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Author: C. K. Raju Publisher: Pearson Education India ISBN: 9788131708712 Category : Calculus Languages : en Pages : 536
Book Description
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.
Author: C. K. Raju Publisher: Pearson Education India ISBN: 9788131708712 Category : Calculus Languages : en Pages : 536
Book Description
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.
Author: Raymond L. Wilder Publisher: Elsevier ISBN: 1483100618 Category : Social Science Languages : en Pages : 195
Book Description
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.
Author: Lynn Gamwell Publisher: Princeton University Press ISBN: 0691165289 Category : Art Languages : en Pages : 576
Book Description
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.
Author: E. Roy Weintraub Publisher: Duke University Press ISBN: 0822383802 Category : Business & Economics Languages : en Pages : 329
Book Description
In How Economics Became a Mathematical Science E. Roy Weintraub traces the history of economics through the prism of the history of mathematics in the twentieth century. As mathematics has evolved, so has the image of mathematics, explains Weintraub, such as ideas about the standards for accepting proof, the meaning of rigor, and the nature of the mathematical enterprise itself. He also shows how economics itself has been shaped by economists’ changing images of mathematics. Whereas others have viewed economics as autonomous, Weintraub presents a different picture, one in which changes in mathematics—both within the body of knowledge that constitutes mathematics and in how it is thought of as a discipline and as a type of knowledge—have been intertwined with the evolution of economic thought. Weintraub begins his account with Cambridge University, the intellectual birthplace of modern economics, and examines specifically Alfred Marshall and the Mathematical Tripos examinations—tests in mathematics that were required of all who wished to study economics at Cambridge. He proceeds to interrogate the idea of a rigorous mathematical economics through the connections between particular mathematical economists and mathematicians in each of the decades of the first half of the twentieth century, and thus describes how the mathematical issues of formalism and axiomatization have shaped economics. Finally, How Economics Became a Mathematical Science reconstructs the career of the economist Sidney Weintraub, whose relationship to mathematics is viewed through his relationships with his mathematician brother, Hal, and his mathematician-economist son, the book’s author.
Author: Raymond L. Wilder Publisher: Courier Corporation ISBN: 0486276201 Category : Mathematics Languages : en Pages : 354
Book Description
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.
Author: Eugene F. Provenzo, Jr. Publisher: SAGE Publications ISBN: 1452265976 Category : Education Languages : en Pages : 1393
Book Description
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
Author: Joshua David Diem Publisher: Cognella Academic Publishing ISBN: 9781631899119 Category : Education Languages : en Pages : 279
Book Description
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.
Author: Audun Holme Publisher: Springer Science & Business Media ISBN: 3662047209 Category : Mathematics Languages : en Pages : 384
Book Description
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.
Author: Raymond L. Wilder Publisher: Courier Corporation ISBN: 0486490610 Category : Mathematics Languages : en Pages : 242
Book Description
Accessible to students and relevant to specialists, this remarkable book by a prominent educator offers a unique perspective on the evolutionary development of mathematics. Rather than conducting a survey of the history or philosophy of mathematics, Raymond L. Wilder envisions mathematics as a broad cultural phenomenon. His treatment examines and illustrates how such concepts as number and length were affected by historic and social events. Starting with a brief consideration of preliminary notions, this study explores the early evolution of numbers, the evolution of geometry, and the conquest of the infinite as embodied by real numbers. A detailed look at the processes of evolution concludes with an examination of the evolutionary aspects of modern mathematics.
Author: C. K. Raju
Author: C. K. Raju
Author: Raymond L. Wilder
Author: Jin Li
Author: Lynn Gamwell
Author: E. Roy Weintraub
Author: Raymond L. Wilder
Author: Eugene F. Provenzo, Jr.
Author: Joshua David Diem
Author: Audun Holme
Author: Raymond L. Wilder