Cultural Foundations Of Mathematics

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Cultural Foundations of Mathematics

C. K. Raju
Cultural Foundations of Mathematics Book PDF

Author : C. K. Raju
Publisher : Pearson Education India
Page : 536 pages
File Size : 53,7 Mb
Release : 2007
Category : Calculus
ISBN : 8131708713

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Cultural Foundations of Mathematics by C. K. Raju Pdf

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.

Cultural Foundations of Learning

Jin Li
Cultural Foundations of Learning Book PDF

Author : Jin Li
Publisher : Cambridge University Press
Page : 401 pages
File Size : 51,9 Mb
Release : 2012-03-26
Category : Education
ISBN : 9780521768290

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Cultural Foundations of Learning by Jin Li Pdf

Describes fundamental differences in learning beliefs between the Western mind model and the East Asian virtue model of learning.

Mathematics and Art

Lynn Gamwell
Mathematics and Art Book PDF

Author : Lynn Gamwell
Publisher : Princeton University Press
Page : 576 pages
File Size : 53,5 Mb
Release : 2016
Category : Art
ISBN : 9780691165288

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Mathematics and Art by Lynn Gamwell Pdf

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 as a Cultural System

Raymond L. Wilder
Mathematics as a Cultural System Book PDF

Author : Raymond L. Wilder
Publisher : Elsevier
Page : 194 pages
File Size : 40,6 Mb
Release : 2014-05-20
Category : Political Science
ISBN : 9781483100616

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Mathematics as a Cultural System by Raymond L. Wilder Pdf

Mathematics as a Cultural System discusses the relationship between mathematics and culture. The book is comprised of eight chapters discussing topics that support the concept of mathematics as a cultural system. Chapter I deals with the nature of culture and cultural systems, while Chapter 2 provides examples of cultural patterns observable in the evolution of mechanics. Chapter III treats historical episodes as a laboratory for the illustration of patterns and forces that have been operative in cultural change. Chapter IV covers hereditary stress, and Chapter V discusses consolidation as a force and process. Chapter VI talks about the singularities in the evolution of mechanics, while Chapter 7 deals with the laws governing the evolution of mathematics. Chapter VIII tackles the role and future of mathematics. The book will be of great interest to readers who are curious about how mathematics relates to culture.

Introduction to the Foundations of Mathematics

Raymond L. Wilder
Introduction to the Foundations of Mathematics Book PDF

Author : Raymond L. Wilder
Publisher : Courier Corporation
Page : 352 pages
File Size : 52,9 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486276205

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Introduction to the Foundations of Mathematics by Raymond L. Wilder Pdf

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Encyclopedia of the Social and Cultural Foundations of Education

Eugene F. Provenzo, Jr.
Encyclopedia of the Social and Cultural Foundations of Education Book PDF

Author : Eugene F. Provenzo, Jr.
Publisher : SAGE Publications
Page : 1392 pages
File Size : 54,9 Mb
Release : 2008-10-29
Category : Education
ISBN : 9781452265971

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Encyclopedia of the Social and Cultural Foundations of Education by Eugene F. Provenzo, Jr. Pdf

More than any other field in education, the social and cultural foundations of education reflect many of the conflicts, tensions, and forces in American society. This is hardly surprising, since the area focuses on issues such as race, gender, socioeconomic class, the impact of technology on learning, what it means to be educated, and the role of teaching and learning in a societal context. The Encyclopedia of the Social and Cultural Foundations of Education provides a comprehensive introduction to the social and cultural foundations of education. With more than 400 entries, the three volumes of this indispensable resource offer a thorough and interdisciplinary view of the field for all those interested in issues involving schools and society. Key Features · Provides an interdisciplinary perspective from areas such as comparative education, educational anthropology, educational sociology, the history of education, and the philosophy of education · Presents essays on major movements in the field, including the Free School and Visual Instruction movements · Includes more than 130 biographical entries on important men and women in education · Offers interpretations of legal material including Brown v. Board of Education(1954) and the GI Bill of Rights · Explores theoretical debates fundamental to the field such as religion in the public school curriculum, rights of students and teachers, surveillance in schools, tracking and detracking, and many more · Contains a visual history of American education with nearly 350 images and an accompanying narrative Key Themes · Arts, Media, and Technology · Curriculum · Economic Issues · Equality and Social Stratification · Evaluation, Testing, and Research Methods · History of Education · Law and Public Policy · Literacy · Multiculturalism and Special Populations · Organizations, Schools, and Institutions · Religion and Social Values · School Governance · Sexuality and Gender · Teachers · Theories, Models, and Philosophical Perspectives · A Visual History of American Education

The Eleven Pictures of Time

C K Raju
The Eleven Pictures of Time Book PDF

Author : C K Raju
Publisher : SAGE Publications India
Page : 590 pages
File Size : 47,5 Mb
Release : 2003-09-11
Category : Social Science
ISBN : 9788132102854

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The Eleven Pictures of Time by C K Raju Pdf

`Magnificent, a true magnum opus....A tremendously important piece of work.... A truly revolutionary book (not merely an excellent book)' - Arun Ghosh Time is a mystery that has perplexed humankind since time immemorial. Resolving this mystery is of significance not only to philosophers and physicists but is also a very practical concern. Our perception of time shapes our values and way of life; it also mediates the interaction between science and religion both of which rest fundamentally on assumptions about the nature of time. C K Raju begins with a critical exposition of various time-beliefs, ranging from the earliest times through Augustine, Newton and Einstein to Stephen Hawking and current notions of chaos and time travel. He traces the role of organised religion in subverting time beliefs for its political ends. The book points out how this resulted in a facile dichotomy between 'linear' and 'cyclic' time, thereby inaugurating a confusion which, according to the author, has handicapped Western thought ever since, eventually influencing the content of science itself. Thus, this book daringly asserts that physical theory, traditionally regarded as amoral and objective, has depended on cultural beliefs about time. The author points out that time beliefs are again being manipulated today as the credibility of science is being exploited to promote a picture of time and, hence, a pattern of human behaviour which is convenient to the agenda of globalisation of culture. The linkages between modern theology and this 'brave new physics' are traced against the wider context of the so-called 'clash of civilisations', and the attempts to remake the world order. The conclusions point to the need to de-theologise time. The author challenges Einstein's understanding of relativity theory and suggests that a 'tilt in the arrow of time', or a small tendency towards cyclicity, will help repair the prevalent confusion about time. A 'tilt' also enables a physics that permits both memory and creativity, so that purpose and spontaneous growth of order are returned to human life. The book ends with a vision of Man as Creator, surprising God. Extensive research in physics, the history of science, comparative religions, and sociology lend weight to the important and challenging conclusions reached by the author. Written as a rejoinder to Stephen Hawking's A Brief History of Time, this book goes much further and, unlike any previous book, it gives a critical exposition of various world religions-Buddhism, Christianity, Hinduism, Islam, and Jainism-while exploring their intricate links, through time beliefs, to current physics on the one hand, and to global political and economic trends, on the other. This book will appeal to scholars and laypersons equally. It will fascinate anyone who reads it and will teach its readers to question the unquestionable.

Ethnomathematics

Arthur B. Powell,Marilyn Frankenstein
Ethnomathematics Book PDF

Author : Arthur B. Powell,Marilyn Frankenstein
Publisher : SUNY Press
Page : 466 pages
File Size : 42,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 079143351X

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Ethnomathematics by Arthur B. Powell,Marilyn Frankenstein Pdf

Presents the emerging field of ethnomathematics from a critical perspective, challenging particular ways in which Eurocentrism permeates mathematics education and mathematics in general.

The Social and Cultural Foundations of Education

Joshua Diem
The Social and Cultural Foundations of Education Book PDF

Author : Joshua Diem
Publisher : Unknown
Page : 296 pages
File Size : 52,8 Mb
Release : 2015-12-10
Category : Electronic
ISBN : 1516555082

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The Social and Cultural Foundations of Education by Joshua Diem Pdf

The essays in The Social and Cultural Foundations of Education: A Reader initiate conversations on fundamental cultural and social topics that are also integral issues in education today. Each selection was chosen because it offers a unique perspective that encourages readers to think about familiar subject matter in new ways. The topics addressed are as diverse as the authors. They include the role that race and racism still play in society, how the climate crisis is being dealt with, the fluid nature of gender and sexuality, and how popular culture offers profoundly important representations into who and what we are as a culture today. Designed to shine a light on present-day dilemmas, The Social and Cultural Foundations of Education: A Reader presents work that may well join the lineage of seminal writing in the discipline. The anthology was designed as a companion text for undergraduate courses in educational foundations, and is also an excellent supplemental reader for classes in social and cultural anthropology and sociology.

Mathematical Enculturation

Alan Bishop
Mathematical Enculturation Book PDF

Author : Alan Bishop
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789400926578

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Mathematical Enculturation by Alan Bishop Pdf

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.

What Is Mathematics, Really?

Reuben Hersh
What Is Mathematics Really Book PDF

Author : Reuben Hersh
Publisher : Oxford University Press
Page : 368 pages
File Size : 41,6 Mb
Release : 1997-08-21
Category : Mathematics
ISBN : 9780198027362

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What Is Mathematics, Really? by Reuben Hersh Pdf

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Time: Towards a Consistent Theory

C.K. Raju
Time Towards a Consistent Theory Book PDF

Author : C.K. Raju
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 51,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9789401583763

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Time: Towards a Consistent Theory by C.K. Raju Pdf

Is time, even locally, like the real line? Multiple structures of time, implicit in physics, create a consistency problem. A tilt in the arrow of time is suggested as the most conservative hypothesis which provides approximate consistency within physics and with topology of mundane time. Mathematically, the assumed constancy of the velocity of light (needed to measure time) implies functional differential equations of motion, that have both retarded and advanced deviating arguments with the hypothesis of a tilt. The novel features of such equations lead to a nontrivial structure of time and quantum-mechanical behaviour. The entire argument is embedded in a pedagogical exposition which amplifies, corrects, and questions the conventionally accepted approach. The exposition includes historical details and explains, for instance, why the entropy law is inadequate for time asymmetry, and why notions such as time asymmetry (hence causality) may be conceptually inadequate. The first three parts of the book are especially suited as supplementary reading material for undergraduate and graduate students and teachers of physics. The new ideas are addressed to researchers in physics and philosophy of science concerned with relativity and the interpretation of quantum mechanics.

Geometry

Audun Holme
Geometry Book PDF

Author : Audun Holme
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 42,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662047200

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Geometry by Audun Holme Pdf

Mathematics is more important than ever, but phrases like "math avoidance" and "math anxiety" are very much in the public vocabulary. In addition to providing an invitation to mathematics in general, this book emphasizes the dynamic character of geometry and its role as part of the foundation for our cultural heritage. Aimed at an informed public and future teachers of mathematics, it seeks to heal the ills of math phobia in society.

Mathematical Foundations of Information Theory

Aleksandr I?Akovlevich Khinchin
Mathematical Foundations of Information Theory Book PDF

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 130 pages
File Size : 44,8 Mb
Release : 1957-01-01
Category : Mathematics
ISBN : 9780486604343

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Mathematical Foundations of Information Theory by Aleksandr I?Akovlevich Khinchin Pdf

First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.

Mathematical Foundations of Statistical Mechanics

Aleksandr I?Akovlevich Khinchin
Mathematical Foundations of Statistical Mechanics Book PDF

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 212 pages
File Size : 49,7 Mb
Release : 1949-01-01
Category : Mathematics
ISBN : 0486601471

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Mathematical Foundations of Statistical Mechanics by Aleksandr I?Akovlevich Khinchin Pdf

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.