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Making up Numbers: A History of Invention in Mathematics

Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp
Paperback ISBN: 978-1-80064-095-5 £20.95
Hardback ISBN: 978-1-80064-096-2 £30.95
PDF ISBN: 978-1-80064-097-9 £0.00

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This book tells a lively story and is crammed with interesting, and often technical, mathematics, which the author nevertheless makes accessible to a wide readership.
Christopher Hollings, University of Oxford



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: A History of Invention in Mathematics
Ekkehard Kopp | October 2020
280 pp. | 6.14" x 9.21" (234 x 156 mm)
ISBN Paperback: 9781800640955
ISBN Hardback: 9781800640962
ISBN Digital (PDF): 9781800640979
DOI: 10.11647/OBP.0236
Subject Codes: BIC: PB (Mathematics), YQM (Educational: Mathematics and numeracy), PBK (Calculus and Mathematical Analysis); BISAC: MAT000000 (MATHEMATICS / General), MAT 015000 (MATHEMATICS / History and Philosophy), MAT027000 (MATHEMATICS / Research); OCLC Number: 1226545401.


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Preface

Prologue: Naming Numbers Download
Ekkehard Kopp

Chapter 1.: Arithmetic in Antiquity Download
Ekkehard Kopp

Chapter 2.: Writing and Solving Equations Download
Ekkehard Kopp

Chapter 3.: Construction and Calculation Download
Ekkehard Kopp

Chapter 4.: Coordinates and Complex Numbers Download
Ekkehard Kopp

Chapter 5.: Struggles with the Infinite Download
Ekkehard Kopp

Chapter 6.: From Calculus to Analysis Download
Ekkehard Kopp

Chapter 7.: Number Systems Download
Ekkehard Kopp

Chapter 8.: Axioms for number systems Download
Ekkehard Kopp

Chapter 9.: Counting beyond the finite Download
Ekkehard Kopp

Chapter 10.: Solid Foundations? Download
Ekkehard Kopp

Epilogue Download
Ekkehard Kopp

Bibliography

Name Index

Index

Mathematical Miscellany Download