1. Sophie Germain Sophie Germain. Sophie Germain. April 1, 1776 June 27, 1831. Additionalmaterial by Larry Riddle. Sophie Germain and Fermat's Last Theorem. http://www.agnesscott.edu/lriddle/women/germain.htm

Sophie Germain April 1, 1776 - June 27, 1831 Written by Amanda Swift, Class of 1995 (Agnes Scott College) Sophie Germain was born in an era of revolution. In the year of her birth, the American Revolution began. Thirteen years later the French Revolution began in her own country. In many ways Sophie embodied the spirit of revolution into which she was born. She was a middle class female who went against the wishes of her family and the social prejudices of the time to become a highly recognized mathematician. Like the member of a revolution, her life was full of perseverance and hard work. It took a long time for her to be recognized and appreciated for her contributions to the field of mathematics, but she did not give up. Even today, it is felt that she was never given as much credit as she was due for the contributions she made in number theory and mathematical physics because she was a woman. Sophie Germain was born in Paris on April 1, 1776 to Ambroise-Francois and Marie Germain. Her family was quite wealthy. Her father was a merchant and later became a director of the Bank of France. Sophie's interest in mathematics began during the French Revolution when she was 13 years old and confined to her home due to the danger caused by revolts in Paris. She spent a great deal of time in her father's library, and one day she ran across a book in which the legend of Archimede's death was recounted. Legend has it that "during the invasion of his city by the Romans Archimedes was so engrossed in the study of a geometric figure in the sand that he failed to respond to the questioning of a Roman soldier. As a result he was speared to death" (Perl 64). This sparked Sophie's interest. If someone could be so engrossed in a problem as to ignore a soldier and then die for it, the subject must be interesting! Thus she began her study of mathematics.

2. NOVA Online | The Proof | Math's Hidden Woman Sophie Germain Seite aus einem deutschsprachigen OnlinePhilosophenlexikon. Sophie Germain wurde 1776 in Paris als mittlere von drei Töchtern geboren. http://www.pbs.org/wgbh/nova/proof/germain.html

Math's Hidden Woman Following is the true story of Sophie Germain, an 18th-century woman who assumed a man's identity in order to pursue her passion attempting to prove Fermat's Last Theorem. From FERMAT'S ENIGMA: The Epic Quest to Solve the World's Greatest Mathematical Problem by Simon Singh Published by Walker and Company ISBN 0-8027-1331-9 To order call 1-800-289-2553 Pythagoras' theorem leads to one of the best understood equations in mathematics: x y z There are many whole number solutions to this equation, e.g., In the 17th century the French mathematician Pierre de Fermat set a challenge for future generations of mathematicians prove that there are no whole number solutions for the following closely related family of equations: x y z x y z x y z x y z etc. Although these equations appear similar to Pythagoras' equation, Fermat's Last Theorem claims that these equations have no solutions. The difficulty in proving that this is the case revolves around the fact that there are an infinite number of equations, and an infinite number of possible values for x, y

3. Germain Sophie Translate this page germain sophie Travaux Sophie Germain est mieux connue pour sa théorie des nombrespremiers, mais elle a également beaucoup travaillé sur l'élasticité. http://www.lycee-international.com/travaux/HISTMATH/germain/

Liste de Mathématiciens Al Khwarizmi Apollonius de Perge Archimède Argand Jean Bezout Etienne Bombelli Rafaele Boole George Cardano Girolamo Cauchy Augustin Chasles Michel De Moivre Abraham De Morgan Augustus Del Ferro Scipione Descartes René Eratosthene Euclide Fermat Pierre Ferrari Ludovico Fibonacci Leonardo Galois Evariste Gauss Carl Germain Sophie Huygens Christiaan Leibniz Gottfried Pascal Blaise Peano Guiseppe Pythagore Tartaglia Nicolo Viete François Zenon d Elée Germain Sophie 1er avril 1776 - 27 juin 1831 Historique Sophie Germain, issue d'une famille aisée, est née de Ambroise-François Germain, qui était alors un commerçant, mais devint plus tard directeur de la Banque de France, et de Marie Germain. Son intéret pour les mathématiques s'éveilla lors de la Révolution Française: agée alors de 13 ans, elle se trouvait cloitrée avec sa famille dans leur maison à cause des menaces révolutionnaires. Elle en profita pour découvrir les nombreux livres de la bibliothèque de son père et s'interessa tout particulièrement à la légende de la mort d'Archimède: celui-ci, lors de l'invasion de la ville par les romains, était si profondément plongé dans l'étude d'une figure géométrique qu'il avait dessinée sur le sable, qu'il ne répondit pas aux questions poséees par un soldat romain; pour celà il fut condamné à mort. Cet intéret pour les mathématiques d'Archimède fascina tant la jeune fille qu'elle se mit aussitot à étudier cette science. Elle mourut à l'age de 55 ans, après une longue lutte contre le cancer du sein.

4. About Sophie Germain Sophie Germain a biography, with links to more carefully selectedweb resources and to print resources. Sophie Germain. (April http://womenshistory.about.com/library/bio/blbio_sophie_germain.htm

zfp=-1 About History Women's History Search in this topic on About on the Web in Products Web Hosting in partnership with Women's History with Jone Johnson Lewis Your Guide to one of hundreds of sites Home Articles Forums ... Help zmhp('style="color:#fff"') This Week's Articles tod('tih'); Today in History Daily Quiz tod('pod'); Picture of the Day Special Subscription Offers Subscribe Now Choose One: Subscribe Customer Service Subjects Essentials/Basics March: WH Month! Biographies World: by Place ... All articles on this topic Stay up-to-date! Subscribe to our newsletter. Advertising Free Credit Report Free Psychics Advertisement Sophie Germain April 1 , 1776 - June 27, 1831) mathematician, number theorist, mathematical physicist Marie-Sophie Germain, Sophia Germain, Sophie Germaine first woman not related to a member by marriage to attend Academie des Sciences meetings first woman invited to attend sessions at the Institut de France Sophie Germain's father was Ambroise-Francois Germain, a wealthy middle class silk merchant and a French politician who served in the Estates Général and later in the Constituent Assembly. He later became a director of the Bank of France. Her mother was Marie-Madeleine Gruguelu, and her sisters, one older and one younger, were named Marie-Madeleine and Angelique-Ambroise. She was known simply as Sophie to avoid confusion with all the Maries in the household. When Sophie Germain was 13, her parents kept her isolated from the turmoil of the French Revolution by keeping her in the house. She fought boredom by reading from her father's extensive library. She may also have had private tutors during this time.

5. Germain Translate this page germain sophie française, 1776-1831 Nombre premier de Sophie Germain on appelle ainsi un nombre premier n tel que 2n + 1 le soit aussi. http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Germain.html

GERMAIN Sophie Sous le pseudonyme masculin de M. Le Blanc elle correspondit avec Gauss (en Allemagne) et avec Lagrange et le prouva partiellement pour une certaine classe d'entiers premiers : Nombre premier de Sophie Germain : on appelle ainsi un nombre premier n tel que 2n + 1 le soit aussi. Calcul des nombres premiers de Sophie Germain : Fermat x n + y n = z n que si n divise l'un au moins des trois entiers x, y ou z. Dirichlet Legendre et descente infinie ) et n = 7 ( Hypatia Agnesi Kovaleskaia Nombres premiers jumeaux : Wronsky Gauss

6. Sophie Germain Sophie Germain. Sophie Germain offered much to the mathematical worldin the areas of number theory and elasticity theory. That same http://www.mathnews.uwaterloo.ca/BestOf/WomenInMath6905.html

Sophie Germain Sophie Germain offered much to the mathematical world in the areas of number theory and elasticity theory. That same world would offer her, a middle class woman in the time of the French revolution, very little in return. The Bastille fell when Sophie was only 13. She was from a middle class family of merchants that protected her through the revolution. As a result, she spent many hours in her father's library where she learned of the story of Archimedes. She was fascinated with his passion for geometry and immediately scoured the library for every book on the subject. From the onset her parents opposed her interest. They deemed her enthusiasm so inappropriate for a young woman that they denied her heat and light to prevent her from studying. They even confiscated her clothing at night, but she wrapped herself in blankets and used a hidden supply of candles to read from. Such was her passion that her parents finally conceded. She continued, tutorless. In 1794 Ecole Polytechnique opened, and as no women were allowed, she acquired the notes from the classes to learn from. At the end of one term she offered some observations that she made to Lagrange under the name of M. LeBlanc. He was impressed, found her, and praised her talents. In 1801 Carl Freidrich Gauss presented a complicated treatise on number theory

7. Sophie Germain Sophie Germain (17761851). Sophie Germain was born in Paris on April1,1776, the daughter of a well-to-do merchant. Having a library http://curie.che.virginia.edu/scientist/germain.html

Sophie Germain (1776-1851) Sophie Germain was born in Paris on April1, 1776, the daughter of a well-to-do merchant. Having a library at home, she managed to find books and was able to teach herself Latin, Greek, and mathematics. Her education was limited by the male dominance of the period. Not allowed to attend school, she was forced to study the notes of other students and turn in reports under a male pseudonym. Lagrange read her reports, amazed by their quality, and upon discovering the author was a woman, sponsored her thereafter. She went on to do important work on Fermat's last theorem. She proved it for any prime number under 100 where specific conditions are met. She also mathematically modeled the vibrations of a flat plate. After having impressed Gauss, he arranged to have her awarded an honorary doctorate from Gottingen, but she died before it had been awarded. She died on September 17, 1851.

8. Sophie Germain Sophie Germain. Until lately, Sophie Germain has been a mathematician hidden in theshadows of other great mathematicians. MarieSophie Germain 1996. Online. http://www.cs.appstate.edu/~sjg/womeninmath/SophieGermain.html

Sophie Germain History of Mathematics Also, in this library, Germain took her education into her own hands. She began reading about and teaching herself mathematics. Her parents, however, thought that this was an inappropriate interest for a female and fought with her to discourage it in the beginning. Germain started studying while her parents slept. As a result, she ended up having to study wrapped in blankets by the light of smuggled candles because her parents had taken away her fire, her light, and even her clothes in an attempt to force her away from her books. These types of beliefs were common in the middle class families of the nineteenth century (Swift 1 and others). Even in the aristocracy, women were only supposed to have enough knowledge of math and science as to make pleasant conversation about the subjects. Because of this, Francesco Algarotti wrote Germain also started correspondences with other great mathematicians. When Adrien Marie Legendre published his femme-savantes of the time. Gauss praised her even more highly after this discovery (Gray 49). Gauss responded: Gauss also credits Germain for encouraging his return to number theory (Gray 49).

9. Sophie Germain - Wikipedia Sophie Germain. From Wikipedia, the free encyclopedia. http://www.wikipedia.org/wiki/Sophie_Germain

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 Sophie Germain From Wikipedia, the free encyclopedia. Marie-Sophie Germain April 1 June 27 ) was a French mathematician She was born to a middle-class merchant family in Paris France , and began studying mathematics at age 13, despite strong attempts to dissuade her from engaging in a 'men's profession' by her parents. Several years later, she managed to get some lecture notes from several courses at Ecole Polytechnique which she studied despite the school not admitting females. Germain was particularly interested in Joseph-Louis Lagrange 's teachings and submitted papers and assignments under the pseudonym Monsieur Le Blanc, a former student of Lagrange's. Lagrange was so impressed by the paper that he asked to meet Le Blanc, and Germain was forced to reveal her identity to him. Lagrange apparently considered her a talented mathematician and became her mentor.

10. Sophie Germain Sophie Germain. Back to Fermat Corner. Sophie Germain was born on 1April 1776 the daughter of a merchant, AmbroiseFrancois Germain. http://www.simonsingh.net/owtasite/Sophie_Germain.html

11. Sophie Germain Sophie germain sophie Germain was one of the few women mathematiciansof her time. Her story is both interesting and inspiring for http://www.missouri.edu/~cst398/fermat/contents/germain.htm

Sophie Germain Sophie Germain was one of the few women mathematicians of her time. Her story is both interesting and inspiring for many an aspiring mathematician. Unfortunately for Germain, most universities were not very open to women who wanted to study mathematics. Fortunately for Germain, she was very clever. Through a creative move, Germain was able to receive the lecture notes and assignments from a former student of a prestigious academy. Even though he had moved away, Germain assumed the identity of Monsieur Antoine-August Le Blanc. "Monsieur Le Blanc" soon became the source of some very brilliant mathematics, and this caught the attention of Joseph-Louis Lagrange, a professor at the academy. Germain soon revealed her true identity to Lagrange, and Germain began to study under the supervision of Lagrange. Soon after, Germain began to work on Fermat's Last Theorem. She developed an ingenious idea to address a certain class of prime numbers for the values of n in the equation x^n + y^n = z^n. These primes, which are now named Germain primes, have the property that if n is prime, then 2n + 1 is also prime. For example, 5 is a Germain prime (2*5 + 1 = 11), and so are 11, 23, and 29. Germain began a correspondence with one of the greatest mathematicians that has ever lived, Carl Friedrich Gauss. In her letters, Germain retained the pseudonym of Monsieur Le Blanc, and she gave a plausibility argument that Fermat's Last Theorem held for her class of primes. Gauss was impressed by her work and continued to correspond with Monsieur Le Blanc. Gauss only learned of Germain's true identity when he found out that his life had been spared from Napoleon's onslaught of Prussia by the request of the lady Sophie Germain.

12. Germain Sophie Germain. 1776 – 1831. This is what happened to Sophie Germain,born in a time when it was frowned upon to allow women to learn. http://www.math.wichita.edu/history/women/germain.html

Sophie Germain How would you feel if your parents kept you from learning? If they took away your light, your clothes, even your warmth. This is what happened to Sophie Germain, born in a time when it was frowned upon to allow women to learn. The daughter of a wealthy upper class French family, Sophie Germain was born in 1776, the year of the American Revolution. Sophie was thirteen years old when the Bastille fell. Paris was an unstable and dangerous city. During the next ten years of the French revolutionary violence, Sophie Germain spent much of her time confined to her house, reading in her father's library. Sophie found the depth and variety of her father's library a great help during the long days of solitude. As she was reading one day she came across a story of the death of the Greek mathematician Archimedes. Although Archimedes was a brilliant man, it was the way he died that left Sophie spellbound. She read how Archimedes was slain through the side with a spear by a Roman soldier who was conquering the citizens of Syracuse. So engrossed was Archimedes in his geometric drawings that he failed to recognize his own danger. Sophie wanted to know what Archimedes was working on. What could be so engaging, so exciting, that a person would ignore their own impending death? Her family agreed with the popular English notion of the time that "brainwork" was not healthy - even dangerous - for girls. They began to forbid Sophie from studying mathematics. Sophie, however, had a strong mind and was determined to educate herself. Night after night she crawled out of bed and studied after everyone else had gone to sleep. When Sophie's parents discovered this they took her lamps, hid her clothes and made sure there was no heat in her room. But Sophie smuggled candles into her room and continued her studies. When her parents found her one morning, sound asleep at her desk with her pen in a frozen ink well, they relented and allowed her studies. Without a tutor, Sophie spent the Reign of Terror, that unsettled time in France, teaching herself differential calculus.

13. Sophie Germain Sophie germain sophie Germain helped to define the world of mathematics. Shewas born April 1, 1776. She is the source of Sophie Germain Primes. http://scioto.dublin.k12.oh.us/web/academics/Math/Bucholtz/Brooke.Web/sophie_ger

Sophie Germain Home Page http://www.scottlan.edu/lriddle/women/germain.htm

14. Germain Sophie Germain (1776 1831). Sophie Germain was born into a middle classParisian family just before the French Revolution. Sophie Germain Primes. http://web.uvic.ca/educ/lfrancis/web/germain.html

Sophie Germain (1776 - 1831) Sophie Germain was born into a middle class Parisian family just before the French Revolution. Because of the dangers of the revolution, Sophie was confined to her house and spent much of her time in her fathers library. It was here that her interests in mathematics began. Sophie taught herself from the books in her father's library as her parents did not feel that it was an interest appropriate to a female. It is said that her parents would take away her clothes, bed, heat and light to discourage her from her endeavours. However, nothing would stop Sophie. In 1794 the Ecole Polytechnique was established in Paris to train French mathematicians and scientists. Women were not allowed to enrol, but Sophie received lecture notes from an acquaintance. Sophie submitted a paper to a professor under a male pseudonym. The professor was so impressed that he wanted to meet the author of the paper. Later this professor was to become her mentor and her way into the circle of emerging French scientists and mathematicians. In 1804 Germain befriended and began corresponding with Carl Friedrich Gauss, a German mathematician who helped guide her work. During this time Sophie did much of her work looking at and trying to prove

15. Sophie Germain: Revolutionary Mathematician Born Paris, April 1, 1776 Died Paris, June 26, 1831 By all accounts, sophie germain was a somewhat withdrawn child. She was the second of three daughters of a Parisian silk merchant, AmbroiseFrançois germain. http://www.sdsc.edu/ScienceWomen/germain.html

Contents Next Born: Paris, April 1, 1776 Died: Paris, June 26, 1831 Revolutionary Mathematician B y all accounts, Sophie Germain was a somewhat withdrawn child. She was the second of three daughters of a Parisian silk merchant, Ambroise-François Germain. One sister married a government official and the other a physician. Sophie never married, lived at home all her life, and pursued her mathematical studies with what her recent biographers term "limitless passion and devotion." Her first biographer, an Italian mathematician named Libri, is the source of two stories told about Germain that seem to frame her personality. As a 13-year-old, while talk of the Revolution swirled in her household, she withdrew to her father's library. There she read about Archimedes, so engrossed in his mathematical musings that he ignored a Roman invader of Syracuse, who thereupon killed him. She may have seen in Archimedes' mathematics "an environment where she too could live untouched by the confusion of social reality." She studied mathematics on her own, and Libri relates that her parents were so opposed to her behavior that she took to studying at night. They responded by leaving her fire unlit and taking her candles. Sophie studied anyway, swaddled in blankets, by the light of smuggled candles.

16. The Top Twenty Sophie Germain Primes This pages, discussing sophie germain Primes, is one of a series of pages listing the 20 largest known primes of selected forms. This page provides definitions, theorems, records and references. http://www.utm.edu/research/primes/lists/top20/SophieGermain.html

Sophie Germain Primes Select a top twenty page Primes in Arithmetic Progression Consecutive Primes in Arithmetic Progression Cullen Primes Cunningham Chain (1st kind) Cunningham Chain (2nd kind) Euler Irregular Fermat Divisors Generalized Fermats Generalized Lucas numbers Generalized repunits Generalized Fermat Divisors (base=10) Generalized Fermat Divisors (base=12) Generalized Fermat Divisors (base=6) Irregular Primes Largest Known Primes Lucas Aurifeuillian primitive part Mersenne Primes Near-repdigit Primes NSW primes Lucas primitive parts Primorial and Factorial Primes Sophie Germain Primes Twin Primes Woodall Primes records references related pages As part of the Prime Pages and its list of the Largest Known Primes , we keep a list of the 5000 largest known primes (currently those with 32254 digits or more) plus twenty each of certain selected forms . This page is about one of those forms. Comments and suggestions requested . This page last updated: 29 March 2003, 06:59am. Definitions and Notes If both p and 2 p +1 are prime , then p is a Sophie Germain prime . The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, and 131. Around 1825 Sophie Germain proved that the first case of

17. Germain Mariesophie germain. Marie-sophie germain was the middle daughter of Ambroise-François,a prosperous silk-merchant, and Marie-Madelaine Gruguelin. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Germain.html

Marie-Sophie Germain Born: 1 April 1776 in Paris, France Died: 27 June 1831 in Paris, France Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Marie-Sophie Germain At the age of thirteen, Sophie read an account of the death of Archimedes at the hands of a Roman soldier. She was moved by this story and decided that she too must become a mathematician. Sophie pursued her studies, teaching herself Latin and Greek. She read Newton and Euler at night while wrapped in blankets as her parents slept - they had taken away her fire, her light and her clothes in an attempt to force her away from her books. Eventually her parents lessened their opposition to her studies, and although Germain neither married nor obtained a professional position, her father supported her financially throughout her life. Sophie obtained lecture notes for many courses from Ecole Polytechnique. At the end of Lagrange 's lecture course on analysis, using the pseudonym M. LeBlanc, Sophie submitted a paper whose originality and insight made Lagrange look for its author. When he discovered "M. LeBlanc" was a woman, his respect for her work remained and he became her sponsor and mathematical counsellor. Sophie's education was, however, disorganised and haphazard and she never received the professional training which she wanted. Germain wrote to Legendre about problems suggested by his 1798 , and the subsequent Legendre - Germain correspondence became virtually a collaboration.

18. NOVA Online | The Proof NOVA Online presents The Proof, including an interview with Andrew Wiles, an essay on sophie germain, and the Pythagorean theorem. http://www.pbs.org/wgbh/nova/proof/

For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem the idea that a certain simple equation had no solutions. Now hear from the man who spent seven years of his life cracking the problem, read the intriguing story of an 18th century woman mathematician who hid her identity in order to work on Fermat's Last Theorem, and demonstrate that a related equation, the Pythagorean Theorem, is true. Text Proof Home Andrew Wiles ... To print NOVA Online is produced for PBS by the WGBH Science Unit

19. Germain Learn about a French mathematician born in 1776 who contributed to number theory, acoustics, and elasticity. Find a picture and references. Mariesophie germain. Born 1 April 1776 in Paris, France http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Germain.html

Marie-Sophie Germain Born: 1 April 1776 in Paris, France Died: 27 June 1831 in Paris, France Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Marie-Sophie Germain At the age of thirteen, Sophie read an account of the death of Archimedes at the hands of a Roman soldier. She was moved by this story and decided that she too must become a mathematician. Sophie pursued her studies, teaching herself Latin and Greek. She read Newton and Euler at night while wrapped in blankets as her parents slept - they had taken away her fire, her light and her clothes in an attempt to force her away from her books. Eventually her parents lessened their opposition to her studies, and although Germain neither married nor obtained a professional position, her father supported her financially throughout her life. Sophie obtained lecture notes for many courses from Ecole Polytechnique. At the end of Lagrange 's lecture course on analysis, using the pseudonym M. LeBlanc, Sophie submitted a paper whose originality and insight made Lagrange look for its author. When he discovered "M. LeBlanc" was a woman, his respect for her work remained and he became her sponsor and mathematical counsellor. Sophie's education was, however, disorganised and haphazard and she never received the professional training which she wanted. Germain wrote to Legendre about problems suggested by his 1798 , and the subsequent Legendre - Germain correspondence became virtually a collaboration.

20. References For Germain References for sophie germain. Biography in Encyclopaedia Britannica. BooksG Bidenkapp, sophie germain, ein weiblicher Denker (Jena, 1910). http://www-gap.dcs.st-and.ac.uk/~history/References/Germain.html

References for Sophie Germain Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: G Bidenkapp, Sophie Germain, ein weiblicher Denker (Jena, 1910). L L Bucciarelli, Sophie Germain : an essay in the history of the theory of elasticity (Dordrecht - Boston, Mass., 1980). U Klens, (Pfaffenweiler, 1994). Articles: Historia Math. A D Dalmedico, Sophie Germain, Scientific American L S Grinstein and P J Campbell (eds.), Women of Mathematics (Westport, Conn., 1987), 47-56. G Micheli, The philosophical works of Sophie Germain (Italian), in Science and philosophy (Milan, 1985), 712-729. J H Sampson, Sophie Germain and the Theory of Numbers, Archive for History of Exact Science H Stupuy, Notice sur la vie et les ouvrs de Sophie Germain, Ouvres philosophique de Sophie Germain (Paris, 1879), 1-92. C Truesdell, Sophie Germain : fame earned by stubborn error, Boll. Storia Sci. Mat. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics University of St Andrews, Scotland

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