St Vincent, J. B. (1822). Anabaena . In Dictionnaire Classique d'Histoire Naturelle vol. 1

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