Mathematics in Western Culture

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 9780195345452

Category: Mathematics

Page: 512

View: 3309

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This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.

5000 Jahre Geometrie

Geschichte Kulturen Menschen

Author: Christoph J. Scriba,Peter Schreiber

Publisher: Springer-Verlag

ISBN: 3662045001

Category: Mathematics

Page: 596

View: 3349

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Lange bevor die Schrift entwickelt wurde, hat der Mensch geometrische Strukturen wahrgenommen und systematisch verwendet: ob beim Weben oder Flechten einfacher zweidimensionaler Muster oder beim Bauen mit dreidimensionalen Körpern. Das Buch liefert einen faszinierenden Überblick über die geometrischen Vorstellungen und Erkenntnisse der Menschheit von der Urgesellschaft bis hin zu den mathematischen und künstlerischen Ideen des 20. Jahrhunderts.

Mathematics for the Nonmathematician

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486316130

Category: Mathematics

Page: 672

View: 9025

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Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.

Mathematics and the Physical World

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 9780486241043

Category: Mathematics

Page: 482

View: 7070

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"Kline is a first-class teacher and an able writer. . . . This is an enlarging and a brilliant book." ? Scientific American "Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science." ? San Francisco Chronicle Since the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book. In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum. This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand ? perhaps for the first time ? the true greatness of mathematical achievements.

Mathematik im mittelalterlichen Islam

Author: J. L. Berggren

Publisher: Springer-Verlag

ISBN: 9783540766889

Category: Mathematics

Page: 200

View: 1391

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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.

Cultural Foundations of Mathematics

The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th C. CE

Author: C. K. Raju

Publisher: Pearson Education India

ISBN: 9788131708712

Category: Calculus

Page: 477

View: 3706

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The Volume Examines, In Depth, The Implications Of Indian History And Philosophy For Contemporary Mathematics And Science. The Conclusions Challenge Current Formal Mathematics And Its Basis In The Western Dogma That Deduction Is Infallible (Or That It Is Less Fallible Than Induction). The Development Of The Calculus In India, Over A Thousand Years, Is Exhaustively Documented In This Volume, Along With Novel Insights, And Is Related To The Key Sources Of Wealth-Monsoon-Dependent Agriculture And Navigation Required For Overseas Trade - And The Corresponding Requirement Of Timekeeping. Refecting The Usual Double Standard Of Evidence Used To Construct Eurocentric History, A Single, New Standard Of Evidence For Transmissions Is Proposed. Using This, It Is Pointed Out That Jesuits In Cochin, Following The Toledo Model Of Translation, Had Long-Term Opportunity To Transmit Indian Calculus Texts To Europe. The European Navigational Problem Of Determining Latitude, Longitude, And Loxodromes, And The 1582 Gregorian Calendar-Reform, Provided Ample Motivation. The Mathematics In These Earlier Indian Texts Suddenly Starts Appearing In European Works From The Mid-16Th Century Onwards, Providing Compelling Circumstantial Evidence. While The Calculus In India Had Valid Pramana, This Differed From Western Notions Of Proof, And The Indian (Algorismus) Notion Of Number Differed From The European (Abacus) Notion. Hence, Like Their Earlier Difficulties With The Algorismus, Europeans Had Difficulties In Understanding The Calculus, Which, Like Computer Technology, Enhanced The Ability To Calculate, Albeit In A Way Regarded As Epistemologically Insecure. Present-Day Difficulties In Learning Mathematics Are Related, Via Phylogeny Is Ontogeny , To These Historical Difficulties In Assimilating Imported Mathematics. An Appendix Takes Up Further Contemporary Implications Of The New Philosophy Of Mathematics For The Extension Of The Calculus, Which Is Needed To Handle The Infinities Arising In The Study Of Shock Waves And The Renormalization Problem Of Quantum Field Theory.

Mathematics Across Cultures

The History of Non-Western Mathematics

Author: Helaine Selin

Publisher: Springer Science & Business Media

ISBN: 9401143013

Category: Mathematics

Page: 479

View: 6833

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Mathematics Across Cultures: A History of Non-Western Mathematics consists of essays dealing with the mathematical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Inca, Egyptian, and African mathematics, among others, the book includes essays on Rationality, Logic and Mathematics, and the transfer of knowledge from East to West. The essays address the connections between science and culture and relate the mathematical practices to the cultures which produced them. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

Author: I. Grattan-Guinness

Publisher: JHU Press

ISBN: 9780801873973

Category: Mathematics

Page: 1806

View: 7426

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Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century. In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure and applied mathematics, including probability and statistics. This indispensable reference work demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy, and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, The Companion Encyclopedia is a valuable research tool for students and teachers in all branches of mathematics. Contents of Volume 1: •Ancient and Non-Western Traditions •The Western Middle Ages and the Renaissance •Calculus and Mathematical Analysis •Functions, Series, and Methods in Analysis •Logic, Set Theories, and the Foundations of Mathematics •Algebras and Number Theory Contents of Volume 2: •Geometries and Topology •Mechanics and Mechanical Engineering •Physics, Mathematical Physics, and Electrical Engineering •Probability, Statistics, and the Social Sciences •Higher Education and Institutions •Mathematics and Culture •Select Bibliography, Chronology, Biographical Notes, and Index

Mathematics in Society and History

Sociological Inquiries

Author: S. Restivo

Publisher: Springer Science & Business Media

ISBN: 9780792317654

Category: Education

Page: 201

View: 2117

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This is the first book by a sociologist devoted exclusively to a general sociology of mathematics. The author provides examples of different ways of thinking about mathematics sociologically. The survey of mathematical traditions covers ancient China, the Arabic-Islamic world, India, and Europe. Following the leads of classical social theorists such as Emile Durkheim, Restivo develops the idea that mathematical concepts and ideas are collective representations, and that it is mathematical communities that create mathematics, not individual mathematicians. The implications of the sociology of mathematics, and especially of pure mathematics, for a sociology of mind are also explored. In general, the author's objective is to explore, conjecture, suggest, and stimulate in order to introduce the sociological perspective on mathematics, and to broaden and deepen the still narrow, shallow path that today carries the sociology of mathematics. This book will interest specialists in the philosophy, history, and sociology of mathematics, persons interested in mathematics education, students of science and society, and people interested in current developments in the social and cultural analysis of science and mathematics.

Mathematical Enculturation

A Cultural Perspective on Mathematics Education

Author: Alan Bishop

Publisher: Springer Science & Business Media

ISBN: 940092657X

Category: Education

Page: 196

View: 9160

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Mathematics is in the unenviable position of being simultaneously one of the most important school subjects for today's children to study and one of the least well understood. Its reputation is awe-inspiring. Everybody knows how important it is and everybody knows that they have to study it. But few people feel comfortable with it; so much so that it is socially quite acceptable in many countries to confess ignorance about it, to brag about one's incompe tence at doing it, and even to claim that one is mathophobic! So are teachers around the world being apparently legal sadists by inflicting mental pain on their charges? Or is it that their pupils are all masochists, enjoying the thrill of self-inflicted mental torture? More seriously, do we really know what the reasons are for the mathematical activity which goes on in schools? Do we really have confidence in our criteria for judging what's important and what isn't? Do we really know what we should be doing? These basic questions become even more important when considered in the context of two growing problem areas. The first is a concern felt in many countries about the direction which mathematics education should take in the face of the increasing presence of computers and calculator-related technol ogy in society.

Sociocultural Research on Mathematics Education

An International Perspective

Author: Bill Atweh,Helen Forgasz,Ben Nebres

Publisher: Routledge

ISBN: 1135653119

Category: Education

Page: 480

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This volume--the first to bring together research on sociocultural aspects of mathematics education--presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. Sociocultural Research on Mathematics Education: An International Perspective is distinguished in several ways: * It is research based. Chapters report on significant research projects; present a comprehensive and critical summary of the research findings; and offer a critical discussion of research methods and theoretical perspectives undertaken in the area. * It is future oriented, presenting recommendations for practice and policy and identifying areas for further research. * It deals with all aspects of formal and informal mathematics education and applications and all levels of formal schooling. As the context of mathematics education rapidly changes-- with an increased demand for mathematically literate citizenship; an increased awareness of issues of equity, inclusivity, and accountability; and increased efforts for globalization of curriculum development and research-- questions are being raised more than ever before about the problems of teaching and learning mathematics from a non-cognitive science perspective. This book contributes significantly to addressing such issues and answering such questions. It is especially relevant for researchers, graduate students, and policymakers in the field of mathematics education.

The Joy of x

Die Schönheit der Mathematik

Author: Steven Strogatz

Publisher: Kein & Aber AG

ISBN: 3036992693

Category: Mathematics

Page: 352

View: 360

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Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.

Hidden Figures - Unerkannte Heldinnen

Author: Margot Lee Shetterly

Publisher: HarperCollins

ISBN: 3959676433

Category: History

Page: 416

View: 731

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1943 stellt das Langley Memorial Aeronautical Laboratory der NACA,die später zur NASA wird, erstmalig afroamerikanische Frauen ein. "Menschliche Rechner" - unter ihnen Dorothy Vaughan, die 1953 Vorgesetzte der brillanten afroamerikanischen Mathematikerin Katherine Johnson wird. Trotz Diskriminierung und Vorurteilen, treiben sie die Forschungen der NASA voran und Katherine Johnsons Berechnungen werden maßgeblich für den Erfolg der Apollo-Missionen. Dies ist ihre Geschichte. "Mit dieser unglaublich mitreißenden und vielschichtigen Erzählung zeigt Shetterly ihr Können. Die Geschichte begeistert in allen Aspekten." Booklist

Mathematics Education in Different Cultural Traditions- A Comparative Study of East Asia and the West

The 13th ICMI Study

Author: Frederick Koon-Shing Leung,Klaus-D. Graf,Francis J. Lopez-Real

Publisher: Springer Science & Business Media

ISBN: 0387297235

Category: Education

Page: 598

View: 1718

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The idea of the ICMI Study 13 is outlined as follows: Education in any social environment is influenced in many ways by the traditions of these environments. This study brings together leading experts to research and report on mathematics education in a global context. Mathematics education faces a split phenomenon of difference and correspondence. A study attempting a comparison between mathematics education in different traditions will be helpful to understanding this phenomenon.

Cultural Perspectives on the Mathematics Classroom

Author: Steve Lerman

Publisher: Springer Science & Business Media

ISBN: 9401711992

Category: Education

Page: 215

View: 8999

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Mathematics teaching and learning have been dominated by a concern for the intellectual readiness of the child, debates over rote learning versus understanding and, recently, mathematical processes and thinking. The gaze into today's mathematics classroom is firmly focused on the individual learner. Recently, however, studies of mathematics in social practices, including the market place and the home, have initiated a shift of focus. Culture has become identified as a key to understanding the basis on which the learner appropriates meaning. The chapters in this timely book attempt to engage with this shift of focus and offer original contributions to the debate about mathematics teaching and learning. They adopt theoretical perspectives while drawing on the classroom as both the source of investigation and the site of potential change and development. The book will be of fundamental interest to lecturers and researchers and to teachers concerned with the classroom as a cultural phenomenon.

Science and Mathematics in Ancient Greek Culture

Author: Christopher Tuplin

Publisher: Oxford University Press on Demand

ISBN: 9780198152484

Category: History

Page: 379

View: 4581

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Ancient Greece was the birthplace of science, which developed in the Hellenized culture of ancient Rome. This book, written by seventeen international experts, examines the role and achievement of science and mathematics in Greek antiquity through discussion of the linguistic, literary, political, religious, sociological, and technological factors which influenced scientific thought and practice. It locates science within ancient Greek society and culture, investigates its impact upon that society, and identifies it as a cultural phenomenon deserving no less attention than literary or artistic creativity.

Geometrie des Universums

von der Göttlichen Komödie zu Riemann und Einstein

Author: Robert Osserman

Publisher: Springer-Verlag

ISBN: 9783528069025

Category: Mathematics

Page: 188

View: 2957

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Osserman erzählt lebendig und anschaulich eine Geschichte der Geometrie, von der Bestimmung der Erdgestalt und -größe durch die alten Griechen über das Problem der Kartierung der Weltkugel bis hin zur gekrümmten Raumzeit, den Fraktalen und Buckyballs. Viele wird überraschen, dass in der Mathematik nicht nur analytisches Denken zählt, sondern dass Imagination, Phantasie und Kreativität viel wichtiger sind. Dies und die Schönheit der Mathematik schlagen die Brücke zur Bildenden Kunst und Literatur, so nimmt Dante in seiner Göttlichen Komödie das Riemannsche Universum vorweg - zudem besteht eine frappante Analogie zwischen Dantes Göttlichem Licht und dem Urknall. Auch menschliche Aspekte kommen nicht zu kurz: Euler, Gauß und Riemann werden zum Beispiel als mathematische Entsprechungen von Bach, Beethoven und Brahms vorgestellt.