Making up Numbers: A History of Invention in Mathematics
Title | Making up Numbers: A History of Invention in Mathematics PDF eBook |
Author | Ekkehard Kopp |
Publisher | Open Book Publishers |
Total Pages | 280 |
Release | 2020-10-23 |
Genre | Mathematics |
ISBN | 1800640978 |
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
Title | Making Up Numbers PDF eBook |
Author | Ekkehard Kopp |
Publisher | |
Total Pages | 280 |
Release | 2020-10-15 |
Genre | |
ISBN | 9781800640962 |
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
Title | Numbers and the Making of Us PDF eBook |
Author | Caleb Everett |
Publisher | Harvard University Press |
Total Pages | 308 |
Release | 2017-03-13 |
Genre | Language Arts & Disciplines |
ISBN | 0674504437 |
“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
The Universal History of Numbers
Title | The Universal History of Numbers PDF eBook |
Author | Georges Ifrah |
Publisher | Wiley |
Total Pages | 660 |
Release | 2000-10-09 |
Genre | Mathematics |
ISBN | 9780471393405 |
"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
A Quick History of Math
Title | A Quick History of Math PDF eBook |
Author | Clive Gifford |
Publisher | Wide Eyed Editions |
Total Pages | 130 |
Release | 2021-04-06 |
Genre | Juvenile Nonfiction |
ISBN | 0711249032 |
Maths + history + jokes - boring bits = A Quick History of Maths. This book begins around 43,000 years ago with a notched baboon leg, the Lebombo bone (the very first mathematical object in the world) and rushes us past Hindu numerals and the invention of zero, via Pythagoras, Pascal and probability, right up to the present day, with big data and the maths that rules our digital lives. Geometri-cool! You will discover: How to count on your fingers (there are more ways than you might think!) Why we have 60 seconds in a minute (hint: it’s to do with the ancient Babylonians) How to count like an Egyptian (using hieroglyphs) Why it’s hip to be square using square numbers A Pythagorean party trick The naked truth of Archimedes’ bath time mathematics How to do matha-magic with magic squares …and much more. In chronological order from pre-history to present day, this is the story of maths itself. It’s 43,000 years of human mathematical endeavor squeezed into one book for your reading pleasure. Illustrated with funny cartoons and packed with fascinating facts, you’ll be laughing and learning how to be a better mathematician.
The Nothing that is
Title | The Nothing that is PDF eBook |
Author | |
Publisher | Oxford University Press, USA |
Total Pages | 238 |
Release | 2000 |
Genre | Mathematics |
ISBN | 0195128427 |
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.
Journey through Mathematics
Title | Journey through Mathematics PDF eBook |
Author | Enrique A. González-Velasco |
Publisher | Springer Science & Business Media |
Total Pages | 479 |
Release | 2011-08-08 |
Genre | Mathematics |
ISBN | 0387921540 |
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.