On The Shaping Of Deduction In Greek Mathematics
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The Shaping Of Deduction In Greek Mathematics
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Author : Reviel Netz
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-18
The Shaping Of Deduction In Greek Mathematics written by Reviel Netz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-18 with History categories.
The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.
On The Shaping Of Deduction In Greek Mathematics
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Author : Reviel Netz
language : en
Publisher:
Release Date : 1995
On The Shaping Of Deduction In Greek Mathematics written by Reviel Netz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
The Shaping Of Deduction In Greek Mathematics
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Author : Reviel Netz
language : en
Publisher:
Release Date : 1999
The Shaping Of Deduction In Greek Mathematics written by Reviel Netz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Logic categories.
An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.
A New History Of Greek Mathematics
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Author : Reviel Netz
language : en
Publisher: Cambridge University Press
Release Date : 2022-09
A New History Of Greek Mathematics written by Reviel Netz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09 with History categories.
Engaging and comprehensive history of Greek mathematics, with full attention to social contexts and its place in world history.
The History Of Mathematical Proof In Ancient Traditions
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Author : Karine Chemla
language : en
Publisher: Cambridge University Press
Release Date : 2012-07-05
The History Of Mathematical Proof In Ancient Traditions written by Karine Chemla and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-05 with Philosophy categories.
This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.
Mathematics For Machine Learning
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Author : Marc Peter Deisenroth
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics For Machine Learning written by Marc Peter Deisenroth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Computers categories.
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.
Circles Disturbed
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Author : Apostolos Doxiadis
language : en
Publisher: Princeton University Press
Release Date : 2012-03-18
Circles Disturbed written by Apostolos Doxiadis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-18 with Mathematics categories.
Why narrative is essential to mathematics Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—"Don't disturb my circles"—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.
The Logical Syntax Of Greek Mathematics
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Author : Fabio Acerbi
language : en
Publisher: Springer Nature
Release Date : 2021-06-21
The Logical Syntax Of Greek Mathematics written by Fabio Acerbi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Mathematics categories.
The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity. In this way, major philosophical themes such as the expression of mathematical generality and the selection of criteria of validity for arguments can be treated without anachronism. Thus, the book is of interest for both historians of ancient philosophy and specialists in Ancient Greek, in addition to historians of mathematics. This volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The first part describes the three stylistic codes of Greek mathematics; the second expounds in detail the mechanism of "validation"; the third deals with the status of mathematical objects and the problem of mathematical generality; the fourth analyzes the main features of the "deductive machine," i.e. the suprasentential logical system dictated by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth deals with the sentential logical system of a mathematical proposition, with special emphasis on quantification, modalities, and connectors. A number of complementary appendices are included as well.
Revolutions And Continuity In Greek Mathematics
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Author : Michalis Sialaros
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-04-23
Revolutions And Continuity In Greek Mathematics written by Michalis Sialaros and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-23 with History categories.
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.
A History Of Mathematics
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Author : Luke Hodgkin
language : en
Publisher: OUP Oxford
Release Date : 2005-06-02
A History Of Mathematics written by Luke Hodgkin and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-02 with Mathematics categories.
A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.