Mathematics in Western Culture

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 9780195345452

Category: Mathematics

Page: 512

View: 5010

DOWNLOAD NOW »
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.

Mathematics in Western Culture

Author: Morris Kline

Publisher: New York : Oxford University Press

ISBN: 019500714X

Category: Literary Criticism

Page: 484

View: 445

DOWNLOAD NOW »
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.

Mathematics in Western Culture

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 0190281138

Category: Mathematics

Page: 512

View: 8049

DOWNLOAD NOW »
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.

Mathematics for the Nonmathematician

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486316130

Category: Mathematics

Page: 672

View: 5751

DOWNLOAD NOW »
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 Across Cultures

The History of Non-Western Mathematics

Author: Helaine Selin

Publisher: Springer Science & Business Media

ISBN: 9401143013

Category: Mathematics

Page: 479

View: 9244

DOWNLOAD NOW »
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.

Mathematics and the Physical World

Author: Morris Kline

Publisher: Courier Corporation

ISBN: 0486136310

Category: Mathematics

Page: 512

View: 6501

DOWNLOAD NOW »
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Euclid—The Creation of Mathematics

Author: Benno Artmann

Publisher: Springer Science & Business Media

ISBN: 1461214122

Category: Mathematics

Page: 349

View: 4197

DOWNLOAD NOW »
Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.

Mathematics and Art

A Cultural History

Author: Lynn Gamwell

Publisher: Princeton University Press

ISBN: 0691165289

Category: Art

Page: 576

View: 5089

DOWNLOAD NOW »
This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked “What is art?” in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.

Mathematics Elsewhere

An Exploration of Ideas Across Cultures

Author: Marcia Ascher

Publisher: Princeton University Press

ISBN: 0691187649

Category: Mathematics

Page: N.A

View: 9799

DOWNLOAD NOW »
Mathematics Elsewhere is a fascinating and important contribution to a global view of mathematics. Presenting mathematical ideas of peoples from a variety of small-scale and traditional cultures, it humanizes our view of mathematics and expands our conception of what is mathematical. Through engaging examples of how particular societies structure time, reach decisions about the future, make models and maps, systematize relationships, and create intriguing figures, Marcia Ascher demonstrates that traditional cultures have mathematical ideas that are far more substantial and sophisticated than is generally acknowledged. Malagasy divination rituals, for example, rely on complex algebraic algorithms. And some cultures use calendars far more abstract and elegant than our own. Ascher also shows that certain concepts assumed to be universal--that time is a single progression, for instance, or that equality is a static relationship--are not. The Basque notion of equivalence, for example, is a dynamic and temporal one not adequately captured by the familiar equal sign. Other ideas taken to be the exclusive province of professionally trained Western mathematicians are, in fact, shared by people in many societies. The ideas discussed come from geographically varied cultures, including the Borana and Malagasy of Africa, the Tongans and Marshall Islanders of Oceania, the Tamil of South India, the Basques of Western Europe, and the Balinese and Kodi of Indonesia. This book belongs on the shelves of mathematicians, math students, and math educators, and in the hands of anyone interested in traditional societies or how people think. Illustrating how mathematical ideas play a vital role in diverse human endeavors from navigation to social interaction to religion, it offers--through the vehicle of mathematics--unique cultural encounters to any reader.

The Mathematics of Egypt, Mesopotamia, China, India, and Islam

A Sourcebook

Author: Victor J. Katz

Publisher: Princeton University Press

ISBN: 9780691114859

Category: Mathematics

Page: 685

View: 5934

DOWNLOAD NOW »
In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.

Visual Culture and Mathematics in the Early Modern Period

Author: Ingrid Alexander-Skipnes

Publisher: Taylor & Francis

ISBN: 1317192060

Category: Art

Page: 204

View: 4066

DOWNLOAD NOW »
During the early modern period there was a natural correspondence between how artists might benefit from the knowledge of mathematics and how mathematicians might explore, through advances in the study of visual culture, new areas of enquiry that would uncover the mysteries of the visible world. This volume makes its contribution by offering new interdisciplinary approaches that not only investigate perspective but also examine how mathematics enriched aesthetic theory and the human mind. The contributors explore the portrayal of mathematical activity and mathematicians as well as their ideas and instruments, how artists displayed their mathematical skills and the choices visual artists made between geometry and arithmetic, as well as Euclid’s impact on drawing, artistic practice and theory. These chapters cover a broad geographical area that includes Italy, Switzerland, Germany, the Netherlands, France and England. The artists, philosophers and mathematicians whose work is discussed include Leon Battista Alberti, Nicholas Cusanus, Marsilio Ficino, Francesco di Giorgio, Leonardo da Vinci and Andrea del Verrocchio, as well as Michelangelo, Galileo, Piero della Francesca, Girard Desargues, William Hogarth, Albrecht Dürer, Luca Pacioli and Raphael.

Mathematics

The Loss of Certainty

Author: Morris Kline

Publisher: Oxford University Press, USA

ISBN: 9780195030853

Category: Mathematics

Page: 366

View: 7104

DOWNLOAD NOW »
Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences

A Beautiful Math

John Nash, Game Theory, and the Modern Quest for a Code of Nature

Author: Tom Siegfried

Publisher: National Academies Press

ISBN: 9780309133807

Category: Science

Page: 272

View: 4163

DOWNLOAD NOW »
Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

Inventing the Mathematician

Gender, Race, and Our Cultural Understanding of Mathematics

Author: Sara N. Hottinger

Publisher: SUNY Press

ISBN: 1438460112

Category: Mathematics

Page: 192

View: 4642

DOWNLOAD NOW »
Considers how our ideas about mathematics shape our individual and cultural relationship to the field. Where and how do we, as a culture, get our ideas about mathematics and about who can engage with mathematical knowledge? Sara N. Hottinger uses a cultural studies approach to address how our ideas about mathematics shape our individual and cultural relationship to the field. She considers four locations in which representations of mathematics contribute to our cultural understanding of mathematics: mathematics textbooks, the history of mathematics, portraits of mathematicians, and the field of ethnomathematics. Hottinger examines how these discourses shape mathematical subjectivity by limiting the way some groups—including women and people of color—are able to see themselves as practitioners of math. Inventing the Mathematician provides a blueprint for how to engage in a deconstructive project, revealing the limited and problematic nature of the normative construction of mathematical subjectivity.

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: 7975

DOWNLOAD NOW »
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.

Language and Culture in Mathematical Cognition

Author: Daniel B. Berch,David C. Geary,Kathleen Mann Koepke

Publisher: Academic Press

ISBN: 0128125756

Category: Psychology

Page: 364

View: 5670

DOWNLOAD NOW »
Language and Culture in Mathematical Cognition, Fourth Edition focuses on the role of linguistic and cultural factors in math cognition and development. It covers a wide range of topics, including analogical mapping in numerical development, arithmetic fact retrieval in the bilingual brain, cross-cultural comparisons of mathematics achievement, the shaping of numerical processing by number word construction, the influence of Head Start programs, the mathematical skills of children with specific language impairments, the role of culture and language in creating associations between number and space, and electrophysiological studies of linguistic traces in core knowledge at the neural level. Includes cutting-edge findings, innovative measures, recent methodological advances and groundbreaking theoretical developments Synthesizes research from various subdomains of math cognition research Covers the full complement of research in mathematical thinking and learning Informs researchers, scholars, educators, students and policymakers

Sacred Mathematics

Japanese Temple Geometry

Author: Hidetoshi Fukagawa,Tony Rothman

Publisher: Princeton University Press

ISBN: 9780691127453

Category: Art

Page: 348

View: 323

DOWNLOAD NOW »
"An enchanting history of Japanese geometry--of a time and place where 'geometers did not cede place to poets.' This intersection of science and culture, of the mathematical, the artistic, and the spiritual, is packed, like circles within circles, with rewarding Aha! epiphanies that drive a mathematician's curiosity."--Siobhan Roberts, author of "King of Infinite Space" "Teachers will welcome this remarkable collection of mathematical problems, history, and art, which will enrich their curriculum and promote both logical thinking and critical evaluation. It is especially important that we maintain an interest in geometry, which needs, and for once gets, more than its share."--Richard Guy, coauthor of "The Book of Numbers" "This remarkable book provides a novel insight into the Japanese mathematics of the past few hundred years. It is fascinating to see the difference in mathematical style from that which we are used to in the Western world, but the book also elegantly illustrates the cross-cultural Platonic nature and profound beauty of mathematics itself."--Roger Penrose, author of "The Road to Reality" "A significant contribution to the history of mathematics. The wealth of mathematical problems--from the very simple to quite complex ones--will keep the interested reader busy for years. And the beautiful illustrations make this book a work of art as much as of science. Destined to become a classic!"--Eli Maor, author of "The Pythagorean Theorem: A 4,000-Year History" "A pleasure to read. "Sacred Mathematics" brings to light the unique style and character of geometry in the traditional Japanese sources--in particular the "sangaku" problems. These problems range from trivial to utterly devilish. I found myself captivated by them, and regularly astounded by the ingenuity and sophistication of many of the traditional solutions."--Glen Van Brummelen, coeditor of "Mathematics and the Historian's Craft"

Zombies in Western Culture

A Twenty-First Century Crisis

Author: John Vervaeke,Christopher Mastropietro,Filip Miscevic

Publisher: Open Book Publishers

ISBN: 178374331X

Category: Social Science

Page: 104

View: 4323

DOWNLOAD NOW »
Why has the zombie become such a pervasive figure in twenty-first-century popular culture? John Vervaeke, Christopher Mastropietro and Filip Miscevic seek to answer this question by arguing that particular aspects of the zombie, common to a variety of media forms, reflect a crisis in modern Western culture. The authors examine the essential features of the zombie, including mindlessness, ugliness and homelessness, and argue that these reflect the outlook of the contemporary West and its attendant zeitgeists of anxiety, alienation, disconnection and disenfranchisement. They trace the relationship between zombies and the theme of secular apocalypse, demonstrating that the zombie draws its power from being a perversion of the Christian mythos of death and resurrection. Symbolic of a lost Christian worldview, the zombie represents a world that can no longer explain itself, nor provide us with instructions for how to live within it. The concept of 'domicide' or the destruction of home is developed to describe the modern crisis of meaning that the zombie both represents and reflects. This is illustrated using case studies including the relocation of the Anishinaabe of the Grassy Narrows First Nation, and the upheaval of population displacement in the Hellenistic period. Finally, the authors invoke and reformulate symbols of the four horseman of the apocalypse as rhetorical analogues to frame those aspects of contemporary collapse that elucidate the horror of the zombie. Zombies in Western Culture: A Twenty-First Century Crisis is required reading for anyone interested in the phenomenon of zombies in contemporary culture. It will also be of interest to an interdisciplinary audience including students and scholars of culture studies, semiotics, philosophy, religious studies, eschatology, anthropology, Jungian studies, and sociology.

The Artist and the Mathematician

Author: Amir D. Aczel

Publisher: Basic Books

ISBN: 0786732881

Category: Mathematics

Page: 256

View: 7353

DOWNLOAD NOW »
Nicolas Bourbaki, whose mathematical publications began to appear in the late 1930s and continued to be published through most of the twentieth century, was a direct product as well as a major force behind an important revolution that took place in the early decades of the twentieth century that completely changed Western culture. Pure mathematics, the area of Bourbaki's work, seems on the surface to be an abstract field of human study with no direct connection with the real world. In reality, however, it is closely intertwined with the general culture that surrounds it. Major developments in mathematics have often followed important trends in popular culture; developments in mathematics have acted as harbingers of change in the surrounding human culture. The seeds of change, the beginnings of the revolution that swept the Western world in the early decades of the twentieth century — both in mathematics and in other areas — were sown late in the previous century. This is the story both of Bourbaki and the world that created him in that time. It is the story of an elaborate intellectual joke — because Bourbaki, one of the foremost mathematicians of his day — never existed.

Mathematics in Early Years Education

Author: Ann Montague-Smith,Tony Cotton,Alice Hansen,Alison J. Price

Publisher: Routledge

ISBN: 1351745115

Category: Education

Page: 274

View: 3164

DOWNLOAD NOW »
This fourth edition of the bestselling Mathematics in Early Years Education provides an accessible introduction to the teaching of mathematics in the early years. Covering all areas of mathematics – number and counting, calculation, pattern, shape, measures and data handling – it provides a wide range of practical activities and guidance on how to support young children’s mathematical development. There is also guidance on managing the transition to KS1 and a strong emphasis throughout on creating home links and working in partnership with parents. This new edition has been fully updated to incorporate the latest research and thinking in this area and includes: why mathematics is important as a way of making sense of the world how attitudes to mathematics can influence teaching and learning how children learn mathematics and what they are capable of learning how technology can support maths teaching maths phobia and the impact society has on maths teaching material on sorting, matching and handling data the importance of educating about finance in today’s world ideas for observation and questioning to assess children’s understanding examples of planned activities suggestions for language development assessment criteria. This textbook is ideal for those training to be teachers through an undergraduate or PGCE route, those training for Early Years Professional Status and those studying early childhood on foundation or honours degrees, as well as parents looking to explore how their young children learn mathematics. This will be an essential text for any early years practitioner looking to make mathematics interesting, exciting and engaging in their classroom.