21. Devrient, Eduard --  Encyclopædia Britannica Ernst eduard kummer University of St.Andrews Biographical sketch of this Germanmathematician known for his works related to number theory and Fermat s Last http://www.britannica.com/eb/article-9030174

Home Browse Newsletters Store ... Subscribe Already a member? Log in Content Related to this Topic This Article's Table of Contents Eduard Devrient Print this Table of Contents Shopping Price: USD $1495 Revised, updated, and still unrivaled. The Official Scrabble Players Dictionary (Hardcover) Price: USD $15.95 The Scrabble player's bible on sale! Save 30%. Merriam-Webster's Collegiate Dictionary Price: USD $19.95 Save big on America's best-selling dictionary. Discounted 38%! More Britannica products Devrient, Eduard  Encyclopædia Britannica Article Page 1 of 1 Eduard Devrient born Aug. 11, 1801, Berlin [Germany] died Oct. 4, 1877, Karlsruhe, Ger. actor, director, manager, translator of Shakespeare into German, and author of the first detailed account of the development of the German theatre, Geschichte der deutschen Schauspielkunst Nephew of the great Romantic actor Ludwig Devrient Devrient, Eduard...

22. The Mathematics Genealogy Project - Ernst Kummer Ernst eduard kummer Biography eduard Wiltheiss, HumboldtUniversität zu Berlin,1879. Leo Wituski, Humboldt-Universität zu Berlin, 1853 http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=18331

23. The Mathematics Genealogy Project - Ernst Kummer Ernst eduard kummer Biography eduard Wiltheiss, HumboldtUniversität zu Berlin,1879. Alexander Wernicke, Humboldt-Universität zu Berlin, 1879 http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=18331&fChrono=1

24. Anecdote - Ernst Eduard Kummer - Simple Arithmetic Anecdotes, Famous People. Funny Stories. Anecdotes from Gates to Yeats. http://www.anecdotage.com/index.php?aid=6382

25. PlanetMath: Kummer's Congruence The following congruence is due to Ernst eduard kummer. Theorem 1 (kummer scongruence) Let $ p$ be a prime. Suppose that $ k\geq 2$ is an even integer http://planetmath.org/encyclopedia/KummersCongruence.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Kummer's congruence (Theorem) Let denote the th Bernoulli number In fact, for all odd , so we will only consider for even . The following congruence is due to Ernst Eduard Kummer: Theorem (Kummer's congruence) Let be a prime . Suppose that is an even integer which is not divisible by . Then the quotient is -integral, that is, as a fraction in lower terms does not divide its denominator . Furthermore, if is another even integer with and then The interested reader should see also the congruence of Clausen and von Staudt for a similar result. As an example of Kummer's congruence, let and . Then: If we pick (so that ) then: which is what the theorem predicted. "Kummer's congruence" is owned by alozano view preamble View style: HTML with images page images TeX source See Also: congruence of Clausen and von Staudt integral element the odd Bernoulli numbers are zero Other names: Kummer congruence Keywords: Kummer, Bernoulli number

26. Kummer - Definition Of Kummer In Encyclopedia Ernst eduard kummer (29 January 1810 in Sorau, Brandenburg, Prussia 14 May 1893in Berlin, Germany) was a German mathematician. Highly skilled in applied http://encyclopedia.laborlawtalk.com/Kummer

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law Ernst Eduard Kummer 29 January in Sorau Brandenburg Prussia 14 May in Berlin Germany ) was a German mathematician . Highly skilled in applied mathematics , Kummer trained German army officers in ballistics ; afterwards, he taught for 10 years in a Gymnasium (the German equivalent of high school), where he inspired the mathematical career of Leopold Kronecker . He retired from teaching and from mathematics in Contents showTocToggle("show","hide") 1 Contributions to mathematics 2 Kummer and Fermat's Last Theorem 3 References 4 External link Contributions to mathematics Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series (contiguity relations). The Kummer surface results from taking the quotient of a two-dimensional abelian variety orbifold : it has 16 singular points, and its geometry was intensively studied in the nineteenth century Kummer and Fermat's Last Theorem Kummer also proved Fermat's last theorem for a considerable class of prime exponents (see regular prime ideal class group ). His methods were closer, perhaps, to

27. 3D-XplorMath Surface Gallery The family was described originally by Ernst eduard kummer In 1864. A kummersurface has sixteen double points, the maximum possible for a surface of degree http://rsp.math.brandeis.edu/3D-XplorMath/Surface/kummer/kummer.html

back to 3D-XplorMath surface gallery Kummer Quartic Additional images: Anaglyph Parallel Stereo Rotate View (Java Applet) A Kummer surface is any one of a one parameter family of algebraic surfaces defined by the polynomial equation of degree four: (x^2 + y^2 + z^2 - aa^2)^2 - lambda*p*q*r*s = 0. Here aa is any real number. lambda = (3*aa^2 - 1.0)/(3 - aa^2) p = 1 - z - sqrt(2)*x q = 1 - z + sqrt(2)*x r = 1 + z + sqrt(2)*y s = 1 + z - sqrt(2)*y The family was described originally by Ernst Eduard Kummer In 1864. A Kummer surface has sixteen double points, the maximum possible for a surface of degree four in three-dimensional space. For the default case aa = 1.3, all these double points are real and they appear in the visualization as the vertices of five tetrahedra. See also: ImplicitSurfaces.pdf Supporting files: Description in PDF a9.com search back to 3D-XplorMath surface gallery palais@brandeis.edu

28. Encyclopaedia Britannica Entry Ernst eduard kummer, in higher arithmetic; and Leopold Kronecker, a specialist On the suggestion of Heinrich eduard Heine, a colleague at Halle who http://www.aam314.vzz.net/EB/Cantor.html

Cantor, Georg (Ferdinand Ludwig Philipp) Born: March 3, 1845, St. Petersburg, Russia Died: Jan. 6, 1918, Halle, Ger. German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another. Early life and training Cantor's parents were Danish. His artistic mother, a Roman Catholic, came from a family of musicians, and his father, a Protestant, was a prosperous merchant. When his father became ill in 1856, the family moved to Frankfurt. Cantor's mathematical talents emerged prior to his 15th birthday while studying in private schools and at gymnasien at Darmstadt first and then at Wiesbaden; eventually, he overcame the objections of his father, who wanted him to become an engineer. After briefly attending the University of ZŸrich, Cantor in 1863 transferred to the University of Berlin to specialize in physics, philosophy, and mathematics. There he was taught by the mathematicians Karl Theodor Weierstrass, whose specialization of analysis probably had the greatest influence on him; Ernst Eduard Kummer, in higher arithmetic; and Leopold Kronecker, a specialist on the theory of numbers who later opposed him. Following one semester at the University of Gšttingen in 1866, Cantor wrote his doctoral thesis in 1867, In re mathematica ars propendi pluris facienda est quam solvendi ("In mathematics the art of asking questions is more valuable than solving problems"), on a question that Carl Friedrich Gauss (q.v.) had left unsettled in his

29. Austrian Literature Online - Kataloge kummer, eduard - 1910 kummer, Erhart, Zahnarzt - 1936 kummer, Ernst eduard - 1975 s.SIMON, Max s.SIMON, Max - 1891 http://webapp.uibk.ac.at/alo/cat/?id=5008280

30. Math Lessons - Ernst Kummer Ernst kummer. Ernst eduard kummer (29 January 1810 in Sorau , Brandenburg,Prussia 14 May 1893 in Berlin, Germany) was a German mathematician. http://www.mathdaily.com/lessons/Ernst_Kummer

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Number theorists Ernst Kummer Ernst Eduard Kummer 29 January in Sorau , Brandenburg Prussia 14 May in Berlin Germany ) was a German mathematician . Highly skilled in applied mathematics , Kummer trained German army officers in ballistics ; afterwards, he taught for 10 years in a Gymnasium (the German equivalent of high school), where he inspired the mathematical career of Leopold Kronecker . He retired from teaching and from mathematics in Contents showTocToggle("show","hide") 1 Contributions to mathematics 2 Kummer and Fermat's Last Theorem 3 References 4 External link Contributions to mathematics Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series (contiguity relations). The Kummer surface results from taking the quotient of a two-dimensional abelian variety orbifold : it has 16 singular points, and its geometry was intensively studied in the

31. Article Review of Ernst eduard kummer. Collected Papers , Historia Mathematica, 4 (1977)475478. Review of Courant in Goettingen and New York by Constance Reid, http://www.math.nyu.edu/faculty/edwardsd/articles.htm

A Generalized Sturm Theorem, Annals of Mathematics The Background of Kummer's Proof of Fermat's Last Theorem for Regular Primes, Arch. Hist. Ex. Sci. Postscript to "The Background of Kummer's Proof ...", Arch. Hist. Ex. Sci. Review of "Ernst Eduard Kummer. Collected Papers", Historia Mathematica Review of "Courant in Goettingen and New York" by Constance Reid, Historia Mathematica, 4 (1977) 479-480 On the Kronecker Nachlass, Historia Mathematica Fermat's Last Theorem, Scientific American Review of Three Books on Algebraic Number Theory, Bull. AMS Review of ``Variationen ueber ein zahlentheoretisches Thema von Gauss,'' Historia Mathematica The Genesis of Ideal Theory, Arch. Hist. Ex. Sci. Read the Masters!, in: "Mathematics Tomorrow," Lynn Steen, ed. , Springer, New York, 1981 Kummer, Eisenstein, and Higher Reciprocity Laws, in: "Number Theory Related to Fermat's Last Theorem," N. Koblitz, ed. , Birkhauser, Boston, 1982 Dedekinds "Bunte Bemerkungen" zu Kroneckers "Grundzuege", with O. Neumann and W. Purkert, Arch. Hist. Ex. Sci.

32. Lexikon Ernst Eduard Kummer eduard kummer aus der freienEnzyklopädie Wikipedia und steht unter der GNU Lizenz. Die Liste der Autoren ist http://lexikon.freenet.de/Ernst_Eduard_Kummer

E-Mail Mitglieder Community Suche ... Hilfe document.write(''); im Web in freenet.de in Shopping Branchen Lexikon Artikel nach Themen alphabetischer Index Artikel in Kategorien Weitere Themen Britneys perverse Spende: Geburt im TV f¼r Hurrikan-Opfer Dirty Talk: K¼bl will Sex mit Ginny, Gina und Giuseppe Audi S4 vs. Porsche 4S: Zwei Sportler, zwei Charaktere Eiskalt verf¼hrt: Kuscheln im einzig- artigen Iglu-Hotel ... Download-Charts: Die beliebtesten Tools im œberblick Sie sind hier: Startseite Lexikon Ernst Eduard Kummer 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 Sch¼lern geh¶rte. Da er w¤hrend 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 f¼r drei Jahrzehnte zu einem der aktivsten Zentren f¼r Mathematik weltweit machte.

33. January 29 - Today In Science History but correctly) that the Earth s axis wobbles a bit. Ernst eduard kummer kummer devoted himself to the study of the ray systems, but treated these http://www.todayinsci.com/1/1_29.htm

Visit our new gallery of Perpetual Motion Machines through the centuries JANUARY 29 - BIRTHS Abdus Salam (source) Born 29 Jan 1926; died 21 Nov 1996. Pakistani nuclear physicist who shared the 1979 Nobel Prize for Physics with Steven Weinberg and Sheldon Lee Glashow. Each had independently formulated a theory explaining the underlying unity of the weak nuclear force and the electromagnetic force. His hypothetical equations, which demonstrated an underlying relationship between the electromagnetic force and the weak nuclear force, postulated that the weak force must be transmitted by hitherto-undiscovered particles known as weak vector bosons, or W and Z bosons. Weinberg and Glashow reached a similar conclusion using a different line of reasoning. The existence of the W and Z bosons was eventually verified in 1983 by researchers using particle accelerators at CERN. Piero Leonardi Born 29 Jan 1908 Italian geologist and prehistorian, known for his research on the stratigraphy and paleontology of the Triassic invertebrates (from 190-225 million years ago) and the Permian vertebrates (from 225-280 million years ago). His works include studies of the tectonics (the movement and deformation of the Earth's surface) and stratigraphy (the description and interpretation of rock successions) of the Dolomite Alps and development of a new theory on their evolution. He also discovered a new Mousterian prehistoric culture, the Bernardinian. Allen B. Du Mont

34. May 14 - Today In Science History Ernst eduard kummer. (source), Died 14 May 1893 (born 29 Jan 1810) Germanmathematician whose introduction of ideal numbers, which are defined as a special http://www.todayinsci.com/5/5_14.htm

Visit our new gallery of Perpetual Motion Machines through the centuries MAY 14 - BIRTHS Yuval Ne'eman (source) Born 14 May 1925 Israli theoretical physicist, who worked independently of Gell-Mann but almost simultaneously (1961) devised a method of grouping baryons in such a way that they fell into logical families. Now known as the Eightfold Way (after Buddha's Eightfold Path to Enlightenment and bliss), the scheme grouped mesons and baryons (e.g., protons and neutrons) into multiplets of 1, 8, 10, or 27 members on the basis of various properties. James Hardy (source) Born 14 May 1918; died 19 Feb 2003. American surgeon who headed teams that performed the first human lung transplant in 1963; the first animal-to-human heart transplant in 1964; and a double-lung transplant that left the heart in place in 1987. Three years before Christiaan Barnard performed the first successful human-to-human heart transplant, on 23 Jan 1964, 68-year-old Boyd Rush was admitted to the hospital. No human was heart available; Hardy decided to use the heart of a chimpanzee named Bino. The newly-transplanted heart beat on its own; but it was too small to maintain independent circulation and Rush died after 90 minutes. Hardy had to endure some severe criticism. Overall, his work helped to alter perceptions about the transplantation process. Mikhail Semyonovich Tswett (source) 72; died 26 Jun 1919.

35. Collected Works In Mathematics And Statistics kummer, Ernst eduard, 18101893, Collected papers Ernst eduard kummer, 2,QA 3 K98 1975, Killam. Kuratowski, Kazimierz, 1896-1980, Selected Papers http://www.mathstat.dal.ca/~dilcher/collwks.html

Collected Works in Mathematics and Statistics This is a list of Mathematics and Statistics collected works that can be found at Dalhousie University and at other Halifax universities. The vast majority of these works are located in the Killam Library on the Dalhousie campus. A guide to other locations is given at the end of this list. If a title is owned by both Dalhousie and another university, only the Dalhousie site is listed. For all locations, and for full bibliographic details, see the NOVANET library catalogue This list was compiled, and the collection is being enlarged, with the invaluable help of the Bibliography of Collected Works maintained by the Cornell University Mathematics Library. The thumbnail sketches of mathematicians were taken from the MacTutor History of Mathematics Archive at the University of St. Andrews. For correction, comments, or questions, write to Karl Dilcher ( dilcher@mscs.dal.ca You can scroll through this list, or jump to the beginning of the letter: A B C D ... X-Y-Z A [On to B] [Back to Top] N.H. Abel

36. Science Jokes: Math Jokes And Archimedes Ernst eduard kummer (18101893), a German algebraist, was rather poor at arithmetic.Whenever he had occasion to do simple arithmetic in class, http://www.juliantrubin.com/mathjokes.html

jokes and science Scientific American Likes Our Site Jokes and Science Home Astronomy Albert Einstein Kids Science Quotes ... New Jokes Top Site Home Fair Projects Science Gates Science Trivia ... Math Jokes and Archimedes Web www.juliantrubin.com Mathematics is made of 40 percent formulas, 40 percent proofs and 40 percent imagination. Top Site From: Adam Blais, the_toast_boy@hotmail.com True story: A student walked into his discreet math class late and in order not to interrupt he put his late slip on the teacher's desk furtively without the teacher noticing. The teacher noticed the slip on his desk afterwards. He commented "I see you put this slip on my desk without me noticing. I guess that's why they call this class discrete mathematics." It was mentioned on CNN that the new prime number discovered recently is four times bigger then the previous record. What is the shortest mathematicians joke? Let epsilon be smaller than zero. Q: What is the first derivative of a cow? A: Prime Rib! A mathematician, a biologist and a physicist are sitting in a street cafe watching people going in and coming out of the house on the other side of the street. First, they see two people going into the house. Time passes. After a while, they notice three persons coming out of the house.

37. The Top Twenty: Irregular Primes Ernst eduard kummer (18101893) had already studied the failure of uniquefactorization in cyclotomic fields and soon formulated a theory of ideals, http://primes.utm.edu/top20/page.php?id=26

38. Richard Dedekind -- Facts, Info, And Encyclopedia Article and facts about Ernst eduard kummer) Ernst eduard kummer s closest follower He based his work on (Click link for more info and facts about kummer) http://www.absoluteastronomy.com/encyclopedia/r/ri/richard_dedekind.htm

Richard Dedekind [Categories: Number theorists, 20th century mathematicians, 19th century mathematicians, German mathematicians, German philosophers, 19th Century philosophers, 1916 deaths, 1831 births] Julius Wilhelm Richard Dedekind (A person of German nationality) German (A person skilled in mathematics) mathematician and (Click link for more info and facts about Ernst Eduard Kummer) Ernst Eduard Kummer 's closest follower in (The branch of pure mathematics dealing with the theory of numerical calculations) arithmetic Dedekind was born in (A city in central Germany) 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 1914; he himself also never married. In 1848, he entered Collegium Carolinum in Brunswick and in 1850 with the solid knowledge in mathematics he entered the (Click link for more info and facts about University of Göttingen) University of Göttingen In (Click link for more info and facts about Göttingen) Göttingen (A unit of magnetic flux density equal to 1 maxwell per square centimeter) Gauss taught mathematics mostly at an elementary level. In the departments of mathematics and physics, Dedekind learnt about

39. Euler And Other Mathematicians' Contribution kummer, though refuted Lamé s proof, introduced a new kind of complex Ernst eduard kummer (18101893). From then on, not much developments were made. http://library.thinkquest.org/28049/Euler.htm

Since Fermat had posed his problem, Euler was the first to make the first big progress. He proved the individual case n=3, in the year 1770, using the technique developed by Fermat himself which is called infinite descent. (please click for the details of the proof) Indeed Fermat used this method in proving the case when n=4. The reasoning is not difficult. The essence of this method is to prove that if there is positive integer solution for the equation, then smaller solutions in integer with exactly the same properties can be derived from the first solution and so on for infinite times. But for a positive integer, it is impossible for it to decrease indefinitely. Hence a contradiction is set up and a proof that there is no solution for the equation is established. Pierre de Fermat (1601-1665) )(a-b*-3 )= a cube where a and b are integers relatively prime and (a+b*-3 ) and (a-b*-3 ) are then as a result "relatively prime", then each of which (a+b*-3 ) and (a-b*-3 is also a cube. He has assumed the same properties for irrational complex number as integers without any solid proof. Leonhard Euler(1707-1783) Fortunately, his proof was fixed by Legendre. In the following ninety years after Euler, there

40. Nat' Academies Press, Prime Obsession: Bernhard Riemann And The Greatest Unsolve kummer, eduard, 135, 372. kummer, Ottilie (née Mendelssohn), 372. L. Lagrange,JosephLouis, 92. Landau, Edmund, 38, 224, 230-232, 238-239, 255-256, 276, http://www.nap.edu/openbook/0309085497/html/414.html

Read more than 3,000 books online FREE! More than 900 PDFs now available for sale HOME ABOUT NAP CONTACT NAP HELP ... ORDERING INFO Items in cart [0] TRY OUR SPECIAL DISCOVERY ENGINE Questions? Call 888-624-8373 Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) Joseph Henry Press ( JHP Find More Like This Book Research ... Dashboard NEW! BUY This Book CHAPTER SELECTOR: Openbook Linked Table of Contents Front Matter, pp. i-xvi Part I: The Prime Number Theorem, pp. 1-2 1. Card Trick, pp. 3-18 2. The Soil, the Crop, pp. 19-31 3. The Prime Number Theorem, pp. 32-47 4. On the Shoulders of Giants, pp. 48-62 5. Riemann's Zeta Function, pp. 63-81 6. The Great Fusion, pp. 82-98 7. The Golden Key, and an Improved Prime Number Theorem, pp. 99-117 8. Not Altogether Unworthy, pp. 118-136 9. Domain Stretching, pp. 137-150 10. A Proof and a Turning Point, pp. 151-166 Part II: The Riemann Hypothesis, pp. 167-168 11. Nine Zulu Queens Ruled China, pp. 169-183 12. Hilber's Eighth Problem, pp. 184-200 13. The Argument Ant and the Value Ant, pp. 201-222

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