pinecone/core-2020-05-10-deduplication huggingface dataset:
A History of Complex Dynamics, from Schröder to Fatou and Julia.By Daniel S. Alexander. Wiesbaden (Vieweg).

AbstractAll books, monographs, journal articles, and other publications (including films and other multisensory materials) relating to the history of mathematics are abstracted in the Abstracts Department. The Reviews Department prints extended reviews of selected publications.Materials for review, except books, should be sent to the Abstracts Editor, Professor David E. Zitarelli, Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122, U.S.A. Books in English for review should be sent to Professor Paul R. Wolfson, Department of Mathematics, West Chester University, West Chester, Pennsylvania 19383, U.S.A. Books in other languages for review should be sent to Professor Catherine Goldstein, Bâtiment 425, Mathématiques, Université de Paris-Sud, F-91405 Orsay Cedex, France.Most reviews are solicited. However, colleagues wishing to review a book are invited to make their wishes known to the appropriate Book Review Editor. (Requests to review books written in the English language should be sent to Prof. Paul R. Wolfson at the above address; requests to review books written in other languages should be sent to Prof. Catherine Goldstein at the above address.) We also welcome retrospective reviews of older books. Colleagues interested in writing such reviews should consult first with the appropriate Book Review Editor (as indicated above, according to the language in which the book is written) to avoid duplication
Ludvig Sylow's Lectures on Algebraic Equations and Substitutions, Christiania (Oslo), 1862: An Introduction and a Summary

AbstractIn 1862–1863 Ludvig Sylow (1832–1918) gave a course on Galois theory at the University of Oslo. His notes for that course have now been published (in Norwegian). They give a good account of their subject as it was seen at that time, and they show that Sylow in 1862 had posed himself the problem which later was to lead him to the famous “Sylow theorems” on the existence of subgroups of a given order in a finite group (published 1872). This course was also the young Sophus Lie's first introduction to the theory of groups. The present article gives an introduction to Sylow's notes, and a summary of them in English.En 1862–1863 Ludvig Sylow (1832–1918) donna un cours à l'Université d'Oslo sur la théorie de Galois. Son manuscript a été récemment publié (en Norvégien). Il donne un bon aperçu du sujet tel qu'il était vu à l'époque, et il montre que Sylow s'était déjà posé le problème qui allait le mener aux célèbres “Théorèmes de Sylow” sur l'existence de sous-groupes d'un ordre donné dans des groupes finis (publiés en 1872). Ce cours fut le premier rencontre du jeune Sophus Lie avec la théorie des groupes. Le présent article est une introduction au manuscript de Sylow, accompagnée d'un abrégé en anglais.Ludvig Sylow (1832–1918) hat 1862–1863 an der Universität Oslo eine Vorlesungsreihe über Galois-Theorie gehalten. Sein Vorlesungsmanuskript (auf Norwegisch) ist jetzt publiziert worden. Es gibt einen guten U?berblick über den damaligen Stand dieser Theorie, und es zeigt daß Sylow sich bereits 1862 die Frage gestellt hat, die ihn später zu den bekannten “Sylowschen Sätzen” geführt hat. Diese Vorlesungen Sylows waren auch die erste Einführung des jungen Sophus Lie in die Gruppentheorie. Der nachstehende Artikel gibt eine Einführung in Sylows Manuskript, und eine Zusammenfassung
Numbers, Magnitudes, Ratios, and Proportions in Euclid'sElements: How Did He Handle Them?

AbstractFor a century or so much Greek mathematics has been interpreted as algebra in geometric and arithmetical disguise. But especially over the last 25 years some historians of mathematics have raised objections to this interpretation, finding it to be misleading and anachronistic, and even wrong. Accepting these criticisms, I consider Euclid'sElementsin this context: if it cannot be read in this algebraic manner, how did he conceive and handle his various types of quantity? The question is not merely of historical interest, for it raises issues about basic relationships between algebra, arithmetic, and geometry
Mathematics in the Metropolis: A Survey of Victorian London

AbstractThis paper surveys the teaching of university-level mathematics in various London institutions during the reign of Queen Victoria. It highlights some of the famous mathematicians who were involved for many years as teachers of this mathematics, including Augustus De Morgan, James Joseph Sylvester, and Karl Pearson. The paper also investigates the wide variety of teaching establishments, including mainly academic institutions (University College, King's College), the military colleges (Royal Military Academy, Woolwich and Royal Naval College, Greenwich), the women's colleges (Bedford and Queen's), and the technical colleges and polytechnics (e.g., Central Technical Institute) which began to appear during the latter part of this period. A comparison of teaching styles and courses offered is a fruitful way of exploring the rich development of university-level mathematics in London between 1837 and 1901.Cet ouvrage examine dans son ensemble l'enseignement mathématique au niveau universitaire dans diverses institutions à Londres pendant la règne de la Reine Victoria. Nous soulignons quelques mathématiciens célèbres qui participèrent dans ce milieu, par exemple, Augustus De Morgan, James Joseph Sylvester, et Karl Pearson. En plus, nous analysons les diverses grandes écoles d'enseignement, y compris surtout des institutions académiques (University College, King's College), des écoles militaires (Royal Military Academy, Woolwich et Royal Naval College, Greenwich), des écoles de femmes (Bedford et Queen's), et des écoles techniques et polytechniques (par exemple, Central Technical Institute) qui commençaient à apparaı&#x0302;tre durant la dernière partie de cette période. Une comparaison des cours enseignés et des différents styles pédagogiques utilisés nous fournit un moyen pour étudier le développement riche des mathématiques au niveau universitaire à Londres entre 1837 et 1901.In dieser Arbeit wird die mathematische Lehre auf Universitätsniveau an verschiedenen Institutionen Londons während der Herrschaft von Queen Victoria untersucht. Einige der berühmten Mathematiker, einschließlich Augustus De Morgan, James Joseph Sylvester und Karl Pearson, die lange Jahre Mathematik lehrten, werden hervorgehoben. In der Arbeit wird auch die große Vielfalt an Lehrinstitutionen untersucht, darunter akademische Institutionen (University College, King's College), Militär-Colleges (Royal Military Academy, Wool_wich und Royal Naval College, Greenwich), Frauen-Colleges (Bedford und Queen's) sowie technische und polytechnische Hochschulen (z.B. Central Technical Institute), die während der zweiten Hälfte dieses Zeitabschnittes entstanden. Ein Vergleich der Lehrtechniken und der angebotenen Kurse bietet eine fruchtbare Methode, die reiche Entwicklung der Mathematik auf Universitätsniveau in London zwischen 1837 und 1901 zu erforschen
The Emancipation of Mathematical Research Publishing in the United States from German Dominance (1878–1945)

AbstractThis article investigates the historical fine structure of the establishment of the American system of mathematical research publishing both quantitatively and qualitatively, with particular reference to German–American relations between 1878 and 1945. On the basis of mostly unpublished material, it focuses on the policies of the American Mathematical Society, the German publishing house Springer-Verlag, and the American Alien Property Custodian during World War II. The historical case study will offer a basis for conclusions about the processes of “internationalization” and “modernization” of mathematics in this century.Statya analiziruet podem amerikanskoi sistemy matematiko-issledovatelskogo opublikovaniya mezhdu 1878 i 1945 g. v kontekste nemetsko–amerikanskikh matematicheskikh otnoshenii. V chastnosti issleduyutsya deistviya amerikanskogo matematicheskogo obshchestva, nemetskogo izdatelstva Springera i amerikanskoi gosudarstvennoi agentury APC, kot. organizovala perepechatku nemetskikh matematicheskikh zurnalov i knig vo vremya Vtoroi Mirovoi Voiny. Issledovaniya predstavlyaet material, kot. mozhet oblegchat diskussiyu o protsessakh ‘internatsionalizirovaniya' i ‘modernizatsii' matematiki v dvadtsatom veke.Der Artikel untersucht quantitativ und qualitativ die historische Feinstruktur des Aufstieges des U.S.-amerikanischen Systems forschungsbezogener mathematischer Publikation. Die Untersuchung erfolgt vor allem vor dem Hintergrund der deutsch–amerikanischen mathematischen Beziehungen zwischen 1878 und 1945. Die Arbeit enthält zum großen Teil unveröffentlichtes Material. Besonderes Augenmerk wird den Strategien der American Mathematical Society, des deutschen Springer-Verlags und des amerikanischen Alien Property Custodian geschenkt. Letzterer organisierte während des Zweiten Weltkriegs den Nachdruck deutscher mathematischer Zeitschriften und Bücher. Das vorgestellte Material kann einer theoretischen Diskussion der Prozesse der “Internationalisierung” und “Modernisierung” der Mathematik im 20.Jahrhundert dienlich sein
Geometry, Analysis, and the Baptism of Slaves: John West in Scotland and Jamaica

AbstractThe achievements of the little-known Scottish mathematician, John West (1756–1817), deserve recognition: hisElements of Mathematics(1784) shows him to be a skilled expositor and innovative geometer while his manuscript,Mathematical Treatises,unpublished until 1838, reveal him also to be an accomplished exponent of “continental” analysis, familiar with works of Lagrange, Laplace, and Arbogast then little studied in Britain.First an assistant at St. Andrews University in Scotland, West then worked in isolation in Jamaica, combining mathematics with the duties of an Anglican rector. His life and his pastoral and mathematical works are here described.Copyright 1998 Academic Press.L'oeuvre du mathématicien écossais méconnu John West (1756–1817) mérite une plus grande renommée. Dans sesElements of Mathematics(1784), il apparaı&#x0302;t comme un commentateur expérimenté et un géomètre original. Son manuscritMathematical Treatises, qui ne fut publié qu'en 1838, le montre comme un interprète accompli de l'analyse “continentale” prônée par Lagrange, Laplace et Arbogast, alors peu étudiés en Grande Bretane.West fut d'abord assistant à l'Université de St. Andrews en Écosse puis travailla, seul, à la Jamaı&#x0308;que, joignant aux mathématiques les devoirs d'un pasteur anglican. Sa vie, ainsi que ses travaux pastoraux et mathématiques sont décrits ici.Copyright 1998 Academic Press.[formuala]Copyright 1998 Academic Press.MSC 1991 subject classifications: 01A50, 01A70, 26–0
The Early History of the Cornell Mathematics Department: A Case Study in the Emergence of the American Mathematical Research Community

AbstractIn this paper I describe the early history of the Cornell University mathematics department in the historical context of the late 19th century. In particular, I show that it is a case study of the emergence of the American mathematical community.Copyright 1998 Academic Press.En este ensayo, describo la premera historia de departamento de matematica de Cornell Universitad en el contexto de Siglo XIX. En particular, demonstro que este departamento es un ejemplo do lar emergencia de communidad matematica de Estados Unidos.Copyright 1998 Academic Press.In dieser Arbeit beschreibe ich die Frühgeschichte des Mathematics Department der Cornell University während des ausgehenden neunzehnten Jahrhunderts. Ich zeige insbesondere, daβ diese Geschichte als Fallstudie für die Entstehung der amerikanischen Mathematikergemeinschaft angesehen werden kann.Copyright 1998 Academic Press.MSC 1991 subject classification: 01A55, 01A73
Mathematical Methods in the Tables of Planetary Motion in Kūshyār ibn Labbān'sJāmicZı̄j

AbstractKūshyār ibn Labbān, an Iranian scientist who flourishedca.A.D. 1000, composed an astronomical handbook entitled theJāmicZı̄j. It has been considered to be derivative of al-Battānı̄'sZı̄j al-S·ābı̄(ca.A.D. 900), and through it, back to Ptolemy'sAlmagest(ca.A.D. 150). We analyze the tables of planetary motion and consider the possible dependences. We explain several unusual features, particularly the double-argument planetary equation of anomaly tables, which are tabulated using an innovative interpolation scheme. Complete directions for the use of the tables are given, as well as definitions of the functions tabulated.Copyright 1998 Academic Press.Kūshyār ibn Labbān, ein iranischer Wissenschaftler, der um 1000 lebte, verfaßte ein astronomisches Handbuch mit dem TitelZı̄g al-gāmic. Man hat geglaubt, daß es von al-Battānı̄sZı̄g as·-S·ābı̄(um 900) abhängt und dadurch auch von Ptolemaeus'Almagest(um 150 n. Chr.). Wir analysieren die Tafeln der Planetenbewegung und betrachten die möglichen Abhängigkeiten. Wir erklären auch einige ungewöhnliche Eigenarten, speziell die Tafeln der Gleichung der Anomalie, die ein doppeltes Argument enthält; sie wurden mit Hilfe eines neuartigen Interpolationsschemas berechnet. Vollständige Anweisungen für den Gebrauch der Tafeln werden ebenso gegeben wie die Definitionen der Funktione, die in Tabellenform gebracht wurden.Copyright 1998 Academic Press.[formula]Copyright 1998 Academic Press.AMS 1991 subject classifications: 01A30, 01A2
On the Rabbinical Approximation of π

AbstractWe discuss the Rabbinical tradition of geometry concerning circular shapes, as it appears in the Babylonian Talmud and in later commentaries. Three explanations of the difference between π and the Rabbinical value for it, so far not widely known among the scientific community, are given.Copyright 1998 Academic Press.Nous discutons ici la tradition rabbinique en géométrie à propos des figures circulaires, telle qu'elle apparaı&#x0302;t dans le Talmud babylonien et dans des commentaires ulterieurs. Trois explications sont proposées pour la différence entre π et la valeur donnée dans la littérature rabbinique. Ces explications semblent peu connues dans la communauté scientifique.Copyright 1998 Academic Press.Wir diskutieren die rabbinische Tradition der Geometrie der kreisförmigen Formen, wie sie im babylonischen Talmud und in späteren Kommentaren erscheint. Wir geben drei Erklärungen für den Unterschied zwischen π und seinem rabbinischen Wert, die unter Wissenschaftlern noch nicht weit bekannt sind.Copyright 1998 Academic Press.MSC 1991 subject classifications: 01A35, 01A1
Newton'sPrincipiaand Inverse-Square Orbits in a Resisting Medium: A Spiral of Twisted Logic

AbstractProposition XV/Theorem XII in Book Two of Newton'sPrincipiadeals with the spiral path of a body attracted by an inverse-square force toward a fixed center and retarded by the medium in which it travels. This article examines the argument offered by Newton as proof of the proposition/theorem and finds it fallacious. Also presented here are accounts of how Newton's purported proof is dealt with in each of three late-20th-century publications—none of which reports detection of the fallacy.Copyright 1998 Academic Press.La Proposition XV (théorème XI) du livre II desPrincipiade Newton traite de la trajectoire en forme de spirale d'un corps attiré vers un centre immobile par une force d'intensité proportionnelle à l'inverse du carré de la distance, et ralenti par le milieu qu'il traverse. Cet article examine le raisonnement offert par Newton pour preuve de la proposition (du théorème) et montre qu'il est incorrect. L'article présente aussi la façon dont la prétendue preuve de Newton a été traitée dans trois publications de la fin du vingtième siècle—aucune d'entres elles ne découvre l'erreur du raisonnement.Copyright 1998 Academic Press.Proposition XV/Theorem XII derPrincipiaBuch Zwei von Newton befaßt sich mit dem spiralförmigen Weg eines Körpers der durch einer Kraft gemäß dem inversen Quadratgesetz zu einen bestimmten Mittlepunkt, und durch das Medium verzögert wird, worin er sich bewegt. Dieser Aufsatz untersucht das von Newton vorgebrachte Argument für den Beweis den Satzes/Theorems, und findet es durch einen Trugschluß beeinträchtigt. Auch wird hier dargelegt, wie der von Newton gegebene Beweiß in jeden der drie Veröffentlichungen des späten zwanzigsten Jahrhunderts behandelt wird—keiner von ihnen berichtet von der Entdeckung des Trugschlußes.Copyright 1998 Academic Press.MSC 1991 subject classifications: 01A45, 70M2
Notes on János Bolyai's Researches in Number Theory

AbstractJános Bolyai was one of the inventors of non-Euclidean geometry. According to his unpublished manuscripts, he also achieved remarkable results in other fields in mathematics. His work in number theory is of special interest because it contains ideas which have hitherto been attributed to other mathematicians.Copyright 1999 Academic Press.Bolyai János a nem-euklidészi geometria egyik megalkotója. Feldolgozatlan kéziratainak tanúsága szerint a matematika más ágaiban is figyelemre méltó eredményeket ért el. Számelméleti munkái azért tarthatnak különös érdeklödésre számot, mivel olyan gondolatokat tartalmaznak, amelyeket eddig más matematikusoknak tulajdonı&#x0301;tottak.Copyright 1999 Academic Press.AMS classification numbers: 01A55; 01A70; 11A41
Horner versus Holdred: An Episode in the History of Root Computation

AbstractIt is well known that Horner's method for the computation of a real root of a polynomial equation was anticipated in Italy by Ruffini. In the present paper it is shown that in England the method was published by Holdred, before Horner. The resulting controversy over priority is discussed, and related letters from contemporary mathematicians are reproduced. It is concluded that the dissemination of the algorithm under the inappropriate designation “Horner's method” is mainly due to De Morgan.Copyright 1999 Academic Press.Il est bien connu que la méthode de Horner pour calculer une racine reélle d'une équation polynôme avait été anticipée en Italie par Ruffini. Dans ce papier il est démontré qu'en Angleterre la méthode fut publiée par Holdred avant Horner. La controverse sur la priorité est discutée, et des lettres de mathé maticiens contemporains sont reproduites. Il est conclu que la dissémination de l'algorithme sous la désignation inappropriée “méthode de Horner” est principalement due à De Morgan.Copyright 1999 Academic Press.MSC 1991 subject classifications: 01A55; 01A70; 01A80; 65-03
Mathematics and Dialectics in the Soviet Union: The Pre-Stalin Period

AbstractDuring the 1920s, Soviet Marxist theorists paid less attention to developments in mathematics in their own country than to various manifestations of “mathematical idealism” in the West. Their criticism concentrated on set-theoretical studies, the theory of probability, mathematical logic, and the foundations of mathematics. Because of their disunity, the Marxist scholars did not present an obstacle to the work of mathematicians, dominated by the much-heralded Moscow school of mathematics, strong in the theory of functions of a real variable and its applications to topology and several other branches of mathematics. The end of the decade was marked by the beginning of Stalinist pressure to establish full ideological control over all branches of mathematics.Copyright 1999 Academic Press.MSC 1991 subject classifications: 01A60; 01A72; 01A74; 01A80
A Real Sheet of Complex Riemannian Function Theory: A Recently Discovered Sketch in Riemann's Own Hand

AbstractWe analyze an only recently identified Riemann autograph that had been in the possession of Georg August Thieme (1831–1910). These are the notes which Bernhard Riemann (1826–1866) made during his conversation with Thieme in order to explain the central points of his theory of functions of a complex variable, in particular his version of the Dirichlet principle. Copyright 1999 Academic Press.Wir analysieren ein erst kürzlich identifiziertes Riemann-Autograph aus dem Besitz von Georg August Thieme (1831–1910). Es handelt sich um Notizen, mittels derer Bernhard Riemann (1826–1866) im Gespräch mit Thieme die zentralen Punkte seiner Theorie der Funktionen einer komplexen Veränderlichen erläutert hat, insbesondere seine Version des Dirichlet-Prinzips. Copyright 1999 Academic Press.MSC 1991 subject classification: 01A55; 30-03; 31-03; 01A72
An Earlier Date for “Cramer's Rule”

AbstractCarl B. Boyer has shown that Colin Maclaurin published “Cramer's Rule” two years before Gabriel Cramer and conjectured that Maclaurin knew the technique as early as 1729. This note establishes Boyer's conjecture through a heretofore unpublished manuscript in the Edinburgh University Library. Copyright 1999 Academic Press.Carl B. Boyer démontre que Colin Maclaurin publia “la Règle de Cramer" deux ans avant Gabriel Cramer, et spécule que Maclaurin fût en possession de la technique dès 1729. Cette note-ci établit la conjecture de Boyer grâce à un manuscrit qui se trouve dans la Bibliothèque de l'Université d'Edimbourg et qui est jusqu'ici inédit. Copyright 1999 Academic Press.AMS Subject Classification: 01A50
The First Lectures in Italy on Galois Theory: Bologna, 1886–1887

AbstractDuring the academic year 1886–1887, Cesare Arzelà (1847–1912) gave a course on Galois theory at the University of Bologna, the first in Italy on this subject. That year, the audience included the future mathematician and historian, Ettore Bortolotti (1866–1947), who took notes on the lectures. Here, the lectures are analyzed first in the context of the development of Galois theory in Europe and then in light of institutional developments at Bologna, especially following the unification in 1861. Arzelà emerges as a creative and effective teacher and mathematician in the discussion of the actual content of the lectures. Copyright 1999 Academic Press.Nell'anno accademico 1886–1887, Cesare Arzelà (1847–1912) tenne un corso sulla teoria di Galois all'Università di Bologna, il primo in Italia su tale argomento. Quell'anno l'uditorio includeva il futuro matematico e storico, Ettore Bortolotti (1866–1947), che trascrisse gli appunti delle lezioni. Nel presente articolo le lezioni sono analizzate prima nel contesto dello sviluppo della teoria di Galois in Europa e poi alla luce degli sviluppi istituzionali a Bologna, soprattutto quelli successivi all'unificazione del 1861. Dalla discussione del contenuto delle lezioni, Arzelà emerge come un insegnante e matematico creativo ed efficace. Copyright 1999 Academic Press.MSC subject classifications: 01A55, 01A72, 01A73
Mathematics for Independence: From Spanish Liberal Exile to the Young American Republics

AbstractThis paper studies one period in the history of mathematical relationships between Spain and Latin America, when right after the first liberating movements at the beginning of the 19th century, the Spanish-exiled liberals in London produced a peculiar kind of mathematical textbook for the new republics, the catechisms. Copyright 1999 Academic Press.Este trabajo estudia un periodo de la historia de los intercambios matemáticos entre España y Latinoamérica inmediatamente posterior a los movimientos liberadores de principios del siglo XIX, cuando los liberales españoles exiliados en Londres produjeron un tipo muy peculiar de textos matemáticos para las nuevas repúblicas americanas, los catecismos. Copyright 1999 Academic Press.AMS 1991 subject classifications: 00A05, 01A55, 01A80
Did Euclid's Circles Have Two Kinds of Radius?

AbstractIt is often asserted that Euclid had no single word for “radius”, but rather used the description “the line drawn from the center”. We examine the linguistic practice of Euclid, Archimedes, and Apollonius and find that it is more subtle than that. Copyright 1999 Academic Press.Il est souvent dit qu'Euclide n'avait pas de mot pour “rayon”, et qu'à sa place il se servait de la description “la ligne tracée à partir du centre”. Nous examinons ici la pratique linguistique d'Euclide, Archimède, et Apollonius, pour montrer que celle-ci est plus subtile que cela. Copyright 1999 Academic Press.MSC 1991 subject classification: 01A20