61. Biografia De Grassmann, Hermann Translate this page grassmann, hermann. (Stettin, 1809- id., 1877) Matemático y lingüista alemán.Realizó diversos trabajos en el campo de la óptica, la acústica y la http://www.biografiasyvidas.com/biografia/g/grassmann.htm

Inicio Buscador Las figuras clave de la historia Reportajes Los protagonistas de la actualidad Grassmann, Hermann (Stettin, 1809- id ., 1877) Matemático y lingüista alemán. Realizó diversos trabajos en el campo de la óptica, la acústica y la electrodinámica, pero destacó sobre todo por sus estudios matemáticos (fue el primero en concebir la geometría de varias dimensiones). Su obra más importante es Enseñanza de la dilatación (1862), donde desarrolló un cálculo operatorio directo para las diversas magnitudes geométricas. Como lingüista, destaca su Diccionario sobre el Rig-veda Inicio Buscador Recomendar sitio

62. Chapterten.html hermann grassmann (18091877) was a banker who was compelled to retire becauseof tuberculosis. In his leisure he occupied himself with mathematics and http://www.utexas.edu/cola/depts/lrc/iedocctr/ie-docs/lehmann/reader/Chapter10.h

CHAPTER TEN HERMAN GRASSMANN CONCERNING THE ASPIRATES AND THEIR SIMULTANEOUS PRESENCE IN THE INITIAL AND FINAL OF ROOTS "Ueber die Aspiraten und ihr gleichzeitiges Vorhandensein im An- und Auslaute der Wurzeln, " Zeitschrift f¼r vergleichende Sprachforschung auf dem Gebiete des Deutschen, Grie chischen und Lateinischen [Lehmann 109-131] Textual Conventions By this demonstration Grassmann also undermined the notion that language developed from an analytic to a synthetic structure through an agglutinative. With it he did away with the close relationship that had been observed previously between genealogical and typological classification. After the publication of his article we find fewer and fewer references to the typological structure of a language in comparative treatments; and when typology is taken up by Finck in the definitive treatment of the nineteenth century approach there is no reference to genealogical classification. The appealing notion of a straightforward development of language had been abandoned. These contributions to general linguistic theory were achieved by explanation of one phonological problem in Indo-European studies. We have noted how von Raumer had hit on the explanation earlier, but had stated it so briefly that it remained without impact. We have also noted Lottner's important preparatory work. Neither reduces Grassmann's achievement. His article is admirably composed. First he examines previous attempts at explanation, then the data. His examination of both is complete When he presents his conclusions there is no question of their validity. His convincing explanation led linguists to deal with entire forms, not merely with single segments. In this way it prepared for the concern with entire utterances, demanded by Sievers. Unfortunately this concern with entire forms and with entire utterances was often neglected subsequently in the attempt to solve the numerous minor problems within the various languages.

63. Enciclopedia :: 100cia.com Translate this page hermann grassmann. (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/Hermann_Grassmann

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64. Sauvage Noble: Grassmann I had no idea that hermann grassmann was also a mathematician! grassmann.We remember him from such things as his Wörterbuch zum Rigveda (indeed, http://caelestis.info/sauvagenoble/2003/12/grassmann.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?blogID=6962487"); main page sauvage noble 19 December 2003 Grassmann I had no idea that Hermann Grassmann was also a mathematician We remember him from such things as his 10:05 AM references 0 comments: Post a Comment main page about This weblog the diarist personalia professionalia contents recent posts They put the fun in funeral Ten-minute hexameter Procrastinate When Classical philologists ... Haecu archives select a month August 2003 September 2003 October 2003 November 2003 December 2003 January 2004 February 2004 March 2004 April 2004 May 2004 June 2004 July 2004 September 2004 October 2004 November 2004 December 2004 January 2005 February 2005 March 2005 April 2005 May 2005 June 2005 July 2005 August 2005 search the web this site select links links on language Anggarrgoon David Romano . info: (we)blog HeiDeas ilani ilani ... Tenser, said the Tensor on antiquity Curculio House of Hagen Laudator Temporis Acti rogueclassicism ... William Blathers also seen Dappled Things Hypotyposeis Piled Higher and Deeper linked to from Blogdigger BlogPulse Blogrolling del.icio.us

65. RV.htm 1547, with mandala, sukta, rc numbers as well as grassmann s numbers; and continuing through the works of hermann grassmann, hermann Oldenberg, http://www.people.fas.harvard.edu/~witzel/RV.htm

HARVARD ORIENTAL SERIES, VOL. 50 : Rig Veda, a metrically restored text Link to Online RV HOS vol. 50 has been released at the end of 1994: Rig Veda, a metrically restored text with an introduction and notes by BAREND A. VAN NOOTEN and GARY B. HOLLAND 1994. Pages, xviii, 667. Royal 8. Price, $50.00. [ISBN 0-674-76971-6] [Introduction pp. i-xiii; edition, pp. 1-547, with mandala, sukta, rc numbers as well as Grassmann's numbers; and including deity, author, and meter.] Also including computer diskettes of the metrical AND the traditional Samhita texts with a quick program for word searches, as well as a simple conversion program allowing users to choose their own style of Romanization. NB: the texts are unformatted. The discette is formatted in DOS style which is easily readable by Macintosh computers these days. On request, we may supply a Mac version in the future. FROM THE AUTHORS' INTRODUCTION The Rig Veda has come down to us in two versions, the Samhita and the Padapatha, neither of which corresponds in all respects to the actual metrical form of the hymns... we have chosen to present the hymns in a format closely approximating the canonic forms of the various meters. ... The discrepancies between the metrical canon and the transmitted form of the hymn have been discussed beginning with the Pratisakhyas, and continuing through the works of Hermann Grassmann, Hermann Oldenberg, and E. Vernon Arnold, but no systematic method for restoring the text in conformance with the metrical canon has been devised. ... Our approach has been to treat the text in the first place as if it were a synchronic document and to use the meter as the principal criterion for analysis. We view this straightforward metrical restoration of the text as a necessary preliminary to any further investigation of the relative chronology of the Rig Veda. ...

66. About "Hermann Grassmann And The Prehistory Of Universal Algebra" hermann grassmann and the Prehistory of Universal Algebra. _Library Home Full Table of Contents Suggest a Link http://mathforum.org/library/view/3253.html

Hermann Grassmann and the Prehistory of Universal Algebra Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannUAlgpaper/GrassmannUAlgpaper.html Author: Desmond Fearnley-Sander Description: A definition of universal algebra, with a sketch of its prehistory. "...abstract algebras are divided by a very simple scheme into self-contained `species'. Within each species a perfect duality is found between families of formal laws and the families of algebras satisfying them. Here the term 'family of algebras of a given species' is used in a technical sense meaning a class closed under taking subalgebras, homomorphic images and direct products - or what is nowadays called a variety. This said, one must point out that undoubtedly the most influential figure in the movement towards abstraction and generality in algebra which culminated in Universal Algebra was Emmy Noether, who died in 1935." Grassmann and Boole; Grassmann's Products; References. Levels: College Languages: English Resource Types: Articles Math Topics: Modern Algebra History and Biography Home The Math Library ... Help http://mathforum.org/

67. Amanda.html hermann grassmann is not credited much for inventing Linear Algebra, however,many believe that he was the inventer. grassmann did not put much of his work http://www.mathsci.appstate.edu/~sjg/class/2240/finalss04/Amanda.html

AmandaHelms.mws INTRODUCTION BACKGROUND more info: ... References: Amanda Helms History of Linear Algebra INTRODUCTION Many concepts that are thousands of years old are used in Linear Algebra; however, Linear Algebra has only techniqually been arond for a few decades. The reason for the creation of linear algebra was to have a way to relate number to geomety. IN teh american mathematical monthly an artical about the creation of linear algebra suggest that : to solve a problem it was necessary to have a modern concept of real numbers (p.809).It is important to know that linear algebra is thought of to be "appplicable to a part of the physical word, chalk figures on a blackboard or objects in space, and geometry" (p.809) BACKGROUND So what is linear algebra? The theory of systems of linear equations is one of teh largest topics of linear algebra. Linear Algebra is thought to be involved at some point in almost any scientific applications. Larson/Edwards text book states that linear applications arised in such diverse areas as enginnering, chemisty, economics, business, ecology, biology, and psychology. The technical definition for linear algebra is teh branch of algebra in which one studies vector (linear) spaces,linear operators such as mapping, and functiond on vector spaces (Elementary Linear Algebra).

68. Chronological List Of Publications grassmann s Dialectics and Category Theory, Proceedings of the 1994 Conference to 150 years of grassmann s Ausdehnungslehre , hermann Günther grassmann http://www.acsu.buffalo.edu/~wlawvere/list.html

F. William Lawvere Chronological list of publications HOME Subject Classification Bottom of page (most recent) 1. Functorial Semantics of Algebraic Theories Proceedings of the National Academy of Science 50 , No. 5 (November 1963), 869-872. 2. Elementary Theory of the Category of Sets Proceedings of the National Academy of Science 52 , No. 6 (December 1964), 1506-1511. Algebraic Theories, Algebraic Categories, and Algebraic Functors, Theory of Models ; North-Holland, Amsterdam (1965), 413-418. Functorial Semantics of Elementary Theories Journal of Symbolic Logic , Abstract, Vol. 31 (1966), 294-295. The Category of Categories as a Foundation for Mathematics La Jolla Conference on Categorical Algebra , Springer-Verlag (1966), 1-20. Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories Springer Lecture Notes in Mathematics No. 61 , Springer-Verlag (1968), 41-61. Ordinal Sums and Equational Doctrines Springer Lecture Notes in Mathematics No. 80 , Springer-Verlag (1969), 141-155. Diagonal Arguments and Cartesian Closed Categories Springer Lecture Notes in Mathematics No. 92

69. Grassmann Graphs hermann grassmann (18091877) started out as a banker, then became mathematicianand introduced the manifold of subspaces of a vector space, and invented http://www.win.tue.nl/~aeb/drg/graphs/Grassmann.html

Grassmann graphs Hermann Grassmann (1809-1877) started out as a banker, then became mathematician and introduced the manifold of subspaces of a vector space, and invented exterior algebra. At the age of 53 he turned from mathematics to Indoeuropean, especially Sanskrit, studies, where Grassmann's law is still well-known: Given a root with final aspirate and an initial consonant capable of aspiration, and given also that the final element loses aspiration (by some separate sound law), then that feature is retracted to the initial element. (E.g., in Greek: thrix, gen. trichos.) Given two consonant groups in a word, separated by a vowel and themselves aspirated, and provided that they are within the same root, then one (and normally the first) is deprived of its breath feature. (E.g., in Greek: thithemi becomes tithemi.) Consider a vector space V of dimension d over the finite field with q elements. Make a graph with as vertices the subspaces of dimension e of V , where two subspaces are adjacent when they meet in a hyperplane of each. The resulting graph is called the Grassmann graph Grassmann( d e q This graph is distance-regular, with diameter min(

70. Mathematicians From DSB Translate this page grassmann, hermann Günther, 1809-1877. Gregory, James, 1638-1675. Gua de Malves,Jean Paul de, ~1712-1786. Gudermann, Christoph, 1798-1852 http://www.henrikkragh.dk/hom/dsb.htm

Last modification: document.write(document.lastModified) emailaddr('webmaster','henrikkragh.dk','Webmaster','hkssmall'); Validate html Mathematicians from the Dictionary of Scientific Biography (DSB) For biographic details of Scandinavian mathematicians (and others), see my link page to DBL (Danish) or to NBL (Norwegian) Abel, Niels Henrik Ampère, André-Marie Argand, Jean Robert Arrhenius, Svante August Artin, Emil Beltrami, Eugenio Berkeley, George Bernoulli, Jakob I Bernoulli, Johann I Bertrand, Joseph Louis François Bessel, Friedrich Wilhelm Bianchi, Luigi Bjerknes, Carl Anton Bjerknes, Vilhelm Frimann Koren Bolyai, Farkas Bolyai, János Bolzano, Bernard Bombelli, Rafael Borchardt, Carl Wilhelm Borel, Émile Félix-Édouard-Justin Bouquet, Jean-Claude Briot, Charles Auguste Bérard, Jacques Étienne Bérard, Joseph Frédéric Cantor, Georg Carathéodory, Constantin Cardano, Girolamo Cauchy, Augustin-Louis Cayley, Arthur Chasles, Michel Chebyshev, Pafnuty Lvovich Clairaut, Alexis-Claude Clausen, Thomas Clebsch, Rudolf Friedrich Alfred Colden, Cadwallader

71. Completa\Bergeron\Bergeronhtml\bibliografía Translate this page 4. Paris Gauthier-Villars, 1899. grassmann, hermann 1947. Teoría de la extensión . grassmann, hermann 1995. A New Branch of Mathematics. Open-Court. http://www.accefyn.org.co/proyecto/bibliografia2/bibliografia2.htm

Proyecto auspiciado por la , la y la Universidad Nacional de Colombia Responsables del proyecto Proyecto Documentos y manuscritos / Documents and manuscripts Libros colombianos: 1800-1950 / Colombian books: 1800-1950 Libros extranjeros / Foreign books ... Personal del proyecto / Participants . Rev. Acad. Colombiana Ci. Ex. Fi. Nat. Rev. Acad. Colombiana Ci. Ex. Fi. Nat. Alfaro, Ricardo J. 1982. Bateman, Alfredo 1972. Cauchy, A.-L. 1821. . Paris: de Bure = Cauchy, A.-L. 1823. . Paris: de Bure = Grassmann, Hermann 1947. .Traducido por: Roxin, Emilio Oscar. Bs. As. Espasa-Calpe. Grassmann, Hermann 1995. A New Branch of Mathematics . Open-Court. Fuentes para el estudio de las ciencias exactas en Colombia Lesk, Michael 1997, Going digital , Scientific American. Nason, Henry Bradford 1887. Biographical Record of the Officers and Graduates of the Rensselaer Polytechnic Institute 18241886 . Editado por Henry B. Nason. Pombo, Lino de 1850. Pombo, Lino de 1858. Safford, Frank 1976. The Ideal of the Practical. Colombia's Struggle to Form a Technical Elite Safford, Frank 1989.

72. Hermann Günther Grassmann (Petsche)-Birkhäuser Geschichte Der Mathematik B Translate this page hermann grassmann, Gymnasiallehrer in Stettin und bekannt als Begründer dern-dimensionalen Vektoralgebra, erwarb sich auch in der Physik und der http://www.springeronline.com/sgw/cda/frontpage/0,11855,1-40295-72-66195235-0,00

Diese Website ist optimiert f¼r die Benutzung mit Java Script. Weitere Fachgebiete Bauwesen BioSciences Computerwissenschaften Geowissenschaften Ingenieurwesen Mathematik Physik Wissenschaftsgeschichte Home Birkh¤user Wissenschaftsgeschichte preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900180-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900170-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900190-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900200-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900369-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900344-0,00.gif'); Bitte w¤hlen Sie Afrika Asien Australien/ Ozeanien Deutschland Europa GroŸbritannien Nordamerika Schweiz S¼damerika Alle Autor/Hrsg. Titel ISBN/ISSN Buchserien preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900050-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,1-0-17-900070-0,00.gif');

73. INDEX OF NAMES grassmann, hermann G. (Germany, 18091877) and axioms for arithmetic, 1152 Gray,Alfred (USA, 1939-1998) and parametric curves, 1009 in Preface, xiii http://www.wolframscience.com/nksonline/index/names/f-j.html?SearchIndex=Hilbert

74. Le Leggi Di Grassmann grassmann da un precedente articolo di hermann von http://www.boscarol.com/pages/storia/10-grassmann.html

Storia della scienza del colore Le leggi di Grassmann Hermann Grassmann Una teoria postulati della teoria, se ne deducono tutti gli altri principi dimostrando che discendono in modo necessario dai postulati, realizzando così un ordinamento della materia in forma deduttiva. Un modello di una teoria è un sistema matematico utilizzato per "rappresentare" la teoria alla quale è in qualche modo analogo. Nell' Ottica Lo fece Hermann Grassmann (1809-1877), professore di matematica in un ginnasio di Stettino (che alla sua nascita era in Prussia, alla sua morte in Germania, oggi in Polonia con il nome di Szczecin) in un celebre articolo del 1853 "Über die Theorie der Farbenmischung" (Sulla teoria della mescolanza dei colori). L'occasione fu offerta a Grassmann da un precedente articolo di Hermann von Helmholtz nel quale l'autore, impegnato nella ricerca di coppie di colori la cui mescolanza desse il bianco ( colori complementari ), affermava di essere riuscito a trovare solo la coppia di complementari giallo e indaco. Helmholtz avanzava allora l'idpotesi che per produrre il bianco fossero necessari almeno tre colori spettrali. Nel suo articolo Grassmann si propone allora di dimostrare all'interno di una teoria che il modello di Newton, al contrario, implica un numero infinito di coppie di colori complementari. Per fondare la teoria Grassmann propone di considerare come termini primitivi gli attributi (psicologici) del colore: tinta (rosso, giallo, verde, blu, ...);

75. Knuth: Selected Papers On Discrete Mathematics David H., 88. page 800, right column (30 Mar 04) grassmann, hermann Günther,513. page 802, right column (20 Sep 03) Krauthgamer, Robert, 176. http://www-cs-faculty.stanford.edu/~knuth/dm.html

Selected Papers on Discrete Mathematics by Donald E. Knuth (Stanford, California: Center for the Study of Language and Information, 2003), xvi+812pp. (CSLI Lecture Notes, no. 106.) ISBN 1575862492 (cloth), 1575862484 (paperback) This is the sixth in a planned series of eight volumes that will contain archival forms of my published papers, together with new material. (The first book in the series was Literate Programming ; the second was Selected Papers on Computer Science ; the third was Digital Typography ; the fourth was Selected Papers on Analysis of Algorithms ; the fifth was Selected Papers on Computer Languages .) The Discrete Mathematics volume is characterized by the following remarks quoted from its preface. This book brings together almost everything that I've written about mathematical topics during the past four decades. I'm grateful for this opportunity to put the materials into a consistent format, and to correct errors in the original publications that have come to my attention. If any of this work deserves to be remembered, it is now in the form that I most wish people to remember it. Some of these papers were written purely as expositions in which I tried to introduce important work of other people and to explain it as well as I could. Other papers contain ideas that were novel when I wrote them down; but even in such cases I did not address the papers to specialists. I tried to make every paper self-contained, so that readers with a general mathematical background would be able to understand the details. My tendency has always been not to emphasize the theorems on the ``bottom line,'' but rather to tell a story of how various results fit together in harmonious patterns.

76. © 1998-2004 Sommerfeld-Projekt. Ausgelesen Am 07. März 2004 grassmann, hermann Ernst (1857-1922);Klein, Felix (1849-1925); Müller, Emil (1861-1927); Prandtl, http://www.lrz-muenchen.de/~Sommerfeld/BriefDat/00920.html

Rudolf Mehmke an Arnold Sommerfeld, 12. November 1903 Archiv: Stuttgart, UB (SN 6 II) Abschrift (2 Seiten) aus Stuttgart; Sprache: deutsch, Schrift: steno. Stichworte Personen: Wissenschaft: Vektorrechnung Tagung, Naturforscher Institution: Deutsche Mathematiker-Vereinigung; Vektorkommission; Wien, TH Start Biographie Projekt Online-Suche

77. The Encyclopedia Of Language And Linguistics Electronic Index grassmann, hermann Gunther (180977) Jones, Sir William (1746-94) Kazama,Kiyozo (1928- ) Kurylowicz, Jerzy (1895-1978) Lehmann, Winfred Philip (1916- ) http://www1.elsevier.com/homepage/sal/ellei/data/classified/e.html

Content Index ELLEI Homepage Animal Communication Anthropology and Language ... Translation BIOGRAPHIES African Languages Abraham, Roy Clive (1890-1963) Armstrong, Robert Gelston (1917-87) Bleek, Wilhelm Heinrich Immanuel (1827-75), and family Cerulli, Enrico (1898-1988) Conti Rossini, Carlo (1872-1949) Crowther, Samuel Ajayi (1806/08-91) Doke, Clement Martyn (1893-1980) Guthrie, Malcolm (1903-72) Koelle, Sigismund Wilhelm (1823-1902) Krapf, Johann Ludwig (1810-81) Lepsius, Carl Richard (1810-84) Lukas, Johannes (1901-90) Meeussen, Achille Emile (1912-78) Meinhof, Carl Friedrich Michael (1857-1944) Polotsky, Hans (Hayyim) Jacob (1905-91) Reinisch, Simon Leo (1832-1919) Tucker, Archibald Norman (1904-80) Turner, Lorenzo Dow (1895-1972) Ullendorff, Edward (1920-) Welmers, William E. (1916-88)

78. Hermann (der Jüngere) Graßmann Translate this page hermann (der Jüngere) grassmann Kein Photo verfügbar. geboren 8. Mai 1857 Stettingestorben 21. Januar 1922 Gießen Konfession evangelisch http://www.catalogus-professorum-halensis.de/grassmannhermanndj.html

geboren: 8. Mai 1857 Stettin gestorben: Konfession: evangelisch Vater: Gymnasialprofessor Quellen:

79. Read This: Briefly Noted hermann grassmann s Extension Theory (Ausdehnungslehre), first published in Extension Theory, by hermann grassmann. History of Mathematics, volume 19. http://www.maa.org/reviews/brief_may00.html

Read This! The MAA Online book review column Briefly Noted May 2000 New technologies create new possibilities. Early in 1999, John B. Cosgrave, using off-the-shelf mathematical software and mathematical ideas due to H. C. Pocklington, found a prime number with exactly 2000 digits. With the year 2000 on the horizon, it was inevitable that the number of digits would be related to the millennium. Cosgrave himself called it his "millennium prime," and its discovery garnered him some attention. For example, Ivars Peterson mentioned it in one of his MathTrek columns Excited by his discovery, Cosgrave wrote a long email message to his niece and nephew explaining some of the ideas that led to the discovery of the millennium prime. This email message now forms the major portion of the booklet A Prime for the Millennium , published by Folding Landscapes Press in Ireland. The booklet is charming, the story well told, and profits from the sales go to the Irish Cancer Society. Not a bad deal at all; check it out. (Fernando Q. Gouvêa)

80. CLIFHISTORY hermann grassmann (18091877) became a Sanskrit scholar, but in his spare Says Hestenes hermann grassmann completed the algebraic formulation of basic http://members.fortunecity.com/jonhays/clifhistory.htm

web hosting domain names photo sharing TRACING THE HISTORY OF "CLIFFORD ALGEBRA" In 1950, while majoring in physics at Columbia U., I read about Clifford Algebra in a book written by the British astronomer and "founder of astrophysics", Sir Arthur Eddington (1882-1944). (Eddington's South American observations of a solar eclipse provided the first confirmation of Albert Einstein's controversial General Theory of Relativity In his book, Eddington said, "I cannot believe that anything so ugly as multiplication of matrices is an essemtial part of the scheme of nature." (Mathematical physicist, N. Salingaros, says: "Eddington apparently defined the real Majorana [spinor] matrices (actually an equivalent set) before Majorana; he introduced the now standard g notation, and also the concept of chirality; he investigated the group structure of the Dirac algebra; and he defined the complex Clifford algebra over an eight-dimensional space which appears today in formulations of supersymmetry and supergravity.") However, it seemed that no Columbia math or physics prof could tell me anything about

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