Making up Numbers: A History of Invention in Mathematics

Making up Numbers: A History of Invention in Mathematics

Author: Ekkehard Kopp

Publisher: Open Book Publishers

Published: 2020-10-23

Total Pages: 280

ISBN-13: 1800640978

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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.


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.

Making Up Numbers

Making Up Numbers

Author: Ekkehard Kopp

Publisher:

Published: 2020-10-15

Total Pages: 280

ISBN-13: 9781800640962

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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.


Book Synopsis Making Up Numbers by : Ekkehard Kopp

Download or read book Making Up Numbers written by Ekkehard Kopp and published by . This book was released on 2020-10-15 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.

Numbers and the Making of Us

Numbers and the Making of Us

Author: Caleb Everett

Publisher: Harvard University Press

Published: 2017-03-13

Total Pages: 308

ISBN-13: 0674504437

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“A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal


Book Synopsis Numbers and the Making of Us by : Caleb Everett

Download or read book Numbers and the Making of Us written by Caleb Everett and published by Harvard University Press. This book was released on 2017-03-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: “A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal

Numbers

Numbers

Author: John Tabak

Publisher: Infobase Publishing

Published: 2014-05-14

Total Pages: 239

ISBN-13: 0816068747

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Presents a survey of the history and evolution of the use of numbers and numerical quantities by different civilizations around the world.


Book Synopsis Numbers by : John Tabak

Download or read book Numbers written by John Tabak and published by Infobase Publishing. This book was released on 2014-05-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a survey of the history and evolution of the use of numbers and numerical quantities by different civilizations around the world.

The Universal History of Numbers

The Universal History of Numbers

Author: Georges Ifrah

Publisher: Wiley

Published: 2000-10-09

Total Pages: 660

ISBN-13: 9780471393405

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"Georges Ifrah is the man. This book, quite simply, rules. . . . It is outstanding . . . a mind-boggling and enriching experience." –The Guardian (London) "Monumental. . . . a fascinating journey taking us through many different cultures."–The Times (London)"Ifrah’s book amazes and fascinates by the scope of its scholarship. It is nothing less than the history of the human race told through figures." –International Herald Tribune Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years. "Dazzling."–Kirkus Reviews "Sure to transfix readers."–PublishersWeekly


Book Synopsis The Universal History of Numbers by : Georges Ifrah

Download or read book The Universal History of Numbers written by Georges Ifrah and published by Wiley. This book was released on 2000-10-09 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Georges Ifrah is the man. This book, quite simply, rules. . . . It is outstanding . . . a mind-boggling and enriching experience." –The Guardian (London) "Monumental. . . . a fascinating journey taking us through many different cultures."–The Times (London)"Ifrah’s book amazes and fascinates by the scope of its scholarship. It is nothing less than the history of the human race told through figures." –International Herald Tribune Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years. "Dazzling."–Kirkus Reviews "Sure to transfix readers."–PublishersWeekly

The Invention of Numbers

The Invention of Numbers

Author: Peter Bentley

Publisher: Weidenfeld & Nicolson

Published: 2016-08-11

Total Pages: 272

ISBN-13: 9781844039111

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Numbers are at the heart of the existence of the universe and everything in it, and yet a lot of us have little understanding of their creation, let alone their part in philosophy, art, music, physics, literature, religion and computing. Dr Bentley's fascinating history of the origins of numbers will unlock the secrets of these things that we take for granted and shows how numbers seem to take on human characteristiscs - as they can be perfect or irrational, amicable or prime, real or imaginary. From zero to infinity, learn about the way numbers have shaped our world, discover amazing facts and enjoy the pure beauty of mathematical logic.


Book Synopsis The Invention of Numbers by : Peter Bentley

Download or read book The Invention of Numbers written by Peter Bentley and published by Weidenfeld & Nicolson. This book was released on 2016-08-11 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers are at the heart of the existence of the universe and everything in it, and yet a lot of us have little understanding of their creation, let alone their part in philosophy, art, music, physics, literature, religion and computing. Dr Bentley's fascinating history of the origins of numbers will unlock the secrets of these things that we take for granted and shows how numbers seem to take on human characteristiscs - as they can be perfect or irrational, amicable or prime, real or imaginary. From zero to infinity, learn about the way numbers have shaped our world, discover amazing facts and enjoy the pure beauty of mathematical logic.

Numbers

Numbers

Author: Graham Flegg

Publisher: Courier Corporation

Published: 2013-05-13

Total Pages: 304

ISBN-13: 0486166511

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Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.


Book Synopsis Numbers by : Graham Flegg

Download or read book Numbers written by Graham Flegg and published by Courier Corporation. This book was released on 2013-05-13 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

The History of Mathematics

The History of Mathematics

Author: David M. Burton

Publisher: WCB/McGraw-Hill

Published: 1991

Total Pages: 712

ISBN-13:

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This text is designed for the junior/senior mathematics major who intends to teach mathematics in high school or college. It concentrates on the history of those topics typically covered in an undergraduate curriculum or in elementary schools or high schools. At least one year of calculus is a prerequisite for this course. This book contains enough material for a 2 semester course but it is flexible enough to be used in the more common 1 semester course.


Book Synopsis The History of Mathematics by : David M. Burton

Download or read book The History of Mathematics written by David M. Burton and published by WCB/McGraw-Hill. This book was released on 1991 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for the junior/senior mathematics major who intends to teach mathematics in high school or college. It concentrates on the history of those topics typically covered in an undergraduate curriculum or in elementary schools or high schools. At least one year of calculus is a prerequisite for this course. This book contains enough material for a 2 semester course but it is flexible enough to be used in the more common 1 semester course.

Journey through Mathematics

Journey through Mathematics

Author: Enrique A. González-Velasco

Publisher: Springer Science & Business Media

Published: 2011-08-08

Total Pages: 479

ISBN-13: 0387921540

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This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation. The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.


Book Synopsis Journey through Mathematics by : Enrique A. González-Velasco

Download or read book Journey through Mathematics written by Enrique A. González-Velasco and published by Springer Science & Business Media. This book was released on 2011-08-08 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation. The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.

The Nothing that is

The Nothing that is

Author:

Publisher: Oxford University Press, USA

Published: 2000

Total Pages: 238

ISBN-13: 0195128427

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In the tradition of "Longitude, " a small and engagingly written book on the history and meaning of zero--a "tour de force" of science history that takes us through the hollow circle that leads to infinity. 32 illustrations.


Book Synopsis The Nothing that is by :

Download or read book The Nothing that is written by and published by Oxford University Press, USA. This book was released on 2000 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the tradition of "Longitude, " a small and engagingly written book on the history and meaning of zero--a "tour de force" of science history that takes us through the hollow circle that leads to infinity. 32 illustrations.