1. Richard Dedekind - Wikipedia Other languages Nederlands. Richard Dedekind. From Wikipedia, thefree encyclopedia. The German mathematician Julius Wilhelm Richard http://www.wikipedia.org/wiki/Richard_Dedekind

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Other languages: Nederlands Richard Dedekind From Wikipedia, the free encyclopedia. Julius Wilhelm Richard Dedekind October 6 February 12 ) was a German mathematician and Kummer 's closest follower in arithmetic Dedekind was born in Brunswick German Braunschweig ) 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

2. Richard Dedekind - Wikipedia Other languages Nederlands. Richard Dedekind. (Redirected from JuliusWilhelm Richard Dedekind). The German mathematician Julius Wilhelm http://www.wikipedia.org/wiki/Julius_Wilhelm_Richard_Dedekind

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Other languages: Nederlands Richard Dedekind (Redirected from Julius Wilhelm Richard Dedekind Julius Wilhelm Richard Dedekind October 6 February 12 ) was a German mathematician and Kummer 's closest follower in arithmetic Dedekind was born in Brunswick German Braunschweig ) 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

3. 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

Richard Dedekind (1831-1916) was born on October 6, 1831, in Brunswick, Germany, the birthplace of Gauss . He was the youngest of four children. In 1848, Dedekind went to Collegium Carolinum, an institution attended by Gauss After four semesters, in 1852 Dedekind completed his Ph.D. work under Gauss Dedekind started his teaching career in 1854. In 1855, Dirichlet succeeded Gauss Dedekind was the first university teacher to lecture on Galois theory. He introduced the concept of a field, replaced the concept of a permutation group by the abstract group concept, and, in 1858, introduced a purely arithmetic definition of continuity. Dedekind is most remembered for his concept of "Dedekind cut", which he introduced in 1872. He was criticized on this theory by mathematicians such a Kronecker , Weierstrass, and Russell. Dedekind edited the works of Gauss , Dirichlet, and Riemann. In 1871, he supplemented Dirichlet's lectures, introducing the notion of an "ideal", a term he coined. Later he developed the theory of ideals. He is also credited for such fundamental concepts as ring and unit. His treatises on number fields stimulated further development of ideal theory. Dedekind also extended Kummer's work on unique factorization domains. His work on abstract algebra influenced Emmy Noether's work on algebra.

4. 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 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 : 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 : application , d' image et de bijection pas le cas pour l'application de Z dans Z Bolzano Cantor L orsqu'une correspondance f de E sur F est biunivoque, la relation x (f o f)(x) = f(f(x)) f (x) o puis : f o f o f = f , f o f o f... o f = f n , on pose alors logiquement f = f et f o f est clairement f . Ainsi cette notation se comporte comme une fonction puissance. f n de x par f.

5. 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

6. Bedeutende Mathematiker Translate this page dedekind richard (1831 - 1916, Braunschweig), Mersenne Marin (1588 - 1648, Paris). NoetherEmmy (1882 - 1935, USA), 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)

7. Richard Dedekind Richard Dedekind. This picture was taken from History of Modern Mathematics VolumeIIdeas and their reception edited by David E. Rowe and John McCleary. http://www.cis.usouthal.edu/~lynn/mathematics/dedekind.html

Richard Dedekind This picture was taken from "History of Modern Mathematics Volume I:Ideas and their reception" edited by David E. Rowe and John McCleary

8. 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

9. Richard Dedekind 1831 - 1981 Eine Würdigung Zu Seinem 150 Geburtstag Dedekind R Translate this page Richard Dedekind 1831 - 1981 Eine Würdigung zu seinem 150 Geburtstag DedekindRichard. Geburtstag. Autor dedekind richard. Rubrik Kategorie http://www.easybuchdirekt.de/Dedekind-Richard-Richard-Dedekind-1831-1-3528084987

Richard Dedekind 1831 - 1981 Eine Würdigung zu seinem 150 Geburtstag Dedekind Richard Titel: Richard Dedekind 1831 - 1981. Eine Würdigung zu seinem 150. Geburtstag. Autor: Dedekind Richard Rubrik: Kategorie: Kraft Hanspeter Geometrische ... Hector Gilbert, Hirsch Intr... Hegemann Werner Bauwelt Funda... Lynch Kevin Bauwelt Fundament... ... Home

10. Richard Dedekind - Acapedia - Free Knowledge, For All Friends of Acapedia Richard Dedekind. From Wikipedia, the free encyclopedia.The German mathematician Julius Wilhelm Richard Dedekind http://acapedia.org/aca/Richard_Dedekind

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11. Dedekind Richard Dedekind, bron Oct. 6, 1831, died Feb. Richard Dedekind(18311916) wasborn on October 6, 1831, in Brunswick, Germany, the birthplace of Gauss. http://www.wactc.wo.k12.ri.us/csstudents02/heathers/math/dedekind.html

Richard Dedekind, bron Oct. 6, 1831, died 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. Richard Dedekind(1831-1916) was born on October 6, 1831, in Brunswick, Germany, the birthplace of Gauss. He was the youngest of four children. Dedekind was the first university teacher to lecture on Galois theory. He introduced the concept of a field, replaced the concept of a permutation group by the abstract group concept, and, in 1858, introduced a purely arithmetic definition of continuity. Dedekind is most remembered for his concept of "Dedekind cut", which he introduced in 1872. He was criticized on this theory by mathematicians such a Kronecker, Weierstrass, and Russell.

12. Dedekind, Richard study of CONTINUITY and definition of the real numbers in terms of dedekind "cuts", the Category Science Math History People......dedekind, richard. richard dedekind, b. Oct. 6, 1831, d. Feb. 12, 1916,was a German mathematician known for his study of CONTINUITY 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. DEDEKIND dedekind richard Julius Wilhelm 18311916,dedekind richard Julius Wilhelm 1831-1916. http://trucsmaths.free.fr/images/matheux/math_dedekind.htm

DEDEKIND Richard Julius Wilhelm DEDEKIND Richard Julius Wilhelm

14. Dedekind, Richard 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

Dedekind, Richard Autor: J. W. Dauben. Traducido por Alexander Velásquez. Homepage de la Escuela e-mail: webmaster@euler.ciens.ucv.ve © 2000 Escuela de Matemáticas Facultad de Ciencias, Universidad Central de Venezuela

15. Dedekind, Richard dedekind, richard. 6.10.1831 (richard Julius Wilhelm) Braunschweig (D), 12.2.1916 Braunschweig, luth., Deutscher. http://www.snl.ch/dhs/externe/protect/textes/D43110.html

Decurtins, Caspar Dedelley, Jacques No 1 Dedekind, Richard 6.10.1831 (Richard Julius Wilhelm) Braunschweig (D), 12.2.1916 Braunschweig, luth., Deutscher. Sohn des Julius, Prof. am Collegium Carolinum (später Polytechnikum) Braunschweig, und der Carol geb. Emperius. Ledig. 1848-50 Mathematikstud. am Collegium Carolinum, 1850-52 in Göttingen. 1852 Promotion bei Johann Carl Friedrich Gauss, 1854 Habilitation. 1858-62 Prof. am Polytechnikum Zürich, 1862-94 Prof. am Polytechnikum Braunschweig. D.s Auffassung der Mathematik, seine bahnbrechenden Ergebnisse in Algebra, Zahlentheorie, Mengenlehre und bezügl. des Aufbaus der reellen Zahlen haben die Mathematik des 20. Jh. tief geprägt. Den sog. Dedekindschen Schnitt entwickelte er in Zürich. Mitglied der Akad. der Wiss. von Berlin, Paris und Rom. 1909 Dr. h.c. der ETH Zürich. Archive ETH-BIB, Nachlass Literatur NDB 3, 552 f. DSB 4, 1-5 Richard Dedekind 1831-1981, hg. von W. Scharlau, 1981 Dt. Biogr. Enz. 2, 461 f. Max-Albert Knus Alle Urheberrechte dieser elektronischen Publikation sind beim Historischen Lexikon der Schweiz, Bern. Für alle elektronisch publizierten Texte gelten dieselben Regeln wie für eine gedruckte Veröffentlichung. Decurtins, Caspar

16. Dedekind, Julius Wilhelm Richard dedekind, Julius Wilhelm richard Julius Wilhelm richard dedekind (6.11.1831 12.02.1916) wurde in Braunschweig als jüngstes von vier Kindern eines Jura-Professors geboren. http://www.mathe.tu-freiberg.de/~hebisch/cafe/dedekind.html

Dedekind, Julius Wilhelm Richard Dedekind war auch musikalisch begabt und komponierte sogar eine kleine Oper. Er heiratete nie und lebte bis zu seinem Tode bei seiner Schwester.

17. Dedekind Biography of richard dedekind (18311916) Julius Wihelm richard dedekind. Born 6 Oct 1831 in Braunschweig, duchy of Braunschweig (now Germany) 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

18. Alphamusic - Essays On Buch dedekind, richard Essays on the Theory of Numbers http://www.alpha-music.de/103/0486210103.html

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19. 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

20. References For Dedekind References for richard dedekind. I dedekind, P Dugac, WD Geyerand W Scharlau,richard dedekind, 18311981, in Eine Würdigung zu seinem 150. http://www-gap.dcs.st-and.ac.uk/~history/References/Dedekind.html

References for Richard Dedekind Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: E T Bell, Men of Mathematics I Dedekind, P Dugac, W-D Geyerand W Scharlau, Richard Dedekind, 1831-1981, in (Braunschweig, 1981). R Dedekind, Gesammelte mathematische Werke (Braunschweig, 1932). R Dedekind, Gesammelte mathematische Werke - Reprint (New York, 1969). P Dugac, Richard Dedekind et les fondements des mathematiques (Paris, 1976). D A Gillies, Frege, Dedekind, and Peano on the foundations of arithmetic (Assen, 1982). Articles: L Corry, Eudoxus' theory of proportions as interpreted by Dedekind (Spanish), Mathesis Historia Math. Arch. Hist. Exact Sci. H M Edwards, Dedekind's invention of ideals, Bull. London Math. Soc. H M Edwards, Dedekind's invention of ideals, in Studies in the history of mathematics (Washington, DC, 1987), 8-20. H M Edwards, The genesis of ideal theory, Arch. Hist. Exact Sciences Historia Mathematica F Gana, Peirce and Dedekind : the definition of finite sets (Italian), Historia Math.

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