4000 Jahre Algebra
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4000 Jahre Algebra
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Author : H.-W. Alten
language : de
Publisher: Springer-Verlag
Release Date : 2013-09-18
4000 Jahre Algebra written by H.-W. Alten and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-18 with Mathematics categories.
Die Entstehung, Entwicklung und Wandlung der Algebra als Teil unserer Kulturgeschichte beschreiben Wissenschaftler von fünf Universitäten. Ursprünge, Anstöße und die Entwicklung algebraischer Begriffe und Methoden werden in enger Verflechtung mit historischen Ereignissen und menschlichen Schicksalen dargestellt. Ein erster Spannungsbogen reicht von den Frühformen des Rechnens mit natürlichen Zahlen und Brüchen zur Lösung einfacher Gleichungen bis hin zur Lösung von Gleichungen dritten und vierten Grades in der Renaissance. Von den misslungenen Versuchen zur Lösung allgemeiner Gleichungen höheren Grades im 17 Jh. zieht sich ein weiterer Bogen zu den berühmten Beweisen des Fundamentalsatzes der Algebra durch Gauß und den genialen Ideen des jungen Galois. Die Wandlung der Algebra von der Gleichungslehre zur Theorie algebraischer Strukturen wird danach ebenso beschrieben, wie die völlig neuen Akzente, die die Computeralgebra in neuester Zeit gesetzt hat. Viele neue farbige Abbildungen bereichern die inhaltlichen Aktualisierungen und Textergänzungen.
4000 Jahre Algebra
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Author : Heinz-Wilhelm Alten
language : de
Publisher: Springer
Release Date : 2008-08-12
4000 Jahre Algebra written by Heinz-Wilhelm Alten and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-12 with Mathematics categories.
Die Autoren beschreiben die Entstehung, Entwicklung und Wandlung der Algebra als Teil unserer Kulturgeschichte. Ursprünge, Anstöße und die Entwicklung algebraischer Begriffe und Methoden werden in enger Verflechtung mit historischen Ereignissen und menschlichen Schicksalen dargestellt. Ein erster Spannungsbogen reicht von den Frühformen des Rechnens mit natürlichen Zahlen und Brüchen zur Lösung einfacher Gleichungen bis hin zur Lösung von Gleichungen dritten und vierten Grades in der Renaissance. Von den misslungenen Versuchen zur Lösung allgemeiner Gleichungen höheren Grades im 17 Jh. zieht sich ein weiterer Bogen zu den genialen Ideen des jungen Galois und den berühmten Beweisen des Fundamentalsatzes der Algebra durch C.F. Gauß. Die Wandlung der Algebra von der Gleichungslehre zur Theorie algebraischer Strukturen wird danach ebenso beschrieben, wie die völlig neuen Akzente, die die Computeralgebra in neuester Zeit gesetzt hat.
Mathematik La Carte Babylonische Algebra
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Author : Franz Lemmermeyer
language : de
Publisher: Springer Spektrum
Release Date : 2022-10-20
Mathematik La Carte Babylonische Algebra written by Franz Lemmermeyer and has been published by Springer Spektrum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-20 with Mathematics categories.
Algebra ohne Buchstaben - geht das? Das geht in der Tat: Schon vor 4000 Jahren haben die Babylonier herausgefunden, wie man quadratische Gleichungen löst; das Rechnen mit Buchstaben, wie wir es auf der Schule gelernt haben, ist dagegen kaum ein halbes Jahrtausend alt. Antworten auf die Frage, wie die Babylonier dabei vorgegangen sind, gibt dieses Buch. Aufbauend auf der Mathematik der ersten neun Schuljahre wird erklärt, wie die Babylonier ihre Zahlen geschrieben haben, wie sie die Grundrechenarten ausgeführt und Wurzeln berechnet haben, und wie sie quadratische Probleme formuliert und dann mit geometrischen Mitteln gelöst haben. Die Virtuosität, mit der sie ihre vergleichsweise bescheidenen Techniken angewandt haben, ist teilweise atemberaubend. Wer sich für einen elementaren Zugang in die Welt der babylonischen Algebra interessiert, wird um dieses Buch kaum herumkommen. Vom gleichen Autor ist in der Reihe bereits erschienen: Mathematik à la Carte - Elementargeometrie an Quadratwurzeln mit einigen geschichtlichen Bemerkungen sowie Mathematik à la Carte - Quadratische Gleichungen mit Schnitten von Kegeln. Der Autor Franz Lemmermeyer hat nach seiner Promotion in Heidelberg und seiner Habilitation in Bonn an Universitäten in den USA und in der Türkei gelehrt und unterrichtet seit 2007 Mathematik am Gymnasium St. Gertrudis in Ellwangen.
3000 Years Of Analysis
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Author : Thomas Sonar
language : en
Publisher: Springer Nature
Release Date : 2020-12-27
3000 Years Of Analysis written by Thomas Sonar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-27 with Mathematics categories.
What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.
Galois Theory For Beginners A Historical Perspective Second Edition
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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-15
Galois Theory For Beginners A Historical Perspective Second Edition written by Jörg Bewersdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Education categories.
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.
Galois Theory For Beginners
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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Galois Theory For Beginners written by Jörg Bewersdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.
5000 Years Of Geometry
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Author : Christoph J. Scriba
language : en
Publisher: Birkhäuser
Release Date : 2015-04-22
5000 Years Of Geometry written by Christoph J. Scriba and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-22 with Mathematics categories.
The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)
Patterns Of Change
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Author : Ladislav Kvasz
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Patterns Of Change written by Ladislav Kvasz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-28 with Mathematics categories.
Kvasz’s book is a contribution to the history and philosophy of mat- matics, or, as one might say, the historical approach to the philosophy of mathematics. This approach is for mathematics what the history and philosophy of science is for science. Yet the historical approach to the philosophy of science appeared much earlier than the historical approach to the philosophy of mathematics. The ?rst signi?cant work in the history and philosophy of science is perhaps William Whewell’s Philosophy of the Inductive Sciences, founded upon their History. This was originally published in 1840, a second, enlarged edition appeared in 1847, and the third edition appeared as three separate works p- lished between 1858 and 1860. Ernst Mach’s The Science of Mech- ics: A Critical and Historical Account of Its Development is certainly a work of history and philosophy of science. It ?rst appeared in 1883, and had six further editions in Mach’s lifetime (1888, 1897, 1901, 1904, 1908, and 1912). Duhem’s Aim and Structure of Physical Theory appeared in 1906 and had a second enlarged edition in 1914. So we can say that history and philosophy of science was a well-established ?eld th th by the end of the 19 and the beginning of the 20 century. By contrast the ?rst signi?cant work in the history and philosophy of mathematics is Lakatos’s Proofs and Refutations, which was p- lished as a series of papers in the years 1963 and 1964.
Episodes In The History Of Modern Algebra 1800 1950
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Author : Jeremy J. Gray
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-08-31
Episodes In The History Of Modern Algebra 1800 1950 written by Jeremy J. Gray and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-31 with Mathematics categories.
Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.
Milestones In Analog And Digital Computing
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Author : Herbert Bruderer
language : en
Publisher: Springer Nature
Release Date : 2021-01-04
Milestones In Analog And Digital Computing written by Herbert Bruderer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Computers categories.
This Third Edition is the first English-language edition of the award-winning Meilensteine der Rechentechnik; illustrated in full color throughout in two volumes. The Third Edition is devoted to both analog and digital computing devices, as well as the world's most magnificient historical automatons and select scientific instruments (employed in astronomy, surveying, time measurement, etc.). It also features detailed instructions for analog and digital mechanical calculating machines and instruments, and is the only such historical book with comprehensive technical glossaries of terms not found in print or in online dictionaries. The book also includes a very extensive bibliography based on the literature of numerous countries around the world. Meticulously researched, the author conducted a worldwide survey of science, technology and art museums with their main holdings of analog and digital calculating and computing machines and devices, historical automatons and selected scientific instruments in order to describe a broad range of masterful technical achievements. Also covering the history of mathematics and computer science, this work documents the cultural heritage of technology as well.