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 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.
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.
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.
Numbers And Numeracy In The Greek Polis
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Author :
language : en
Publisher: BRILL
Release Date : 2021-12-20
Numbers And Numeracy In The Greek Polis written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-20 with History categories.
We tend to think of numbers as inherently objective and precise. Yet the diverse ways in which ancient Greeks used numbers illustrates that counting is actually shaped by context-specific and culturally-dependent choices: what should be counted and how, who should count, and how should the results be shared? This volume is the first to focus on the generation and use of numbers in the polis to quantify, communicate and persuade. Its papers demonstrate the rich insights that can be gained into ancient Greek societies by reappraising seemingly straightforward examples of quantification as reflections of daily life and cultural understandings.
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.
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.
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Visualization Explanation And Reasoning Styles In Mathematics
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Author : P. Mancosu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Visualization Explanation And Reasoning Styles In Mathematics written by P. Mancosu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.