41. ORESME XU Jan 2004 GH Hardy (Chris Christensen) Percy MacMahon (Dan Curtin) Hermann Weyl (DavidKullman) Abu Rayhan alBiruni louis mordell (Danny Otero) http://cerebro.xu.edu/~otero/oresme_jan_04.html

Please Email comments or suggestions to: curtin@nku.edu or to: otero@xavier.xu.edu The Twelfth Meeting of the ORESME Reading Group January 30-31, 2004 Xavier University Members in attendance: Chris Christensen, Northern Kentucky University Daniel Curtin, Northern Kentucky University Charles Holmes, Miami University Kevin Kirby, Northern Kentucky University David Kullman, Miami Univeristy Daniel Otero, Xavier University Richard Pulskamp, Xavier University We gathered for Friday night dinner at 6pm at the Bonefish Grill in Oakley. (It so happened that another NKU contingent was also at the restaurant with a math ed candidate for an open position in their department!) We reconvened at XU in new and impressive digs on the seventh floor of the Schott Building, thanks to our host, member Dick Pulskamp. After a brief review of the career of Polya taken from an article in Notable Mathematicians , we viewed the nearly-hour-long video that Polya made for the MAA in 1966 with a class of undergraduates, called Let Us Teach Guessing . In the video, he works with the students to formulate a conjecture about the number of cells into which

42. Shalen Abstract UGA Math Abstract In this talk we will solve the problem posed in the title, one firstsolved by louis mordell in the 1960s. More interesting than the question http://www.math.uga.edu/~szwang/colloquium/abst-schaefer.html

University of Georgia Mathematics Department Colloquium Ed Schaefer Santa Clara University August 31, 2000 When is an integer the product of two and of three consecutive integers? Abstract: In this talk we will solve the problem posed in the title, one first solved by Louis Mordell in the 1960s. More interesting than the question itself, perhaps, is the method of solution, which serves to introduce the beautiful subject of elliptic curves. This is a field of lively current research interest and the gateway to techniques used in the recent acclaimed proof of Fermat's Last Theorem and to problems of cryptography.

43. Engineering 19571968 Donald louis mordell. 1968-1974 George Lee d Ombrain. 1974 Thomas H.Barton, Acting Dean. 1975-1984 Gerald W. Farnell. 1984 Pierre Bélanger http://www.archives.mcgill.ca/resources/guide/vol1/rg35.htm

Engineering R.G. 35: FACULTY OF ENGINEERING DEANS OF THE FACULTY 1878-1908 Henry Taylor Bovey 1908-1922 Frank Dawson Adams 1923-1924 Henry Martyn McKay, Acting Dean 1924-1930 Henry Martyn McKay 1931-1941 Ernest Brown 1942-1951 John Johnston O'Neil 1952-1957 Robert Edwards Jamieson 1957-1968 Donald Louis Mordell 1968-1974 George Lee d'Ombrain 1974 Thomas H. Barton, Acting Dean 1975-1984 Gerald W. Farnell ADMINISTRATIVE RECORDS, 1907-1975 Faculty Records, 1907-1975 Minutes of the Faculty, 1907-1952, 1974-1975, 50 cm (c.1-c.4, c.6) Minutes of the Faculty are indexed by name and subject from 1907 until September 1949. There is no index for the post 1949 period. Minutes before 1907 were probably destroyed in the 1907 Macdonald Engineering Building fire. Annual Reports, 1896, 1961-1968, 5 cm (c.5, c.15, c.40) These reports were submitted to the Principal and/or Corporation. Records of the Office of the Dean, 1907-1984 Administrative Records, 1907-1977, 6 m (c.5-c.31, c.179, c.182-c.184, c.192, c.198, c.200) PARTS RESTRICTED

44. Nick's Mathematical Puzzles: Solution 78 mordell Curve louis Joel mordell The Mathematics of Fermat s Last Theorem Diophantine Equation3rd Powers. Source Original http://www.qbyte.org/puzzles/p078s.html

Puzzles: Index Home About Accessibility Solution to puzzle 78: Perfect square Find all integer solutions of y = x x = y + 432 is a perfect cube if, and only if, 6 (y + 432) = 216(y + 432) is a perfect cube. But 216(y + 432) = (y + 36) - (y - 36) Hence (6x) + (y - 36) = (y + 36) By Fermat's Last Theorem , a n + b n = c n Euler , with a gap filled by Legendre Further reading Mordell Curve Louis Joel Mordell The Mathematics of Fermat's Last Theorem Diophantine Equation3rd Powers Source: Original Puzzles: Index Home About Accessibility

45. Royal Society | About The Society | History Of Science | Biographies Of Fellows mordell, louis Joel. Biographical Memoirs 1973 vol 19 pp 493520, plate, by JWSCassels. Moreton, Henry John Reynolds, 3rd Earl of Ducie http://www.royalsoc.ac.uk/page.asp?id=2376

46. Royal Society | About The Society | Awards, Medals And Prize Lectures | | Sylves 1949 louis Joel mordell, for his distinguished researches in pure mathematics,especially for his discoveries in the theory of numbers. http://www.royalsoc.ac.uk/page.asp?id=1767

47. Mathematical Quotes louis Joel mordell (18881972; Three Lectures on Fermat s Last Theorem , p.4). Sometimes a good idea comes to you when you are not looking for it. http://math.sfsu.edu/beck/quotes.html

Mathematical Quotes "It is an important and popular fact that things are not always as what they seem. For instance, on the planet earth, man has always assumed that he was more intelligent than dolphins because he had achieved so much: the wheel, New York, wars. [...] Butconversely, the dolphins had always believed that they were far more intelligent than men; for precisely the same reasons." "42. (The answer to life, the universe, and everything.)" Douglas Adams ( The hitchhiker's guide to the galaxy Scott Adams "If you don't like your analyst, see your local algebraist!" Gert Almkvist (founder and director of The Institute for Algebraic Meditation) Bill Amend "logloglog n has been proved to go to infinity, but has never been observed to do so." Anon "You can only be truly accomplished at something you love. Don't make money the goal. Instead, pursue the things you love doing, and do them so well that people can't take their eyes off you. All the other tangible rewards will come as a result." Maya Angleou "It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out."

48. Untitled Document louis JOEL mordell DE MORGAN MEDALLIST 1941. Professor mordell received the DeMorgan Medal on 11 December 1941. Extract from the President s address http://www.lms.ac.uk/newsletter/330/330_11.html

LOUIS JOEL MORDELL DE MORGAN MEDALLIST 1941

49. Here Are The Names Currently [April 1999] In The Index At Http Aad PA van Moorthy, Hari T. Morales, Domingo Moran, William Morawetz, CSmordell, LJ mordell, louis Joel Moreau de Maupertuis, Pierrelouis Moreau, http://www.math.niu.edu/~rusin/known-math/99/photos

50. A Guide To The H. S. Vandiver Papers, 1889-1977 mordell, louis Joel, twenty letters, see also box seventeen folder five,19591961. Morishima, Taro, nine letters, see also box seventeen, folder five http://www.lib.utexas.edu/taro/utcah/00303/00303-P.html

Main Version Raw XML File (104k) A Guide to the H. S. Vandiver Papers, 1889-1977 Descriptive Summary Creator Vandiver, Harry Shultz, 1882- Title: H. S. Vandiver Papers, Dates: Abstract This collection consists of correspondence (about 2350 items), research notes, bibliographies, lecture notes, notebooks, drafts of publications, reprints, and photographs documenting the career of H. S. Vandiver. Accession No. Extent 17 ft. of manuscript material, plus books Laguage Materials are written in English. Repository Archives of American Mathematics, Center for American History, The University of Texas at Austin Biographical Note H. S. Vandiver was a number theorist and member of The University of Texas at Austin faculty from 1925 until his retirement in 1966. Among other research interests, Vandiver was an authority on Fermat's last theorem. Born October 21 in Philadelphia, Pennsylvania Began publishing problems and solutions in the American Mathematical Monthly and communicating with G. D. Birkhoff Attended graduate courses at University of Pennsylvania, did not obtain a degree

51. Louis Mordell Université Montpellier II louis Poinsot louis-Antoine de Bougainville louisMordell (1888-1972). Cette image et la biographie complète en anglais résident http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1572

52. Research at Notre Dame, louis mordell (who was there temporarily) heaped scorn on AndréWeil for having done just that with his theorem, and Alex Heller showed http://www.math.ubc.ca/~hoek/Research/research.html

My Research Story Like Ludwig van Beethoven's, my creative life falls into three periods, but unlike his, my middle one was perfectly fallow : an unsightly hiatus mars my list of publications in the seventies, the hippie decade. Rather than trying your patience with some unlikely explanation for this shameful blot on my escutcheon, I shall concentrate on outlining the contents of the first and third periods. Roughly speaking, the former is abstract and theoretical, delighting in concepts and valuing form over substance, while the latter is concrete and computational, using modest tools and preferring ugly facts to shapely froth. This points to a second difference between Ludwig and myself : while he stubbornly followed his genius, I found nothing better to follow than the fashion of the day. In the 1950's the accepted wisdom was that mathematics was a deductive science based on axioms. Here at UBC (where I started and ended my career), there were still some dinosaurs who took pride in not knowing what a Banach algebra was, but the in-crowd cultivated general topology and ring theory. Robert Langlands, a fellow student, occasionally liked to organise informal seminars to plough through something he wanted to learn. In the summer of 57 he had chosen Jabobson's new book on the structure of rings just my cup of tea. (To be continued)

53. History Of Computing University Of Manchester 6) louis mordell a pure mathematician who made important contributions in numbertheory. 7) Sydney Goldstein was one of the most influential theoretical http://www.public-domain-content.com/History_of_computing/University_of_Manchest

54. Biografisk Register Translate this page mordell, louis Joel (1888-1972) Morley, Frank Müller, Johannes (aliasRegiomontanus) (1436-76) Möbius, August Ferdinand (1790-1868) Napier, John (1550-1617) http://www.geocities.com/CapeCanaveral/Hangar/3736/biografi.htm

Biografisk register Matematikerne er ordnet alfabetisk på bakgrunn av etternavn. Linker angir at personen har en egen artikkel her. Fødsels- og dødsår oppgis der dette har vært tilgjengelig. Abel, Niels Henrik Abu Kamil (ca. 850-930) Ackermann, Wilhelm (1896-1962) Adelard fra Bath (1075-1160) Agnesi, Maria G. (1718-99) al-Karaji (rundt 1000) al-Khwarizmi, Abu Abd-Allah Ibn Musa (ca. 790-850) Anaximander (610-547 f.Kr.) Apollonis fra Perga (ca. 262-190 f.Kr.) Appel, Kenneth Archytas fra Taras (ca. 428-350 f.Kr.) Argand, Jean Robert (1768-1822) Aristoteles (384-322 f.Kr.) Arkimedes (287-212 f.Kr.) Arnauld, Antoine (1612-94) Aryabhata (476-550) Aschbacher, Michael Babbage, Charles (1792-1871) Bachmann, Paul Gustav (1837-1920) Bacon, Francis (1561-1626) Baker, Alan (1939-) Ball, Walter W. R. (1892-1945) Banach, Stéfan (1892-1945) Banneker, Benjamin Berkeley, George (1658-1753) Bernoulli, Jacques (1654-1705) Bernoulli, Jean (1667-1748) Bernstein, Felix (1878-1956) Bertrand, Joseph Louis Francois (1822-1900) Bharati Krsna Tirthaji, Sri (1884-1960)

55. To Infinity! In 1923, louis mordell proved an amazing theorem, which implies that there is areasonable way to describe the rational points on $ E$ . http://modular.fas.harvard.edu/edu/Fall2001/124/lectures/lecture25/lecture25/nod

Next: The Group Law Up: Points on Elliptic Curves Previous: Points on Elliptic Curves To Infinity! At first glance, the above construction doesn't work if . [draw picture]. Fortunately, there is a natural sense in which the graph of is missing one point, and when this one missing point is the third point of intersection. The graph of that we drew above is a graph in the plan . The plane is a subset of the projective plane , which I will define in just a moment. The closure of the graph of in has exactly one extra point, which has rational coordinates, and which we denote by . Formally, can be viewed as the set of triples with not all modulo the equivalence relation for any nonzero . Denote by the equivalence class of . The closure of the graph of is the graph of and the extra point is Venerable Problem: Find an algorithm that, given an elliptic curve over , outputs a complete description of the set of rational points on This problem is difficult. In fact, so far it has stumped everyone! There is a conjectural algorithm, but nobody has succeeded in proving that it is really an algorithm, in the sense that it terminates for any input curve . Several of your profs at Harvard, including Barry Mazur, myself, and Christophe Cornut (who will teach Math 129 next semester) have spent, or will probably spend, a huge chunk of their life thinking about this problem. (Am I being overly pessimistic?)

56. John Derbyshire’s November Diary On National Review Online mathematician Axel Thue back in 1909, and some subsequent investigations bythe American number theorist louis Joel mordell later in the last century. http://www.nationalreview.com/derbyshire/derbyshire200411300819.asp

cddcodebase = "/";cddcodebase454632 = "/"; HELP E-mail Author Author Archive Send to a Friend ... Print Version November 30, 2004, 8:19 a.m. November Diary The dangers of parody, MOPEs, and more. Dangers of satire and parody. Late in October I posted on NRO a column titled " The Stars Speak Vadge Endshaver , and put into their mouths the kind of outrageous and preposterous things that stars say when they venture into politics. (Though, let me tell you, it was hard to come up with anything more o. and p. than the things actual celebrities had actually been saying.) All through November I have been coping with a persistent dribble of e-mails from readers saying: "How come I never heard of these people?...Did someone really say that?...That's awful ! Why didn't I read this anywhere else?..." I mentioned this to Jay Nordlinger. He told me that when The Weekly Standard started doing parody on its inside back page, the editors were besieged with inquiries from readers asking where they could read some background to these "stories." The editors got so fed up with this, they began over-stamping the parody page with a big, unmistakable legend: "PARODY," a precaution they have continued to the present day. Perhaps I should do something similar with my own flights of fancy. Our trial lawyers at work.

57. Biography-center - Letter M mordell, louis wwwhistory.mcs. st-and.ac.uk/~history/Mathematicians/mordell.html;Mordred, Moyroud, louis Marius www.invent.org/hall_of_fame/108.html http://www.biography-center.com/m.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish M 798 biographies M iley, James www.redhotjazz.com/bubber.html M ola, Francesco Pier www.getty.edu/art/collections/bio/a583-1.html M ozart, W.a. www.island-of-freedom.com/MOZART.HTM www-history.mcs.st-and.ac.uk/~histo ry/Mathematicians/Meray.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Mobius.html Ma net, Edouard www.guggenheimcollection.org/site/artist_bio_96.html Ma rais, Jean jeanmarais.free.fr/ Ma rgulis, Gregori www-history.mcs.st-and.ac.uk/~history/Mathematicians/Ma rgulis.html Ma rx, Harpo www.marx-brothers.org/living/harpo.htm MacArthur, Douglas www.pbs.org/wgbh/pages/amex/macarthur/peopleeven ts/pandeAMEX106.html Macarthur, Elizabeth www.abc.net.au/btn/australians/macarthu.htm MacArthur, Mary P.H.

58. Elliptic Curves And Elliptic Functions Many years ago (1921), louis mordell proved the theorem named after him, thatthe group of all rational points on an elliptic curve (over Q) is finitely http://www.mbay.net/~cgd/flt/flt03.htm

Elliptic Curves and Elliptic Functions For a quick definition of many of the terms used here, you may refer to the Glossary Contents: What is an elliptic curve? The group structure of an elliptic curve Arithmetic on elliptic curves Further basic concepts and results What is an elliptic curve? An elliptic curve is not an ellipse! The reason for the name is a little more indirect. It has to do, as we shall explain shortly, with "elliptic integrals", which arise in computing the arc length of an ellipse. But this happenstance of nomenclature isn't too significant, since an elliptic curve has different, and much more interesting, properties as compared to an ellipse. Instead, an elliptic curve is simply the locus of points in the x-y plane that satisfy an algebraic equation of the form (with some additional minor technical conditions). This is deliberately vague as to what sort of values x and y represent. In the most elementary case, they are real numbers, in which case the elliptic curve is easily graphed in the usual Cartesian plane. But the theory is much richer when x and y may be any complex numbers (in C ). And for arithmetic purposes, x and y may lie in some other field, such as the rational numbers

59. Birch And Swinnerton-Dyer Conjecture - Definition Of Birch And Swinnerton-Dyer C In 1922 louis mordell proved that the group of rational points on an ellipticcurve has a finite basis. This means that for any elliptic curve there is a http://encyclopedia.laborlawtalk.com/Birch_and_Swinnerton-Dyer_conjecture

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law In mathematics , the Birch and Swinnerton-Dyer conjecture relates the rank of the abelian group of points over a number field of an elliptic curve E to the order of zero of the associated L-function L(E,s) at s As of 2004 , it has been proved only in special cases. Contents showTocToggle("show","hide") 1 Background 2 History 3 Current status 4 External links Background In 1922 Louis Mordell proved that the group of rational points on an elliptic curve has a finite basis. This means that for any elliptic curve there is a finite sub-set of the rational points on the curve from which all other rational points may be generated. If the number of rational points on a curve is infinite then some points in a finite basis must have infinite order. The number of basis points with infinite order is called the rank of the curve, and is an important invariant property of an elliptic curve. If the rank of an elliptic curve is then the curve has only a finite number of rational points. On the other hand, if the rank of the curve is greater than 0, then the curve has an infinite number of rational points.

60. ZALA Films: N Is A Number: Film Synopsis In England he met several of the world s leading mathematiciansGH Hardy, JELittlewood and louis mordell among them. Throughout this period Erdös continued http://www.zalafilms.com/films/nisfilm2.html

continued from page 2 After finishing his Ph.D. in 1934 at the University of Budapest, Erdös went to Manchester. In England he met several of the world's leading mathematicians-G. H. Hardy, J. E. Littlewood and Louis Mordell among them. Throughout this period Erdös continued to spend his summers in Hungary, but in 1938 the Nazi invasion of Czechoslovakia convinced him that Hungary was no longer a safe place for a young Jewish intellectual. He accepted a position at Princeton University's Institute for Advanced Study, but soon moved on to other American schools. During the war, he lost touch with his mother and most of his friends. It was only in late 1945 that a letter from his mother informed him of the relatives and friends murdered by the Nazis. His father, two aunts and two uncles were dead and the Anonymous Group was decimated. Because of the new Communist regime in Hungary, Erdös was unable to visit his mother until 1948-just as anti-Communist hysteria peaked in the United States-a country he calls "Samland" (for Uncle Sam). His visits home earned Erdös an FBI interview that resulted in the loss of his re-entry permit to the United States until the late 1950s. In Hungary, Erdös became an important link to the West, providing a whole generation of Hungarian mathematicians access to a world from which they had been cut off by a Communist regime imposed by the Soviet Union-a country Erdös calls "Joedom" (after Stalin). The tragedies of the 20th century that marked Erdös's life are often invoked in his wry humor. Melvyn Nathanson, an American colleague, calls Erdös "the Bob Hope of mathematics," and when Erdös brings down the house during a Cambridge lecture, we can see why. An example of the subtle Erdös humor emerges in Erdös's rendition of "Jack and Jill," in which he substitutes "Sam and Joe," because Jack and Jill were originally nicknames for Elizabethan politicians, and Sam and Joe might just as well be considered their 20th century equivalents.

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