Making Up Numbers A History Of Invention In Mathematics
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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.
Making Up Numbers
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Author : Ekkehard Kopp
language : en
Publisher:
Release Date : 2020-10-15
Making Up Numbers written by Ekkehard Kopp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with 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.
The Universal History Of Numbers
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Author : Georges Ifrah
language : en
Publisher: Wiley
Release Date : 2000-10-09
The Universal History Of Numbers written by Georges Ifrah and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-09 with Mathematics categories.
"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
Numbers And The Making Of Us
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Author : Caleb Everett
language : en
Publisher: Harvard University Press
Release Date : 2017-03-13
Numbers And The Making Of Us written by Caleb Everett and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-13 with Language Arts & Disciplines categories.
“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 Invention Of Numbers
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Author : Peter Bentley
language : en
Publisher: Weidenfeld & Nicolson
Release Date : 2016-08-11
The Invention Of Numbers written by Peter Bentley and has been published by Weidenfeld & Nicolson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-11 with categories.
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.
The Universal History Of Numbers
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Author : Georges Ifrah
language : en
Publisher: Harvill Press
Release Date : 1998
The Universal History Of Numbers written by Georges Ifrah and has been published by Harvill Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
The book explores the science of numeration as it has developed all over the world, from Europe to China, via the Classical World, Mesopotamia, South America and, above all, India and the Arab lands.
The Nothing That Is
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Author : Robert Kaplan
language : en
Publisher: Oxford University Press
Release Date : 1999-10-28
The Nothing That Is written by Robert Kaplan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-28 with Mathematics categories.
A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treating zero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called "dangerous Saracen magic" and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything. Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists. The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.
Java Application Performance And Memory Management
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Author : Matt Greencroft
language : en
Publisher: Multicode Ltd
Release Date : 2022-02-02
Java Application Performance And Memory Management written by Matt Greencroft and has been published by Multicode Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-02 with Computers categories.
The process to transition from being a new Java developer to a confident and competent coder is a difficult one. In this book, author and long-time Java trainer Matt Greencroft guides you through some of the topics that will help you make significant steps along this journey. It is packed with important topics that experienced programmers should know and understand, together with practical advice on how to tune your applications and the JVM to get the best possible performance. Rather than containing a theoretical, highly detailed understanding of the internals of the Java Virtual Machine, this book takes a practical approach. You’ll learn enough to get a good understanding of how the JVM works and how memory is managed in Java, how to make great coding choices, how to configure the JVM, and how to evaluate and benchmark different options to assess their performance metrics in a robust and manageable way. Whether you have an existing application with performance issues to address, have taken one of Matt’s courses and are selecting this book as supporting material, or are simply wanting to advance your career by becoming a better programmer, this book will give you lots of stills and practical experience.
Introduction To Systems Biology
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Author : Thomas Sauter
language : en
Publisher: Open Book Publishers
Release Date : 2023-03-09
Introduction To Systems Biology written by Thomas Sauter 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 2023-03-09 with Computers categories.
This book is an introduction to the language of systems biology, which is spoken among many disciplines, from biology to engineering. Authors Thomas Sauter and Marco Albrecht draw on a multidisciplinary background and evidence-based learning to facilitate the understanding of biochemical networks, metabolic modeling and system dynamics. Their pedagogic approach briefly highlights core ideas of concepts in a broader interdisciplinary framework to guide a more effective deep dive thereafter. The learning journey starts with the purity of mathematical concepts, reveals its power to connect biological entities in structure and time, and finally introduces physics concepts to tightly align abstraction with reality. This workbook is all about self-paced learning, supports the flipped-classroom concept, and kick-starts with scientific evidence on studying. Each chapter comes with links to external YouTube videos, learning checklists, and Integrated real-world examples to gain confidence in thinking across scientific perspectives. The result is an integrated approach that opens a line of communication between theory and application, enabling readers to actively learn as they read. This overview of capturing and analyzing the behavior of biological systems will interest adherers of systems biology and network analysis, as well as related fields such as bioinformatics, biology, cybernetics, and data science.
Numbers
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Author : Graham Flegg
language : en
Publisher:
Release Date : 1993
Numbers written by Graham Flegg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Number theory categories.