Mathematics and Statistics at the University of Vermont
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Differential Calculus and by Era Integral Calculus, Which Are Related by in Early Cultures in Classical Antiquity the Fundamental Theorem of Calculus
History of calculus - Wikipedia, the free encyclopedia 1/1/10 5:02 PM History of calculus From Wikipedia, the free encyclopedia History of science This is a sub-article to Calculus and History of mathematics. History of Calculus is part of the history of mathematics focused on limits, functions, derivatives, integrals, and infinite series. The subject, known Background historically as infinitesimal calculus, Theories/sociology constitutes a major part of modern Historiography mathematics education. It has two major Pseudoscience branches, differential calculus and By era integral calculus, which are related by In early cultures in Classical Antiquity the fundamental theorem of calculus. In the Middle Ages Calculus is the study of change, in the In the Renaissance same way that geometry is the study of Scientific Revolution shape and algebra is the study of By topic operations and their application to Natural sciences solving equations. A course in calculus Astronomy is a gateway to other, more advanced Biology courses in mathematics devoted to the Botany study of functions and limits, broadly Chemistry Ecology called mathematical analysis. Calculus Geography has widespread applications in science, Geology economics, and engineering and can Paleontology solve many problems for which algebra Physics alone is insufficient. Mathematics Algebra Calculus Combinatorics Contents Geometry Logic Statistics 1 Development of calculus Trigonometry 1.1 Integral calculus Social sciences 1.2 Differential calculus Anthropology 1.3 Mathematical analysis -
Der Vierfarbensatz. Geschichte, Topologische Grundlagen Und
Der Vierfarbensatz Geschichte, topologische Grundlagen und Beweisidee von Prof. Dr. RudolfjFritsch Universität München unter Mitarbeit von Gerda Fritsch, Gräfelfing Wissenschaftsverlag Mannheim • Leipzig - Wien • Zürich Mathematische Institut dar Universität München Die Deutsche Bibliothek - CIP-Einheitsaufnahme Fritsch, Rudolf: Der Vierfarbensatz: Geschichte, topologische Grundlagen und Beweisidee / von Rudolf Fritsch. Unter Mitarb. von Gerda Fritsch. - Mannheim; Leipzig; Wien; Zürich: BI-Wiss.-Verl., 1994 ISBN 3-411-15141-2 Gedruckt auf säurefreiem Papier mit neutralem pH-Wert (bibliotheksfest) Alle Rechte, auch die der Übersetzung in fremde Sprachen, vorbehalten. Kein Teil dieses Werkes darf ohne schriftliche Einwilligung des Verlages in irgendeiner Form (Fotokopie, Mikrofilm oder ein anderes Verfahren), auch nicht für Zwecke der Unterrichtsgestaltung, reproduziert oder unter Verwendung elektronischer Systeme verarbeitet, vervielfältigt oder verbreitet werden. © Bibliographisches Institut & F. A. Brockhaus AG, Mannheim 1994 Druck: RK Offsetdruck GmbH, Speyer Bindearbeit: Progressdruck GmbH, Speyer Printed in Germany ISBN 3-411-15141-2 Für Dorothee Veronika Bernhard Inhalt s Verzeichnis Statt eines Vorworts 3 Wie man dieses Buch lesen kann 6 1 Geschichte 7 2 (Topologische) Landkarten 45 2.1 Heuristische Vorüberlegungen 45 2.2 Grenzlinien 48 2.3 Formale Definition 61 Ecken 63 Länder 64 Zusammenhang von Landkarten 66 Reduktion auf Landkarten aus Streckenzügen 67 2.4 Grundlegende Beispiele 70 2.5 Landesgrenzen 75 2.6 Gemeinsame Grenzlinien -
Maria Gaetana Agnesi Melissa De La Cruz
Maria Gaetana Agnesi Melissa De La Cruz Maria Gaetana Agnesi's life Maria Gaetana Agnesi was born on May 16, 1718. She also died on January 9, 1799. She was an Italian mathematician, philosopher, theologian, and humanitarian. Her father, Pietro Agnesi, was either said to be a wealthy silk merchant or a mathematics professor. Regardless, he was well to do and lived a social climber. He married Anna Fortunata Brivio, but had a total of 21 children with 3 female relations. He used his kids to be known with the Milanese socialites of the time and Maria Gaetana Agnesi was his oldest. He hosted soires and used his kids as entertainment. Maria's sisters would perform the musical acts while she would present Latin debates and orations on questions of natural philosophy. The family was well to do and Pietro has to make sure his children were under the best training to entertain well at these parties. For Maria, that meant well-esteemed tutors would be given because her father discovered her great potential for an advanced intellect. Her education included the usual languages and arts; she spoke Italian and French at the age of 5 and but the age of 11, she also knew how to speak Greek, Hebrew, Spanish, German and Latin. Historians have given her the name of the Seven-Tongued Orator. With private tutoring, she was also taught topics such as mathematics and natural philosophy, which was unusual for women at that time. With the Agnesi family living in Milan, Italy, Maria's family practiced religion seriously. -
EVARISTE GALOIS the Long Road to Galois CHAPTER 1 Babylon
A radical life EVARISTE GALOIS The long road to Galois CHAPTER 1 Babylon How many miles to Babylon? Three score miles and ten. Can I get there by candle-light? Yes, and back again. If your heels are nimble and light, You may get there by candle-light.[ Babylon was the capital of Babylonia, an ancient kingdom occupying the area of modern Iraq. Babylonian algebra B.M. Tablet 13901-front (From: The Babylonian Quadratic Equation, by A.E. Berryman, Math. Gazette, 40 (1956), 185-192) B.M. Tablet 13901-back Time Passes . Centuries and then millennia pass. In those years empires rose and fell. The Greeks invented mathematics as we know it, and in Alexandria produced the first scientific revolution. The Roman empire forgot almost all that the Greeks had done in math and science. Germanic tribes put an end to the Roman empire, Arabic tribes invaded Europe, and the Ottoman empire began forming in the east. Time passes . Wars, and wars, and wars. Christians against Arabs. Christians against Turks. Christians against Christians. The Roman empire crumbled, the Holy Roman Germanic empire appeared. Nations as we know them today started to form. And we approach the year 1500, and the Renaissance; but I want to mention two events preceding it. Al-Khwarismi (~790-850) Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was born during the reign of the most famous of all Caliphs of the Arabic empire with capital in Baghdad: Harun al Rashid; the one mentioned in the 1001 Nights. He wrote a book that was to become very influential Hisab al-jabr w'al-muqabala in which he studies quadratic (and linear) equations. -
Formulation of the Group Concept Financial Mathematics and Economics, MA3343 Groups Artur Zduniak, ID: 14102797
Formulation of the Group Concept Financial Mathematics and Economics, MA3343 Groups Artur Zduniak, ID: 14102797 Fathers of Group Theory Abstract This study consists on the group concepts and the four axioms that form the structure of the group. Provided below are exam- ples to show different mathematical opera- tions within the elements and how this form Otto Holder¨ Joseph Louis Lagrange Niels Henrik Abel Evariste´ Galois Felix Klein Camille Jordan the different characteristics of the group. Furthermore, a detailed study of the formu- lation of the group theory is performed where three major areas of modern group theory are discussed:The Number theory, Permutation and algebraic equations the- ory and geometry. Carl Friedrich Gauss Leonhard Euler Ernst Christian Schering Paolo Ruffini Augustin-Louis Cauchy Arthur Cayley What are Group Formulation of the group concept A group is an algebraic structure consist- The group theory is considered as an abstraction of ideas common to three major areas: ing of different elements which still holds Number theory, Algebraic equations theory and permutations. In 1761, a Swiss math- some common features. It is also known ematician and physicist, Leonhard Euler, looked at the remainders of power of a number as a set. All the elements of a group are modulo “n”. His work is considered as an example of the breakdown of an abelian group equipped with an algebraic operation such into co-sets of a subgroup. He also worked in the formulation of the divisor of the order of the as addition or multiplication. When two el- group. In 1801, Carl Friedrich Gauss, a German mathematician took Euler’s work further ements of a group are combined under an and contributed in the formulating the theory of abelian groups. -
The History of the Abel Prize and the Honorary Abel Prize the History of the Abel Prize
The History of the Abel Prize and the Honorary Abel Prize The History of the Abel Prize Arild Stubhaug On the bicentennial of Niels Henrik Abel’s birth in 2002, the Norwegian Govern- ment decided to establish a memorial fund of NOK 200 million. The chief purpose of the fund was to lay the financial groundwork for an annual international prize of NOK 6 million to one or more mathematicians for outstanding scientific work. The prize was awarded for the first time in 2003. That is the history in brief of the Abel Prize as we know it today. Behind this government decision to commemorate and honor the country’s great mathematician, however, lies a more than hundred year old wish and a short and intense period of activity. Volumes of Abel’s collected works were published in 1839 and 1881. The first was edited by Bernt Michael Holmboe (Abel’s teacher), the second by Sophus Lie and Ludvig Sylow. Both editions were paid for with public funds and published to honor the famous scientist. The first time that there was a discussion in a broader context about honoring Niels Henrik Abel’s memory, was at the meeting of Scan- dinavian natural scientists in Norway’s capital in 1886. These meetings of natural scientists, which were held alternately in each of the Scandinavian capitals (with the exception of the very first meeting in 1839, which took place in Gothenburg, Swe- den), were the most important fora for Scandinavian natural scientists. The meeting in 1886 in Oslo (called Christiania at the time) was the 13th in the series. -
Mathematical Genealogy of the Union College Department of Mathematics
Gemma (Jemme Reinerszoon) Frisius Mathematical Genealogy of the Union College Department of Mathematics Université Catholique de Louvain 1529, 1536 The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. Johannes (Jan van Ostaeyen) Stadius http://www.genealogy.math.ndsu.nodak.edu/ Université Paris IX - Dauphine / Université Catholique de Louvain Justus (Joost Lips) Lipsius Martinus Antonius del Rio Adam Haslmayr Université Catholique de Louvain 1569 Collège de France / Université Catholique de Louvain / Universidad de Salamanca 1572, 1574 Erycius (Henrick van den Putte) Puteanus Jean Baptiste Van Helmont Jacobus Stupaeus Primary Advisor Secondary Advisor Universität zu Köln / Université Catholique de Louvain 1595 Université Catholique de Louvain Erhard Weigel Arnold Geulincx Franciscus de le Boë Sylvius Universität Leipzig 1650 Université Catholique de Louvain / Universiteit Leiden 1646, 1658 Universität Basel 1637 Union College Faculty in Mathematics Otto Mencke Gottfried Wilhelm Leibniz Ehrenfried Walter von Tschirnhaus Key Universität Leipzig 1665, 1666 Universität Altdorf 1666 Universiteit Leiden 1669, 1674 Johann Christoph Wichmannshausen Jacob Bernoulli Christian M. von Wolff Universität Leipzig 1685 Universität Basel 1684 Universität Leipzig 1704 Christian August Hausen Johann Bernoulli Martin Knutzen Marcus Herz Martin-Luther-Universität Halle-Wittenberg 1713 Universität Basel 1694 Leonhard Euler Abraham Gotthelf Kästner Franz Josef Ritter von Gerstner Immanuel Kant -
All About Abel Dayanara Serges Niels Henrik Abel (August 5, 1802-April 6,1829) Was a Norwegian Mathematician Known for Numerous Contributions to Mathematics
All About Abel Dayanara Serges Niels Henrik Abel (August 5, 1802-April 6,1829) was a Norwegian mathematician known for numerous contributions to mathematics. Abel was born in Finnoy, Norway, as the second child of a dirt poor family of eight. Abels father was a poor Lutheran minister who moved his family to the parish of Gjerstad, near the town of Risr in southeast Norway, soon after Niels Henrik was born. In 1815 Niels entered the cathedral school in Oslo, where his mathematical talent was recognized in 1817 by his math teacher, Bernt Michael Holmboe, who introduced him to the classics in mathematical literature and proposed original problems for him to solve. Abel studied the mathematical works of the 17th-century Englishman Sir Isaac Newton, the 18th-century German Leonhard Euler, and his contemporaries the Frenchman Joseph-Louis Lagrange and the German Carl Friedrich Gauss in preparation for his own research. At the age of 16, Abel gave a proof of the Binomial Theorem valid for all numbers not only Rationals, extending Euler's result. Abels father died in 1820, leaving the family in straitened circumstances, but Holmboe and other professors contributed and raised funds that enabled Abel to enter the University of Christiania (Oslo) in 1821. Abels first papers, published in 1823, were on functional equations and integrals; he was the first person to formulate and solve an integral equation. He had also created a proof of the impossibility of solving algebraically the general equation of the fifth degree at the age of 19, which he hoped would bring him recognition. -
Academic Genealogy of the Oakland University Department Of
Basilios Bessarion Mystras 1436 Guarino da Verona Johannes Argyropoulos 1408 Università di Padova 1444 Academic Genealogy of the Oakland University Vittorino da Feltre Marsilio Ficino Cristoforo Landino Università di Padova 1416 Università di Firenze 1462 Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo Angelo Poliziano Florens Florentius Radwyn Radewyns Geert Gerardus Magnus Groote Università di Mantova 1433 Università di Mantova Università di Firenze 1477 Constantinople 1433 DepartmentThe Mathematics Genealogy Project of is a serviceMathematics of North Dakota State University and and the American Statistics Mathematical Society. Demetrios Chalcocondyles http://www.mathgenealogy.org/ Heinrich von Langenstein Gaetano da Thiene Sigismondo Polcastro Leo Outers Moses Perez Scipione Fortiguerra Rudolf Agricola Thomas von Kempen à Kempis Jacob ben Jehiel Loans Accademia Romana 1452 Université de Paris 1363, 1375 Université Catholique de Louvain 1485 Università di Firenze 1493 Università degli Studi di Ferrara 1478 Mystras 1452 Jan Standonck Johann (Johannes Kapnion) Reuchlin Johannes von Gmunden Nicoletto Vernia Pietro Roccabonella Pelope Maarten (Martinus Dorpius) van Dorp Jean Tagault François Dubois Janus Lascaris Girolamo (Hieronymus Aleander) Aleandro Matthaeus Adrianus Alexander Hegius Johannes Stöffler Collège Sainte-Barbe 1474 Universität Basel 1477 Universität Wien 1406 Università di Padova Università di Padova Université Catholique de Louvain 1504, 1515 Université de Paris 1516 Università di Padova 1472 Università -
Mathematical Genealogy of the Wellesley College Department Of
Nilos Kabasilas Mathematical Genealogy of the Wellesley College Department of Mathematics Elissaeus Judaeus Demetrios Kydones The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. http://www.genealogy.math.ndsu.nodak.edu/ Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion 1436 Mystras Johannes Argyropoulos Guarino da Verona 1444 Università di Padova 1408 Cristoforo Landino Marsilio Ficino Vittorino da Feltre 1462 Università di Firenze 1416 Università di Padova Angelo Poliziano Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1477 Università di Firenze 1433 Constantinople / Università di Mantova Università di Mantova Leo Outers Moses Perez Scipione Fortiguerra Demetrios Chalcocondyles Jacob ben Jehiel Loans Thomas à Kempis Rudolf Agricola Alessandro Sermoneta Gaetano da Thiene Heinrich von Langenstein 1485 Université Catholique de Louvain 1493 Università di Firenze 1452 Mystras / Accademia Romana 1478 Università degli Studi di Ferrara 1363, 1375 Université de Paris Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro François Dubois Jean Tagault Janus Lascaris Matthaeus Adrianus Pelope Johann (Johannes Kapnion) Reuchlin Jan Standonck Alexander Hegius Pietro Roccabonella Nicoletto Vernia Johannes von Gmunden 1504, 1515 Université Catholique de Louvain 1499, 1508 Università di Padova 1516 Université de Paris 1472 Università di Padova 1477, 1481 Universität Basel / Université de Poitiers 1474, 1490 Collège Sainte-Barbe -
A History of Mathematics in America Before 1900.Pdf
THE BOOK WAS DRENCHED 00 S< OU_1 60514 > CD CO THE CARUS MATHEMATICAL MONOGRAPHS Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Publication Committee GILBERT AMES BLISS DAVID RAYMOND CURTISS AUBREY JOHN KEMPNER HERBERT ELLSWORTH SLAUGHT CARUS MATHEMATICAL MONOGRAPHS are an expression of THEthe desire of Mrs. Mary Hegeler Carus, and of her son, Dr. Edward H. Carus, to contribute to the dissemination of mathe- matical knowledge by making accessible at nominal cost a series of expository presenta- tions of the best thoughts and keenest re- searches in pure and applied mathematics. The publication of these monographs was made possible by a notable gift to the Mathematical Association of America by Mrs. Carus as sole trustee of the Edward C. Hegeler Trust Fund. The expositions of mathematical subjects which the monographs will contain are to be set forth in a manner comprehensible not only to teach- ers and students specializing in mathematics, but also to scientific workers in other fields, and especially to the wide circle of thoughtful people who, having a moderate acquaintance with elementary mathematics, wish to extend their knowledge without prolonged and critical study of the mathematical journals and trea- tises. The scope of this series includes also historical and biographical monographs. The Carus Mathematical Monographs NUMBER FIVE A HISTORY OF MATHEMATICS IN AMERICA BEFORE 1900 By DAVID EUGENE SMITH Professor Emeritus of Mathematics Teacliers College, Columbia University and JEKUTHIEL GINSBURG Professor of Mathematics in Yeshiva College New York and Editor of "Scripta Mathematica" Published by THE MATHEMATICAL ASSOCIATION OF AMERICA with the cooperation of THE OPEN COURT PUBLISHING COMPANY CHICAGO, ILLINOIS THE OPEN COURT COMPANY Copyright 1934 by THE MATHEMATICAL ASSOCIATION OF AMKRICA Published March, 1934 Composed, Printed and Bound by tClfe QlolUgUt* $Jrr George Banta Publishing Company Menasha, Wisconsin, U. -
Some Curves and the Lengths of Their Arcs Amelia Carolina Sparavigna
Some Curves and the Lengths of their Arcs Amelia Carolina Sparavigna To cite this version: Amelia Carolina Sparavigna. Some Curves and the Lengths of their Arcs. 2021. hal-03236909 HAL Id: hal-03236909 https://hal.archives-ouvertes.fr/hal-03236909 Preprint submitted on 26 May 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Some Curves and the Lengths of their Arcs Amelia Carolina Sparavigna Department of Applied Science and Technology Politecnico di Torino Here we consider some problems from the Finkel's solution book, concerning the length of curves. The curves are Cissoid of Diocles, Conchoid of Nicomedes, Lemniscate of Bernoulli, Versiera of Agnesi, Limaçon, Quadratrix, Spiral of Archimedes, Reciprocal or Hyperbolic spiral, the Lituus, Logarithmic spiral, Curve of Pursuit, a curve on the cone and the Loxodrome. The Versiera will be discussed in detail and the link of its name to the Versine function. Torino, 2 May 2021, DOI: 10.5281/zenodo.4732881 Here we consider some of the problems propose in the Finkel's solution book, having the full title: A mathematical solution book containing systematic solutions of many of the most difficult problems, Taken from the Leading Authors on Arithmetic and Algebra, Many Problems and Solutions from Geometry, Trigonometry and Calculus, Many Problems and Solutions from the Leading Mathematical Journals of the United States, and Many Original Problems and Solutions.