000			04024nam a2200397 i 4500
001			xb31296117
006			m d
007			cr n
008			201106s20202020enkac sb 001 0 eng d
020			_a9781800640979 _q(pdf)
020			_z9781800640955 (Paperback)
020			_z9781800640962 (Hardback)
040			_aStSaUL _beng _erda
100	1		_aKopp, Ekkehard, _eauthor.
245	1	0	_aMaking up numbers _h[electronic resource] : _ba history of invention in mathematics / _cEkkehard Kopp.
264		1	_bOpen Book Publishers,
300			_a1 online resource (280 pages) : _billustrations, portraits.
500			_aAvailable through Open Book Publishers.
504			_aIncludes bibliography (pages 259-260) and indexes.
505	0		_aPreface -- Prologue: Naming Numbers / Ekkehard Kopp -- Chapter 1. Arithmetic in Antiquity / Ekkehard Kopp -- Chapter 2. Writing and Solving Equations / Ekkehard Kopp -- Chapter 3. Construction and Calculation / Ekkehard Kopp -- Chapter 4. Coordinates and Complex Numbers / Ekkehard Kopp -- Chapter 5. Struggles with the Infinite / Ekkehard Kopp -- Chapter 6. From Calculus to Analysis / Ekkehard Kopp -- Chapter 7. Number Systems / Ekkehard Kopp -- Chapter 8. Axioms for number systems / Ekkehard Kopp -- Chapter 9. Counting beyond the finite / Ekkehard Kopp -- Chapter 10. Solid Foundations? / Ekkehard Kopp -- Epilogue / Ekkehard Kopp -- Bibliography -- Name Index -- Index.
506			_aOpen access resource providing free access.
520			_a"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. he 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."--Publisher's website.
538			_aMode of access: World Wide Web.
540			_aThis work is licensed under a Creative Commons Attribution 4.0 International license (CC BY 4.0). For more detailed information consult the publisher's website.
650		0	_aArithmetic _xResearch.
650		0	_aMathematics _xResearch.
650		0	_aNumbers, Natural.
650		0	_aNumbers, Real.
710	2		_aOpen Book Publishers, _epublisher.
856	4	0	_uhttp://doi.org/10.11647/OBP.0236 _zConnect to e-book
856	4	2	_uhttp://www.openbookpublishers.com/shopimages/products/cover/1279 _zConnect to cover image
999			_c29178 _d29178