Revolutions In Mathematics

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Revolutions in Mathematics

Author : Donald Gillies
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198514862
Total Pages : 353 pages
Book Rating : 4.5/5 (148 download)

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Book Synopsis Revolutions in Mathematics by : Donald Gillies

Download or read book Revolutions in Mathematics written by Donald Gillies and published by Oxford University Press on Demand. This book was released on 1995 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essays in this book provide the first comprehensive treatment of the concept of revolution in mathematics. In 1962 an exciting discussion of revolutions in the natural sciences was prompted by the publication of Kuhn's The Structure of Scientific Revolutions. A fascinating but little knownoffshoot of this debate was begun in the USA in the mid-1970s: can the concept of revolutions be applied to mathematics as well as science? Michael Crowe declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave someexamples.The original papers of Crowe, Dauben, and Mehrtens are reprinted in this book, together with additional chapters giving their current views. To this are added new contributions from nine further experts in the history of mathematics who each discuss an important episode and consider whether it was arevolution.This book is an excellent reference work and an ideal course text for both graduate and undergraduate courses in the history and philosophy of science and mathematics.

Revolutions and Continuity in Greek Mathematics

Author : Michalis Sialaros
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110565277
Total Pages : 401 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Revolutions and Continuity in Greek Mathematics by : Michalis Sialaros

Download or read book Revolutions and Continuity in Greek Mathematics written by Michalis Sialaros and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-23 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.

Changing Images in Mathematics

Author : Umberto Bottazini
Publisher : Routledge
ISBN 13 : 113469881X
Total Pages : 318 pages
Book Rating : 4.1/5 (346 download)

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Book Synopsis Changing Images in Mathematics by : Umberto Bottazini

Download or read book Changing Images in Mathematics written by Umberto Bottazini and published by Routledge. This book was released on 2013-06-17 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on some of the major developments in the history of contemporary (19th and 20th century) mathematics as seen in the broader context of the development of science and culture. Avoiding technicalities, it displays the breadth of contrasting images of mathematics favoured by different countries, schools and historical movements, showing how the conception and practice of mathematics changed over time depending on the cultural and national context. Thus it provides an original perspective for embracing the richness and variety inherent in the development of mathematics. Attention is paid to the interaction of mathematics with themes whose proper treatment have been neglected by the traditional historiography of the discipline, such as the relationship between mathematics, statistics and medicine.

The mathematical revolution inspired by computing

Author : J. H. Johnson
Publisher :
ISBN 13 :
Total Pages : 329 pages
Book Rating : 4.:/5 (19 download)

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Book Synopsis The mathematical revolution inspired by computing by : J. H. Johnson

Download or read book The mathematical revolution inspired by computing written by J. H. Johnson and published by . This book was released on 1991 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Philosophy of Mathematics and Natural Laws

Author : Noel Curran
Publisher : Routledge
ISBN 13 : 0429808089
Total Pages : 208 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis The Philosophy of Mathematics and Natural Laws by : Noel Curran

Download or read book The Philosophy of Mathematics and Natural Laws written by Noel Curran and published by Routledge. This book was released on 2019-07-23 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1997, this title is a sequel to Dr Noel Curran's first book The Logical Universe: The Real Universe (published by Ashgate under the Avebury imprint, 1994). The philosophy of mathematics in this book is based on ideas of Sir William Rowan Hamilton on the ordinal character of numbers, the real numbers, the measure numbers, scalar numbers and the extension to vectors. The final extension is to Hamilton’s quaternions. This algebra is interpreted as the mathematics of spin. This led to a a new theory of time and space which is Euclidian. The motion of spin is absolute, no frame of reference is required. If time is assumed to have a beginning it would be asymmetric with an arrow. This concept is applied to the laws of nature, which are symmetrical. This is another Copernican Revolution in three aspects: absolute time is restored, time has an arrow - is asymmetric, and thirdly the theory is based on the motion of spin which is absolute and more fundamental than the motion of translation. This opens the way to the final unification of physics.

Revolutions in Differential Equations

Author : M. J. Kallaher
Publisher : Cambridge University Press
ISBN 13 : 9780883851609
Total Pages : 108 pages
Book Rating : 4.8/5 (516 download)

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Book Synopsis Revolutions in Differential Equations by : M. J. Kallaher

Download or read book Revolutions in Differential Equations written by M. J. Kallaher and published by Cambridge University Press. This book was released on 1999-11-11 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the direction in which the field of differential equations, and its teaching, is going.

Circularity

Author : Ron Aharoni
Publisher : World Scientific
ISBN 13 : 9814723703
Total Pages : 180 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Circularity by : Ron Aharoni

Download or read book Circularity written by Ron Aharoni and published by World Scientific. This book was released on 2016-04-21 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Circularity" is the story of a Janus-faced conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question "What is humor". The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct. See Press Release: Vicious circles -- confusing, instructive, amusing? Contents:The Dark Side — Paradoxes:MagicFree WillThe Mind–Body ProblemThe Illuminated Side — Scientific Breakthroughs:Large Infinities and Still Larger OnesGödel's Incompleteness TheoremTuring Invents the ComputerFor the Experienced Hikers Readership: Researchers in mathematics, philosophy and general public.

Revolutions of Geometry

Author : Michael L. O'Leary
Publisher : John Wiley & Sons
ISBN 13 : 047059179X
Total Pages : 608 pages
Book Rating : 4.4/5 (75 download)

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Book Synopsis Revolutions of Geometry by : Michael L. O'Leary

Download or read book Revolutions of Geometry written by Michael L. O'Leary and published by John Wiley & Sons. This book was released on 2010-02-22 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Guides readers through the development of geometry and basic proof writing using a historical approach to the topic In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems. Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries. The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics. Well organized and clearly written, Revolutions of Geometry is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.

Recent Revolutions in Mathematics

Author : Albert Stwertka
Publisher : Franklin Watts
ISBN 13 : 9780531104187
Total Pages : 111 pages
Book Rating : 4.1/5 (41 download)

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Book Synopsis Recent Revolutions in Mathematics by : Albert Stwertka

Download or read book Recent Revolutions in Mathematics written by Albert Stwertka and published by Franklin Watts. This book was released on 1987 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys new theories and research in the field of mathematics, discussing such topics as non-Euclidean geometry, fractals, chaos, and Godel's proof.

Critical Issues in Mathematics Education

Author : Philip Clarkson
Publisher : Springer Science & Business Media
ISBN 13 : 0387096736
Total Pages : 252 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Critical Issues in Mathematics Education by : Philip Clarkson

Download or read book Critical Issues in Mathematics Education written by Philip Clarkson and published by Springer Science & Business Media. This book was released on 2008-09-22 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critical Issues in Mathematics Education presents the significant contributions of Professor Alan Bishop within the mathematics education research community. Six critical issues, each of which have had paramount importance in the development of mathematics education research, are reviewed and include a discussion of current developments in each area. Teacher decision making, spatial/visualizing geometry, teachers and research, cultural/social aspects of mathematics education, sociopolitical issues, and values serve as the basic issues discussed in this examination of mathematics education over the last fifty years during which Professor Bishop has been active in the field. A comprehensive discussion of each of these topics is realized by offering the reader a classic research contribution of Professor Bishop’s together with commentary and invited chapters from leading experts in the field of mathematics education. Critical Issues in Mathematics Education will make an invaluable contribution to the ongoing reflection of mathematic education researchers worldwide, but also to policy makers and teacher educators who wish to understand some of the key issues with which mathematics education has been and still is concerned, and the context within which Professor Bishop’s key contributions to these research issues were made.

The Making of Mathematics

Author : Carlo Cellucci
Publisher : Springer Nature
ISBN 13 : 3030897311
Total Pages : 457 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis The Making of Mathematics by : Carlo Cellucci

Download or read book The Making of Mathematics written by Carlo Cellucci and published by Springer Nature. This book was released on 2022-03-07 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.

The Kuhnian Image of Science

Author : Moti Mizrahi
Publisher : Rowman & Littlefield
ISBN 13 : 178660342X
Total Pages : 224 pages
Book Rating : 4.7/5 (866 download)

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Book Synopsis The Kuhnian Image of Science by : Moti Mizrahi

Download or read book The Kuhnian Image of Science written by Moti Mizrahi and published by Rowman & Littlefield. This book was released on 2017-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than 50 years after the publication of Thomas Kuhn’s seminal book, The Structure of Scientific Revolutions, this volume assesses the adequacy of the Kuhnian model in explaining certain aspects of science, particularly the social and epistemic aspects of science. One argument put forward is that there are no good reasons to accept Kunh’s incommensurability thesis, according to which scientific revolutions involve the replacement of theories with conceptually incompatible ones. Perhaps, therefore, it is time for another “decisive transformation in the image of science by which we are now possessed.” Only this time, the image of science that needs to be transformed is the Kuhnian one. Does the Kuhnian image of science provide an adequate model of scientific practice? If we abandon the Kuhnian picture of revolutionary change and incommensurability, what consequences would follow from that vis-à-vis our understanding of scientific knowledge as a social endeavour? The essays in this collection continue this debate, offering a critical examination of the arguments for and against the Kuhnian image of science as well as their implications for our understanding of science as a social and epistemic enterprise.

Revolution in Science

Author : I. Bernard Cohen
Publisher : Harvard University Press
ISBN 13 : 9780674767782
Total Pages : 742 pages
Book Rating : 4.7/5 (677 download)

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Book Synopsis Revolution in Science by : I. Bernard Cohen

Download or read book Revolution in Science written by I. Bernard Cohen and published by Harvard University Press. This book was released on 1985 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohen's exploration seeks to uncover nothing less than the nature of all scientific revolutions, the stages by which they occur, their time scale, specific criteria for determining whether or not there has been a revolution, and the creative factors in producing a revolutionary new idea.

The Mathematics of Life

Author : Ian Stewart
Publisher : Basic Books
ISBN 13 : 0465024408
Total Pages : 368 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis The Mathematics of Life by : Ian Stewart

Download or read book The Mathematics of Life written by Ian Stewart and published by Basic Books. This book was released on 2011-06-07 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world -- and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world -- and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.

Conceptual Revolutions

Author : Wenceslao J. González
Publisher : Netbiblo
ISBN 13 : 8497459334
Total Pages : 266 pages
Book Rating : 4.4/5 (974 download)

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Book Synopsis Conceptual Revolutions by : Wenceslao J. González

Download or read book Conceptual Revolutions written by Wenceslao J. González and published by Netbiblo. This book was released on 2011 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Changing Images in Mathematics

Author : Umberto Bottazini
Publisher : Routledge
ISBN 13 : 1134698747
Total Pages : 305 pages
Book Rating : 4.1/5 (346 download)

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Book Synopsis Changing Images in Mathematics by : Umberto Bottazini

Download or read book Changing Images in Mathematics written by Umberto Bottazini and published by Routledge. This book was released on 2013-06-17 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on some of the major developments in the history of contemporary (19th and 20th century) mathematics as seen in the broader context of the development of science and culture. Avoiding technicalities, it displays the breadth of contrasting images of mathematics favoured by different countries, schools and historical movements, showing how the conception and practice of mathematics changed over time depending on the cultural and national context. Thus it provides an original perspective for embracing the richness and variety inherent in the development of mathematics. Attention is paid to the interaction of mathematics with themes whose proper treatment have been neglected by the traditional historiography of the discipline, such as the relationship between mathematics, statistics and medicine.

The History of Mathematics: A Source-Based Approach: Volume 1

Author : June Barrow-Green
Publisher : American Mathematical Soc.
ISBN 13 : 147044352X
Total Pages : 488 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The History of Mathematics: A Source-Based Approach: Volume 1 by : June Barrow-Green

Download or read book The History of Mathematics: A Source-Based Approach: Volume 1 written by June Barrow-Green and published by American Mathematical Soc.. This book was released on 2019-05-08 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the first volume of the two-volume set, takes readers from the beginning of counting in prehistory to 1600 and the threshold of the discovery of calculus. It is notable for the extensive engagement with original—primary and secondary—source material. The coverage is worldwide, and embraces developments, including education, in Egypt, Mesopotamia, Greece, China, India, the Islamic world and Europe. The emphasis on astronomy and its historical relationship to mathematics is new, and the presentation of every topic is informed by the most recent scholarship in the field. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.