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Taming The Unknown

Author: Victor J. Katz
Publisher: Princeton University Press
ISBN: 1400850525
Size: 68.20 MB
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What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra’s remarkable growth through different epochs around the globe.

Elementare Zahlentheorie

Author: Edmund Landau
Publisher: American Mathematical Soc.
ISBN: 0821836528
Size: 42.77 MB
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Landau's monumental treatise is a virtual encyclopedia of number theory and is universally recognized as the standard work on the subject. The text is in German.

Erfindung Des Computers Elektronenrechner Entwicklungen In Deutschland England Und Der Schweiz

Author: Herbert Bruderer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110599317
Size: 57.52 MB
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Das preisgekrönte Werk „Meilensteine der Rechentechnik" liegt in der 2., völlig neu bearbeiteten und stark erweiterten Auflage vor. Die beiden Bände, die im Ganzen rund 1600 Seiten umfassen, sind ein Gesamtwerk, lassen sich aber auch einzeln nutzen. Diese Schrift behandelt sowohl analoge wie digitale Geräte und geht auf benachbarte Bereiche wie Automatenbau (z.B. Figuren- und Musikautomaten) sowie wissenschaftliche Instrumente (z.B. Himmelskunde, Vermessungswesen, Uhrmacherkunst) ein. Gestreift werden zudem frühe Schreibmaschinen und programmgesteuerte mechanische Webstühle. Schwerpunkte des ersten Bandes sind: Grundlagen, mechanische Rechenmaschinen, Rechenschieber, historische Automaten, Entwicklung der Rechenkunst, Schritt-für-Schritt-Anleitungen für analoge und digitale Rechengeräte. Alle wichtigen Fachbegriffe werden erklärt. Die weltweit prachtvollsten Rundbaurechenmaschinen und Androiden werden in Wort und Bild vorgestellt. Das Buch enthält ferner grundsätzliche Betrachtungen zu Themen wie Digitalisierung und künstliche Intelligenz sowie zur Rolle der Technikgeschichte und der Erhaltung des technischen Kulturguts. Der zweite Band widmet sich überwiegend den Elektronenrechnern: Erfindung des Computers, weltweite Entwicklung der Rechentechnik, insbesondere in Deutschland, England und der Schweiz. Er schließt überdies je ein Fachwörterbuch Deutsch-Englisch und Englisch-Deutsch ein. Die sollen das Lesen anspruchsvoller fremdsprachiger Texte und Übersetzungen fördern. Hinzu kommt eine umfassende weltweite Bibliografie. Beide Bände berichten über aufsehenerregende neue Funde von Dokumenten und Gegenständen (u.a. weltgrößte serienmäßig gefertigte Rechenwalze, weltweit kleinster mechanischer Parallelrechner, erster mechanischer Prozessrechner), sie eignen sich auch als Nachschlagewerke. Sie sind allgemein verständlich und richten sich an alle, die Freude haben an Technik-, Mathematik-, Informatik- und Kunstgeschichte. Mehrsprachige Bibliografie zur Mathematik-, Informatik, Technik- und Naturwissenschaftsgeschichte mit über 5000 Einträgen, Fachwörterbuch Deutsch-Englisch und Englisch-Deutsch mit je 4000 Einträgen, 18 Schritt-für-Schritt-Anleitungen für die Bedienung historischer analoger und digitaler Geräte, 100 tabellarische Übersichten, zahlreiche Zeittafeln, ausführliches Personen-, Orts- und Sachverzeichnis. Herbert Bruderer ist Dozent i.R. am Departement für Informatik der Eidgenössischen Technischen Hochschule (ETH) Zürich und Technikhistoriker. Er hat zahlreiche Bücher zur Informatik verfasst und ist mehrfacher Preisträger.

Mathematik Im Mittelalterlichen Islam

Author: J. L. Berggren
Publisher: Springer-Verlag
ISBN: 9783540766889
Size: 17.43 MB
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Die Mathematik im mittelalterlichen Islam hatte großen Einfluss auf die allgemeine Entwicklung des Faches. Der Autor beschreibt diese Periode der Geschichte der Mathematik und bezieht sich dabei auf die arabischsprachigen Quellen. Zu den behandelten Themen gehören Dezimalrechnen, Geometrie, ebene und sphärische Trigonometrie, Algebra sowie die Approximation von Wurzeln von Gleichungen. Das Buch wendet sich an Mathematikhistoriker und -studenten, aber auch an alle Interessierten mit Mathematikkenntnissen der weiterführenden Schule.

Handbook On The History Of Mathematics Education

Author: Alexander Karp
Publisher: Springer Science & Business Media
ISBN: 146149155X
Size: 47.30 MB
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This is the first comprehensive International Handbook on the History of Mathematics Education, covering a wide spectrum of epochs and civilizations, countries and cultures. Until now, much of the research into the rich and varied history of mathematics education has remained inaccessible to the vast majority of scholars, not least because it has been written in the language, and for readers, of an individual country. And yet a historical overview, however brief, has become an indispensable element of nearly every dissertation and scholarly article. This handbook provides, for the first time, a comprehensive and systematic aid for researchers around the world in finding the information they need about historical developments in mathematics education, not only in their own countries, but globally as well. Although written primarily for mathematics educators, this handbook will also be of interest to researchers of the history of education in general, as well as specialists in cultural and even social history.

Turning Points In The History Of Mathematics

Author: Hardy Grant
Publisher: Birkhäuser
ISBN: 1493932640
Size: 21.87 MB
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This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

Algebra A Very Short Introduction

Author: Peter M. Higgins
Publisher: OUP Oxford
ISBN: 0191047457
Size: 42.42 MB
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Algebra marked the beginning of modern mathematics, moving it beyond arithmetic, which involves calculations featuring given numbers, to problems where some quantities are unknown. Now, it stands as a pillar of mathematics, underpinning the quantitative sciences, both social and physical. This Very Short Introduction explains algebra from scratch. Over the course of ten logical chapters, Higgins offers a step by step approach for readers keen on developing their understanding of algebra. Using theory and example, he renews the reader's aquaintance with school mathematics, before taking them progressively further and deeper into the subject. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.