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.
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 Electronic books categories.
This book provides a way into understanding a momentous development in human intellectual history: the phenomenon of deductive argument in classical Greek mathematics. The argument rests upon a close description of the practices of Greek mathematics, principally the use of lettered diagrams and the regulated, formulaic use of language.
Ludic Proof
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Author : Reviel Netz
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-22
Ludic Proof 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 2021-07-22 with Philosophy categories.
This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western mathematics.
A New History Of Greek Mathematics
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Author : Reviel Netz
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-01
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 2022-09-01 with Philosophy categories.
The ancient Greeks played a fundamental role in the history of mathematics and their ideas were reused and developed in subsequent periods all the way down to the scientific revolution and beyond. In this, the first complete history for a century. Reviel Netz offers a panoramic view of the rise and influence of Greek mathematics and its significance in world history. He explores the Near Eastern antecedents and the social and intellectual developments underlying the subject's beginnings in Greece in the fifth century BCE. He leads the reader through the proofs and arguments of key figures like Archytas, Euclid and Archimedes, and considers the totality of the Greek mathematical achievement which also includes, in addition to pure mathematics, such applied fields as optics, music, mechanics and, above all, astronomy. This is the story not only of a major historical development, but of some of the finest mathematics ever created.
The Transformation Of Mathematics In The Early Mediterranean World
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Author : Reviel Netz
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-10
The Transformation Of Mathematics In The Early Mediterranean World 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 2004-06-10 with Philosophy categories.
The transformation of mathematics from ancient Greece to the medieval Arab-speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of mathematics based on the localized solution (and grounded in the polemical practices of early Greek science) we see a transition to a practice of mathematics based on the systematic approach (and grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). With three chapters ranging chronologically from Hellenistic mathematics, through late Antiquity, to the medieval world, Reviel Netz offers an alternate interpretation of the historical journey of pre-modern mathematics.
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.
The Works Of Archimedes Volume 1 The Two Books On The Sphere And The Cylinder
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Author : Archimedes
language : en
Publisher: Cambridge University Press
Release Date : 2004-04-08
The Works Of Archimedes Volume 1 The Two Books On The Sphere And The Cylinder written by Archimedes 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 2004-04-08 with Mathematics categories.
Volume 1 of the first authoritative translation of Archimedes' works into English.
The Works Of Archimedes
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Author : Archimedes
language : en
Publisher:
Release Date : 1897
The Works Of Archimedes written by Archimedes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1897 with Geometry categories.
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.
Making Up Numbers A History Of Invention In Mathematics
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Author : Ekkehard Kopp
language : en
Publisher: Open Book Publishers
Release Date : 2020-10-23
Making Up Numbers A History Of Invention In Mathematics written by Ekkehard Kopp and has been published by Open Book Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-23 with Mathematics categories.
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.