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Making up Numbers

A History of Invention in Mathematics

by Ekkehard Kopp

Making up Numbers

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Book Description

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.

This open book is licensed under a Creative Commons License (CC BY). You can download Making up Numbers ebook for free in PDF format (10.0 MB).

Table of Contents

Naming Numbers
Chapter 1
Arithmetic in Antiquity
Chapter 2
Writing and Solving Equations
Chapter 3
Construction and Calculation
Chapter 4
Coordinates and Complex Numbers
Chapter 5
Struggles with the Infinite
Chapter 6
From Calculus to Analysis
Chapter 7
Number Systems
Chapter 8
Axioms for number systems
Chapter 9
Counting beyond the finite
Chapter 10
Solid Foundations?

Book Details

Making up Numbers
Science and Mathematics
Open Book Publishers
ISBN13 Digital
ISBN10 Digital
PDF Size
10.0 MB

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