1. Richard Dedekind - Wikipedia, The Free Encyclopedia Richard Dedekind. From Wikipedia, the free encyclopedia. Reference. Essays onthe Theory of Numbers, Richard Dedekind, Dover Publications, Inc., 1963. http://en.wikipedia.org/wiki/Richard_Dedekind

Richard Dedekind From Wikipedia, the free encyclopedia. Julius Wilhelm Richard Dedekind October 6 February 12 ) was a German mathematician and Ernst Eduard Kummer 's closest follower in arithmetic Dedekind was born in Braunschweig Brunswick ) the youngest of four children of Julius Levin Ulrich Dedekind. He later rejected his first names Julius Wilhelm. He lived with his unmarried sister Julia until her death in , he himself also never married. In , he entered Collegium Carolinum in Brunswick and in with the solid knowledge in mathematics he entered the University of Göttingen In Göttingen Gauss taught mathematics mostly at an elementary level. In the departments of mathematics and physics, Dedekind learnt about number theory . Among Dedekind's main professors was Moritz Abraham Stern who at that time wrote many works on number theory. He made his short doctoral thesis supervised by Gauss Über die Theorie der Eulerschen Integrale On the Theory of Eulerian integrals ). His thesis was dexterous and autonomous but it didn't show any of the special talent which was visible on almost every page of Dedekind's later works. Nevertheless, Gauss must certainly have seen Dedekind's gift for mathematics. Dedekind received his doctorate in and he was Gauss's last student.

2. Richard Dedekind Richard Dedekind(18311916) was born on October 6, 1831, in Brunswick, Germany,the birthplace of Gauss. He was the youngest of four children. http://www.math.ukans.edu/~engheta/bio/dedekind.html

3. Quotation By Richard Dedekind Richard Dedekind (1831 1916). As professor in the Polytechnic Schoolin Zürich I found myself for the first time obliged to lecture http://www-gap.dcs.st-and.ac.uk/~history/Quotations2/1006.html

Richard Dedekind Opening of the paper in which Dedekind cuts were introduced.

4. Bedeutende Mathematiker Translate this page dedekind richard (1831 - 1916, Braunschweig), Mersenne Marin (1588 - 1648, Paris). NewtonSir Isaac (1643 - 1727), dedekind richard (1831 - 1916, Braunschweig). http://www.mathematik.ch/mathematiker/

Home Geschichte Mathematiker Zitate ... Suche Bedeutende Mathematiker alphabetisch nach Geburtsdatum Abel Niels (1802 -1829, Froland, Norwegen) Thales von Milet (um 625 - 546 v. Chr.) Appolonios von Perge (262 - 190 v.Chr., Pergamon?) Pythagoras von Samos (um 580 - 496 v. Chr., Kroton) Archimedes (287 - 212 v. Chr., Syrakus) Zenon von Elea (um 490 - um 430 v.Chr.) Aristoteles (384 - 322 v. Chr., Chalkis) Aristoteles (384 - 322 v. Chr., Chalkis) Banach Stefan (1892 - 1945, Lwów) Euklid von Alexandria (um 360 - um 300 v. Chr. ?) Bernoulli Jakob (1654 - 1705, Basel) Archimedes (287 - 212 v. Chr., Syrakus) Bernoulli Johann (Bruder von Jakob) (1667 - 1748, Basel) Appolonios von Perge (262 - 190 v.Chr., Pergamon?) Bernoulli Daniel (Sohn von Johann) (1700 - 1782, Basel) Ries Adam (1492 - 1559, Annaberg) Bessel Friedrich Wilhelm (1784 - 1846, Königsberg) Cardano Geronimo (1501 - 1576, Rom) Cantor Georg (1845-1918, Halle) Viète (Vieta) François (1540 - 1603, Paris) Cauchy Augustin Louis (1789 - 1857, Paris) Neper (Napier) John (1550 - 1617, Edinburgh) Cardano Geronimo (1501 - 1576, Rom)

5. Richard Dedekind - Wikipedia, The Free Encyclopedia Richard Dedekind. (Redirected from Dedekind). Reference. Essays on the Theory ofNumbers, Richard Dedekind, Dover Publications, Inc., 1963. ISBN 0486-21010-3. http://en.wikipedia.org/wiki/Dedekind

Richard Dedekind From Wikipedia, the free encyclopedia. (Redirected from Dedekind Julius Wilhelm Richard Dedekind October 6 February 12 ) was a German mathematician and Ernst Eduard Kummer 's closest follower in arithmetic Dedekind was born in Braunschweig Brunswick ) the youngest of four children of Julius Levin Ulrich Dedekind. He later rejected his first names Julius Wilhelm. He lived with his unmarried sister Julia until her death in , he himself also never married. In , he entered Collegium Carolinum in Brunswick and in with the solid knowledge in mathematics he entered the University of Göttingen In Göttingen Gauss taught mathematics mostly at an elementary level. In the departments of mathematics and physics, Dedekind learnt about number theory . Among Dedekind's main professors was Moritz Abraham Stern who at that time wrote many works on number theory. He made his short doctoral thesis supervised by Gauss Über die Theorie der Eulerschen Integrale On the Theory of Eulerian integrals ). His thesis was dexterous and autonomous but it didn't show any of the special talent which was visible on almost every page of Dedekind's later works. Nevertheless, Gauss must certainly have seen Dedekind's gift for mathematics. Dedekind received his doctorate in and he was Gauss's last student.

6. Richard Dedekind Richard Dedekind. Julius Wilhelm Richard Dedekind (October 6, 1831 February 12, 1916) was a German mathematician and Ernst Eduard http://www.fact-index.com/r/ri/richard_dedekind.html

Main Page See live article Alphabetical index Richard Dedekind Julius Wilhelm Richard Dedekind October 6 February 12 ) was a German mathematician and Ernst Eduard Kummer 's closest follower in arithmetic Dedekind was born in Braunschweig Brunswick ) the youngest of four children of Julius Levin Ulrich Dedekind. He later rejected his first names Julius Wilhelm. He lived with his unmarried sister Julia until her death in , he himself also never married. In , he entered Collegium Carolinum in Brunswick and in with the solid knowledge in mathematics he entered the University of Göttingen In Göttingen Gauss taught mathematics mostly at an elementary level. In the departments of mathematics and physics, Dedekind learnt about number theory . Among Dedekind's main professors was Moritz Abraham Stern who at that time wrote many works on number theory. He made his short doctoral thesis supervised by Gauss Über die Theorie der Eulerschen Integrale On the Theory of Eulerian integrals ). His thesis was dexterous and autonomous but it didn't show any of the special talent which was visible on almost every page of Dedekind's later works. Nevertheless, Gauss must certainly have seen Dedekind's gift for mathematics. Dedekind received his doctorate in and he was Gauss's last student.

7. Richard Dedekind Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 February 12, 1916) was a German mathematician and Ernst Eduard http://www.guajara.com/wiki/en/wikipedia/r/ri/richard_dedekind.html

Guajara in other languages: Spanish Deutsch French Italian Richard Dedekind Julius Wilhelm Richard Dedekind October 6 February 12 ) was a German mathematician and Ernst Eduard Kummer 's closest follower in arithmetic Dedekind was born in Braunschweig Brunswick ) the youngest of four children of Julius Levin Ulrich Dedekind. He later rejected his first names Julius Wilhelm. He lived with his unmarried sister Julia until her death in , he himself also never married. In , he entered Collegium Carolinum in Brunswick and in with the solid knowledge in mathematics he entered the University of Göttingen In Göttingen Gauss taught mathematics mostly at an elementary level. In the departments of mathematics and physics, Dedekind learnt about number theory . Among Dedekind's main professors was Moritz Abraham Stern who at that time wrote many works on number theory. He made his short doctoral thesis supervised by Gauss Über die Theorie der Eulerschen Integrale On the Theory of Eulerian integrals ). His thesis was dexterous and autonomous but it didn't show any of the special talent which was visible on almost every page of Dedekind's later works. Nevertheless, Gauss must certainly have seen Dedekind's gift for mathematics. Dedekind received his doctorate in and he was Gauss's last student.

8. Dedekind Translate this page dedekind richard, allemand, 1831-1916. Né, comme Gauss, à Brunswick,il sera son élève à Göttingen. À la mort de Gauss (1855 http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Dedekind.html

DEDEKIND Richard, allemand, 1831-1916 Gauss Dirichlet Weber Cantor La construction axiomatique des ensembles de nombres Dedekind donna une construction axiomatique de l'ensemble N Peano corps Stetigkeit und Irrationalzahlen Eudoxe ) : tout rationnel r partage Q en deux classes C et C coupure dans Q ) : ce sont les nombres irrationnels Pythagore et les nombres incommensurables : continu connexe N et Q , dont l'ordre prolonge celui de Q fondamental . Et si la correspondance nombre point Dedekind utilisa en fait la notation R rationnels . C'est Peano qui proposa Q , du mot italien quoziente = quotient. L'appellation corps pour un corps de nombres, comme R pour celui des rationnels. Le concept formel de corps Weber en 1893. Le terme real Cantor (1883). La notation Z pour l'ensemble des entiers relatifs, Z Zahl nombre Weierstrass : Cantor : Un théorème célèbre de Dedekind : Ce théorème fondamental est appliqué systématiquement dans l'étude des suites ou des séries : dans l'usage des critères de convergence qui se ramènent à l'étude d'une suite. test ) de Dedekind du Bois-Reymond Si la série S a n S( b n+1 -b n est absolument convergente S a n b n est convergente.

9. Richard Dedekind Richard Dedekind. 18311916. http://dbeveridge.web.wesleyan.edu/wescourses/2001f/chem160/01/Who's Who/richard

Home Science Humanities Cantor ... Mendel Richard Dedekind Biography Photo Gallery Links to Outside Sources German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts. Although not fully recognized in his lifetime, his treatment of the ideas of the infinite and of what constitutes a real number continues to influence modern mathematics. Biography born October 6 entered University of Gottingen with solid math background from Collegium Carolinum in Brunswick received doctorate, last pupil of Gauss awarded habilitation degrees, began teaching at Gottingen began friendship with Dirichlet appointed to Polytechnikum in Zurich and began teaching appointed to Brunswick Polytechnikum (Callegium Carolinum upgraded), elected to the Gottingen Academy supplemented Dirichlet's lectures and introduced notion of an "ideal," a term he coined published paper on "Dedekind cuts" to define real numbers met Cantor published paper on purely arithmetic definition of continuity elected to Berlin Academy published joint paper with Heinrich Weber which applies his theory of ideals to the theory of Reimann Surfaces retired from Brunswick Polytechnikum elected to Academy of Rome, the Leopoldino-Carolina Naturae Curiosorum Academia, and the Academie des Sciences in Paris

10. Richard Dedekind Richard Dedekind. Julius Wilhelm Richard Dedekind (Ríjen 6, 1831 Únor 12, 1916) byl Nemec matematik a Ernst Eduard Kummer s http://wikipedia.infostar.cz/r/ri/richard_dedekind.html

švodn­ str¡nka Tato str¡nka v origin¡le Richard Dedekind Julius Wilhelm Richard Dedekind Ř­jen 6 šnor 12 ) byl Němec matematik a Ernst Eduard Kummer ' s nejbližš­ n¡sledovn­k v aritmetika Dedekind byl narozen½ v Braunschweig Brunswick ) nejmladÅ¡­ čtyř dět­ Juliuse Levin Ulrich Dedekind. On později odm­tl jeho křestn­ jm©na Julius Wilhelm. On žil s jeho svobodnou sestrou Julia until ji smrt v , on s¡m tak© nikdy se vzal. V , on přihl¡Å¡en½ Collegium Carolinum v Brunswicku a v se znalostmi pevn© l¡tky v matematice on přihl¡Å¡en½ Univerzita G � ttingen V G � ttingen Gauss učil matematiku větÅ¡inou u z¡kladn­ ºrovně. V oddělen­ch matematiky a fyziky, Dedekind učen½ okolo teorie č­sel . Mezi Dedekind je hlavn­ profesoři byli Moritz Abraham z¡Ä kdo v tom čas psal mnoho prac­ na teorii č­sel. On vyroben½ jeho kr¡tk¡ disertačn­ pr¡ce ř­dil Gauss � ber umř­t Theorie der Eulerschen Integrale Na teorii Eulerian integrals ). Jeho teze byla zručn¡ a autonomn­, ale to neukazovalo někter©ho speci¡ln­ho talentu kter½ byl viditeln½ na t©měř každ© straně Dedekind m¡ pozdnějÅ¡­ pr¡ce. Přesto, Gauss muset jistě viděli Dedekind je d¡rek pro matematiku. Dedekind přj­mal jeho doktor¡t v a on byl Gauss je posledn­ student.

11. Richard Julius Wilhelm Dedekind RICHARD JULIUS WILHELM DEDEKIND. (1831 1916). Richard Dedekind was a German mathematicianwho was born in 1831 in Brunswick. His father was a professor of law. http://www.engr.iupui.edu/~orr/webpages/cpt120/mathbios/rdedek.htm

RICHARD JULIUS WILHELM DEDEKIND Richard Dedekind was a German mathematician who was born in 1831 in Brunswick. His father was a professor of law. Dedekind studied at Gottingen where he later taught. He also taught at the Zurich polytechnic for a few years. He then became the professor of mathematics in the technical school of Brunswick where he taught for half a century. He was a bachelor and he lived with his unmarried sister, Julie, until her death in 1914. Dedekind made many original and important contributions to the theory of algebraic numbers. He died at the age of 85 in 1916. In 1872, he published a book, Continuity and Irrational Numbers , in which he attempted to remove all ambiguities and doubts as to how irrational numbers fitted into the domain of arithmetic. Some items to be considered in this work are as follows (all numbers are shown in base ten arithmetic): A rational number can be expressed in the form of a fraction a/b where a and b are integers. A number which cannot be expressed as a rational fraction is an irrational number. For example, . The class of real numbers is made up of rational and irrational numbers. A rational number can be expressed in decimal notation and where the decimal does not terminate (end in zeroes), it repeats itself periodically. For example, 10/13 =.769230.769230.769230 and 14/11 = 1.27.27.27. An irrational number when expressed as a decimal does not terminate or exhibit the periods. It is impossible to exactly express numbers such as

12. Dedekind, Richard study of CONTINUITY and definition of the real numbers in terms of dedekind cuts , the nature of number and mathematical induction, definition of finite and infinite sets; algebraic number fields, concept of RINGS. http://euler.ciens.ucv.ve/English/mathematics/dedekind.html

Dedekind, Richard Richard Dedekind, b. Oct. 6, 1831, d. Feb. 12, 1916, was a German mathematician known for his study of CONTINUITY and definition of the real numbers in terms of Dedekind "cuts"; his analysis of the nature of number and mathematical induction, including the definition of finite and infinite sets; and his influential work in NUMBER THEORY, particularly in algebraic number fields. Among his most notable contributions to mathematics were his editions of the collected works of Peter DIRICHLET, Carl GAUSS, and Georg Riemann. Dedekind's study of Dirichlet's work led to his own study of algebraic number fields, as well as his introduction of ideals. He developed this concept into a theory of ideals that is of fundamental importance in modern algebra. Dedekind also introduced such fundamental concepts as RINGS. Author: J. W. Dauben Homepage e-mail: webmaster@euler.ciens.ucv.ve © 2000 Mathematics School Science Faculty, Central University of Venezuela

13. Richard Dedekind --  Encyclopædia Britannica Cite this article. richard dedekind. born Oct. 6, 1831, Braunschweig, duchy of MLA style " richard dedekind." Encyclopædia Britannica. 2004. Encyclopædia Britannica Premium Service http://www.britannica.com/eb/article?eu=30201

14. Dedekind, Julius Wilhelm Richard. The Columbia Encyclopedia, Sixth Edition. 2001 The Columbia Encyclopedia, Sixth Edition. 2001. dedekind, Julius Wilhelm richard. 18311916, German mathematician. dedekind studied at Göttingen under the German mathematician http://www.bartleby.com/65/de/Dedekind.html

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15. Dedekind Julius Wihelm richard dedekind. Born 6 richard dedekind s father wasa professor at the Collegium Carolinum in Brunswick. His mother http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Dedekind.html

Julius Wihelm Richard Dedekind Born: 6 Oct 1831 in Braunschweig, duchy of Braunschweig (now Germany) Died: 12 Feb 1916 in Braunschweig, duchy of Braunschweig (now Germany) Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Richard Dedekind 's father was a professor at the Collegium Carolinum in Brunswick. His mother was the daughter of a professor who also worked at the Collegium Carolinum. Richard was the youngest of four children and never married. He was to live with one of his sisters, who also remained unmarried, for most of his adult life. He attended school in Brunswick from the age of seven and at this stage mathematics was not his main interest. The school, Martino-Catharineum, was a good one and Dedekind studied science, in particular physics and chemistry. However, physics became less than satisfactory to Dedekind with what he considered an imprecise logical structure and his attention turned towards mathematics. Listing and Wilhelm Weber . The two departments combined to initiate a seminar which Dedekind joined from its beginning. There he learnt number theory which was the most advanced material he studied. His other courses covered material such as the differential and integral calculus, of which he already had a good understanding. The first course to really make Dedekind enthusiastic was, rather surprisingly, a course on experimental physics taught by

16. Dedekind Biography of richard dedekind (18311916) Julius Wihelm richard dedekind. Born 6 Oct 1831 in Braunschweig, duchy of Braunschweig (now Germany richard dedekind's father was a professor at the http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dedekind.html

Julius Wihelm Richard Dedekind Born: 6 Oct 1831 in Braunschweig, duchy of Braunschweig (now Germany) Died: 12 Feb 1916 in Braunschweig, duchy of Braunschweig (now Germany) Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Richard Dedekind 's father was a professor at the Collegium Carolinum in Brunswick. His mother was the daughter of a professor who also worked at the Collegium Carolinum. Richard was the youngest of four children and never married. He was to live with one of his sisters, who also remained unmarried, for most of his adult life. He attended school in Brunswick from the age of seven and at this stage mathematics was not his main interest. The school, Martino-Catharineum, was a good one and Dedekind studied science, in particular physics and chemistry. However, physics became less than satisfactory to Dedekind with what he considered an imprecise logical structure and his attention turned towards mathematics. Listing and Wilhelm Weber . The two departments combined to initiate a seminar which Dedekind joined from its beginning. There he learnt number theory which was the most advanced material he studied. His other courses covered material such as the differential and integral calculus, of which he already had a good understanding. The first course to really make Dedekind enthusiastic was, rather surprisingly, a course on experimental physics taught by

17. Books By Richard Dedekind At Walmart.com - Every Day Low Prices Find books written by richard dedekind. Select from 1000's of books at Walmart.com, we have a great selection of highquality merchandise, friendly service and, of course, Every Day Low Prices. http://rdre1.inktomi.com/click?u=http://na.link.decdna.net/n/3532/4200/www.walma

18. Escuela De Matemáticas - UCV Translate this page dedekind, richard. richard dedekind, nacido en Oct. 6, 1831, muertoen Feb. 12, 1916, fue un matemático alemán conocido por su http://euler.ciens.ucv.ve/matematicos/dedekind.html

Los Matemáticos más famosos de todos los Tiempos: Niels Henrik Abel Arquímedes Banach, Stefan Bessel, Friedrich ... Dedekind, Richard Autor: J. W. Dauben. Traducido por Alexander Velásquez. Webmaster@euler.ciens.ucv.ve Av. Los Ilustres, Facultad de Ciencias, Esc. de Matemáticas Piso 3, Los Chaguaramos Caracas 1020 - Venezuela. Telf. 58-212-605.1512/1197/1484/1480 Fax: 58-212-605.1512/1190/1480 © 2004 Escuela de Matemáticas - UCV - Ultima modificación: Jueves, 01 Junio 2000

19. Dedekind, Richard dedekind, richard (183916). dedekind grew up in Germany and in1850 entered the University of Gottingen. There he studied with http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib

Dedekind, Richard (183916) Dedekind grew up in Germany and in 1850 entered the University of Gottingen. There he studied with Bernhard Riemann and Carl Gauss He began lecturing in probability, and then later began his serious study of number theory. Dedekind became a professor at Brunswick Polytechnic and stayed there for many years. Like Gauss, Dedekind preferred to study the theoretical aspects of number theory. His work on irrational numbers gave the subject a logical foundation. In his later years, Dedekind met and worked with Cantor on the concept of the infinite

20. PlanetMath Dedekind Cuts The purpose of dedekind cuts is to provide a sound logical foundation for the real number system. dedekind's Press, Oxford, 1969. 2. dedekind, richard. Essays on the Theory of Numbers http://www.planetmath.org/encyclopedia/DedekindCuts.html

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