The Shaping Of Deduction In Greek Mathematics

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The Shaping of Deduction in Greek Mathematics

Author : Reviel Netz
Publisher : Cambridge University Press
ISBN 13 : 9780521541206
Total Pages : 356 pages
Book Rating : 4.5/5 (412 download)

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Book Synopsis The Shaping of Deduction in Greek Mathematics by : Reviel Netz

Download or read book The Shaping of Deduction in Greek Mathematics written by Reviel Netz and published by Cambridge University Press. This book was released on 2003-09-18 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Reviel Netz
Publisher :
ISBN 13 : 9780511050534
Total Pages : 327 pages
Book Rating : 4.0/5 (55 download)

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Book Synopsis The Shaping of Deduction in Greek Mathematics by : Reviel Netz

Download or read book The Shaping of Deduction in Greek Mathematics written by Reviel Netz and published by . This book was released on 1999 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The History of Mathematical Proof in Ancient Traditions

Author : Karine Chemla
Publisher : Cambridge University Press
ISBN 13 : 1139510584
Total Pages : pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis The History of Mathematical Proof in Ancient Traditions by : Karine Chemla

Download or read book The History of Mathematical Proof in Ancient Traditions written by Karine Chemla and published by Cambridge University Press. This book was released on 2012-07-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A New History of Greek Mathematics

Author : Reviel Netz
Publisher : Cambridge University Press
ISBN 13 : 1108991912
Total Pages : 541 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis A New History of Greek Mathematics by : Reviel Netz

Download or read book A New History of Greek Mathematics written by Reviel Netz and published by Cambridge University Press. This book was released on 2022-09-01 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ludic Proof

Author : Reviel Netz
Publisher : Cambridge University Press
ISBN 13 : 9781009069809
Total Pages : 271 pages
Book Rating : 4.0/5 (698 download)

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Book Synopsis Ludic Proof by : Reviel Netz

Download or read book Ludic Proof written by Reviel Netz and published by Cambridge University Press. This book was released on 2021-07-22 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Circles Disturbed

Author : Apostolos Doxiadis
Publisher : Princeton University Press
ISBN 13 : 1400842689
Total Pages : 593 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Circles Disturbed by : Apostolos Doxiadis

Download or read book Circles Disturbed written by Apostolos Doxiadis and published by Princeton University Press. This book was released on 2012-03-18 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Works of Archimedes

Author : Archimedes
Publisher :
ISBN 13 :
Total Pages : 524 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Works of Archimedes by : Archimedes

Download or read book The Works of Archimedes written by Archimedes and published by . This book was released on 1897 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics for Machine Learning

Author : Marc Peter Deisenroth
Publisher : Cambridge University Press
ISBN 13 : 1108569323
Total Pages : 392 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Making up Numbers: A History of Invention in Mathematics

Author : Ekkehard Kopp
Publisher : Open Book Publishers
ISBN 13 : 1800640978
Total Pages : 280 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Making up Numbers: A History of Invention in Mathematics by : Ekkehard Kopp

Download or read book Making up Numbers: A History of Invention in Mathematics written by Ekkehard Kopp and published by Open Book Publishers. This book was released on 2020-10-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Short History of Greek Mathematics

Author : James Gow
Publisher :
ISBN 13 :
Total Pages : 350 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A Short History of Greek Mathematics by : James Gow

Download or read book A Short History of Greek Mathematics written by James Gow and published by . This book was released on 1884 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conceptual Mathematics

Author : F. William Lawvere
Publisher : Cambridge University Press
ISBN 13 : 0521894859
Total Pages : 409 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Conceptual Mathematics by : F. William Lawvere

Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

The Oxford Handbook of the History of Mathematics

Author : Eleanor Robson
Publisher : Oxford University Press on Demand
ISBN 13 : 0199213127
Total Pages : 927 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis The Oxford Handbook of the History of Mathematics by : Eleanor Robson

Download or read book The Oxford Handbook of the History of Mathematics written by Eleanor Robson and published by Oxford University Press on Demand. This book was released on 2009 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook explores the history of mathematics, addressing what mathematics has been and what it has meant to practise it. 36 self-contained chapters provide a fascinating overview of 5000 years of mathematics and its key cultures for academics in mathematics, historians of science, and general historians.

A Book of Curves

Author : Edward Harrington Lockwood
Publisher : Cambridge University Press
ISBN 13 : 9781001224114
Total Pages : 290 pages
Book Rating : 4.2/5 (241 download)

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Book Synopsis A Book of Curves by : Edward Harrington Lockwood

Download or read book A Book of Curves written by Edward Harrington Lockwood and published by Cambridge University Press. This book was released on 1967 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the drawing of plane curves, cycloidal curves, spirals, glissettes and others.

Selected Essays on Pre- and Early Modern Mathematical Practice

Author : Jens Høyrup
Publisher : Springer Nature
ISBN 13 : 303019258X
Total Pages : 969 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Selected Essays on Pre- and Early Modern Mathematical Practice by : Jens Høyrup

Download or read book Selected Essays on Pre- and Early Modern Mathematical Practice written by Jens Høyrup and published by Springer Nature. This book was released on 2019-09-20 with total page 969 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice. This book is of interest to, and provides methodological inspiration for, historians of science or mathematics and students of these disciplines.

A History of Mathematics

Author : Luke Hodgkin
Publisher : OUP Oxford
ISBN 13 : 0191664367
Total Pages : 296 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis A History of Mathematics by : Luke Hodgkin

Download or read book A History of Mathematics written by Luke Hodgkin and published by OUP Oxford. This book was released on 2013-02-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Pappus of Alexandria: Book 4 of the Collection

Author : Heike Sefrin-Weis
Publisher : Springer Science & Business Media
ISBN 13 : 1849960054
Total Pages : 347 pages
Book Rating : 4.8/5 (499 download)

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Book Synopsis Pappus of Alexandria: Book 4 of the Collection by : Heike Sefrin-Weis

Download or read book Pappus of Alexandria: Book 4 of the Collection written by Heike Sefrin-Weis and published by Springer Science & Business Media. This book was released on 2010-04-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although not so well known today, Book 4 of Pappus’ Collection is one of the most important and influential mathematical texts from antiquity. The mathematical vignettes form a portrait of mathematics during the Hellenistic "Golden Age", illustrating central problems – for example, squaring the circle; doubling the cube; and trisecting an angle – varying solution strategies, and the different mathematical styles within ancient geometry. This volume provides an English translation of Collection 4, in full, for the first time, including: a new edition of the Greek text, based on a fresh transcription from the main manuscript and offering an alternative to Hultsch’s standard edition, notes to facilitate understanding of the steps in the mathematical argument, a commentary highlighting aspects of the work that have so far been neglected, and supporting the reconstruction of a coherent plan and vision within the work, bibliographical references for further study.

The Transformation of Mathematics in the Early Mediterranean World

Author : Reviel Netz
Publisher : Cambridge University Press
ISBN 13 : 0521829968
Total Pages : 210 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis The Transformation of Mathematics in the Early Mediterranean World by : Reviel Netz

Download or read book The Transformation of Mathematics in the Early Mediterranean World written by Reviel Netz and published by Cambridge University Press. This book was released on 2004-06-10 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 a radically new interpretation of the historical journey of pre-modern mathematics.