*First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.*

**Author**: Ivor Grattan-Guiness

**Publisher:** Routledge

**ISBN:** 9781134887484

**Category:** History

**Page:** 856

**View:** 813

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First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
"First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company."--Provided by publisher.
First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
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: Â•Ancient and Non-Western Traditions Â•The Western Middle Ages and the Renaissance Â•Calculus and Mathematical Analysis Â•Functions, Series, and Methods in Analysis Â•Logic, Set Theories, and the Foundations of Mathematics Â•Algebras and Number Theory Contents of Volume 2: Â•Geometries and Topology Â•Mechanics and Mechanical Engineering Â•Physics, Mathematical Physics, and Electrical Engineering Â•Probability, Statistics, and the Social Sciences Â•Higher Education and Institutions Â•Mathematics and Culture Â•Select Bibliography, Chronology, Biographical Notes, and Index
From the Calculus to Set Theory traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and the foundations of mathematics in the early twentieth century. It chronicles the work of mathematicians from Descartes and Newton to Russell and Hilbert and many, many others while emphasizing foundational questions and underlining the continuity of developments in higher mathematics. The other contributors to this volume are H. J. M. Bos, R. Bunn, J. W. Dauben, T. W. Hawkins, and K. Møller-Pedersen.
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects. There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. Science educators will be grateful for this unique, encyclopaedic handbook, Gerald Holton, Physics Department, Harvard University This handbook gathers the fruits of over thirty years’ research by a growing international and cosmopolitan community Fabio Bevilacqua, Physics Department, University of Pavia
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
This work confirms what many contemporary thinkers have claimed: that all human actions, sensations, thoughts and even emotions are derived from the synthesis of neural firings in the brain. How this happens and the precise nature of their interaction, feedback, and synthesis, however, has not been fully described - until now.
Comprehensive yet accessible, a classic survey of the history and systems of psychology — from pre-Socratic philosophers to contemporary contributions from cognitive science and neuroscience is presented. Part I traces psychology's historical foundations from its beginnings to its emergence as a formal discipline in the 1870s. Part II deals with the major twentieth-century systems of psychology. Is ideal for those without an advanced academic background in history, philosophy, or biology.

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*First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.*

**Author**: Ivor Grattan-Guiness

**Publisher:** Routledge

**ISBN:** 9781134887484

**Category:** History

**Page:** 856

**View:** 813

*First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.*

**Author**: Ivor Grattan-Guiness

**Publisher:** Routledge

**ISBN:** 9781134888320

**Category:** History

**Page:** 976

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**Author**: I. Grattan-Guinness

**Publisher:**

**ISBN:** 0415037859

**Category:** Mathematics

**Page:** 1806

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*"First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company."--Provided by publisher.*

**Author**: Ivor Grattan-Guiness

**Publisher:**

**ISBN:** 1315541971

**Category:** PHILOSOPHY

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*The positions of Sanhak Paksa (Doctor of Mathematics), Sanhak Kyosu (Professor of Mathematics) and Sansa (mathematician) were created.*

**Author**: Ivor Grattan-Guiness

**Publisher:** Routledge

**ISBN:** 9781134887552

**Category:** History

**Page:** 856

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**Mathematical** games and puzzles , logic . B. Duhamel , Jean Marie Constant ... Mechanics , physics , **history** , **philosophy** . Dupin , Pierre Charles François ...

**Author**: I. Grattan-Guinness

**Publisher:** JHU Press

**ISBN:** 0801873975

**Category:** Mathematics

**Page:** 1806

**View:** 762

*The other contributors to this volume are H. J. M. Bos, R. Bunn, J. W. Dauben, T. W. Hawkins, and K. Møller-Pedersen.*

**Author**: I. Grattan-Guinness

**Publisher:** Princeton University Press

**ISBN:** 9780691219660

**Category:** Mathematics

**Page:** 320

**View:** 936

*The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel.*

**Author**: I. Grattan-Guinness

**Publisher:** Princeton University Press

**ISBN:** 1400824044

**Category:** Mathematics

**Page:** 624

**View:** 871

*Hervé l ' Huillier , Practical geometry in the Middle Ages and the Renaissance , in
: Ivor Grattan - Guinness ( Hrsg . ) , Companion Encyclopedia of the History and
Philosophy of the Mathematical Sciences , Vol . 1 , London u . a . 1994 , S . 189 f
...*

**Author**: Irmgard Hantsche

**Publisher:**

**ISBN:** STANFORD:36105019445035

**Category:** Cartography

**Page:** 304

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**Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences**, Routledge, London, pp. 1089–1100. Cipolla, C.: 1967, Clocks and Culture: ...

**Author**: Michael R. Matthews

**Publisher:** Springer

**ISBN:** 9789400776548

**Category:** Education

**Page:** 2532

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*There is a large body of historical literature that is in need of just the kind of synthesis and masterly overview that this work provides.*

**Author**: I. Grattan-Guinness

**Publisher:**

**ISBN:** 0691058571

**Category:** Mathematics

**Page:** 690

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*... is growing rapidly due to the advent of ugh-speed. affordable computers.
Tapabrata Maiti Iowa Slate University Companion Encyclopedia of the History
and Philosophy of the Mathematical Sciences, Vols. 1 and 2. I. GRATTAN-
GuiNESS(ed.) ...*

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**Publisher:**

**ISBN:** UOM:39015059048820

**Category:** Statistics

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*Roasted Dictionnaire de la Ford Titaal in Boledar Inob lected un This was
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*This review shows that , in science and no less in mathematics , ideas are
developed by many people . ... Most of the exact sciences would not exist . ...
*

**Author**: Thomas L. Saaty

**Publisher:** Rws Publications

**ISBN:** CORNELL:31924085783011

**Category:** Medical

**Page:** 481

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*In I. Grattan-Guiness (Ed.), Companion encyclopedia of the history and
philosophy of the mathematical sciences. Vol. 1. (pp. 701-707). London, New
York: Routledge. Cole, S. (1992). Making science. Between nature and society.
Cambridge: ...*

**Author**: American Society for Information Science

**Publisher:**

**ISBN:** 00028231

**Category:** Documentation

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**View:** 773

*They include Convolution in French Mathematics , 1800-1840 ( 3 v . , 1990 ) ;
Companion Encyclopedia of the History and Philosophy of the Mathematical
Sciences ( CH , Sep'94 , 32-0364 ) ; and The Fontana History of the Mathematical
...*

**Author**:

**Publisher:**

**ISBN:** UOM:39015063397361

**Category:** Academic libraries

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*A Historical Perspective Manya Janaky Raman. Halmos ( 2 ) , P. R. ... From Frege
to Gödel : A Source Book in Mathematical Logic , 1879-1931 . ... Companion
Encyclopedia of the History and Philosophy of the Mathematical Sciences .
London ...*

**Author**: Manya Janaky Raman

**Publisher:**

**ISBN:** UCAL:C3406608

**Category:**

**Page:** 94

**View:** 827

*Indian mathematics . In I. Gratton - Guiness ( Ed . ) , Companion encyclopedia of
the history and philosophy of mathematical sciences ( Vol . 1 ) . London :
Routledge , 118-130 . HEARNSHAW , L. S. ( 1987 ) . The shaping of modern
psychology ...*

**Author**: James F. Brennan

**Publisher:**

**ISBN:** UVA:X004114066

**Category:** Psychology

**Page:** 374

**View:** 554

*Høyrup , Jens , Babylonian Mathematics : Companion Encyclopedia of the
History and Philosophy of the Mathematical Sciences 1 ( 1994 ) 21-29 . 469.
Høyrup , Jens , The Babylonian Cellar Text BM 85200 + VAT 6599. Retranslation
and ...*

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**Publisher:**

**ISBN:** STANFORD:36105021787333

**Category:** Middle East

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