{"product_id":"where-do-numbers-come-from-paperback-9781108738385","title":"Where Do Numbers Come From? (Paperback \/ softback) 9781108738385","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eWhere Do Numbers Come From?\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA clear, entertaining development of the number systems required in any course of modern mathematics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eT. W. Körner (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108738385, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 24 October 2019\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e270 pages, 1 b\/w illus.  255 exercises\u003cbr\u003e22.8 x 15.2 x 1.5 cm, 0.4 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'Where Do Numbers Come From? certainly adds to the pleasure of mathematics as well as narrating a journey that surely every mathematician should undertake at some stage. As such, I enthusiastically recommend it to all Gazette readers.' Nick Lord, The Mathematical Gazette\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eWhy do we need the real numbers? How should we construct them? These questions arose in the nineteenth century, along with the ideas and techniques needed to address them. Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for those students, with historical asides and exercises to foster understanding. Starting with the natural (counting) numbers and then looking at the rational numbers (fractions) and negative numbers, the author builds to a careful construction of the real numbers followed by the complex numbers, leaving the reader fully equipped with all the number systems required by modern mathematical analysis. Additional chapters on polynomials and quarternions provide further context for any reader wanting to delve deeper.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e Part I. The Rationals: 1. Counting sheep\u003cbr\u003e 2. The strictly positive rationals\u003cbr\u003e 3. The rational numbers\u003cbr\u003e Part II. The Natural Numbers: 4. The golden key\u003cbr\u003e 5. Modular arithmetic\u003cbr\u003e 6. Axioms for the natural numbers\u003cbr\u003e Part III. The Real Numbers (and the Complex Numbers): 7. What is the problem?\u003cbr\u003e 8. And what is its solution?\u003cbr\u003e 9. The complex numbers\u003cbr\u003e 10. A plethora of polynomials\u003cbr\u003e 11. Can we go further?\u003cbr\u003e Appendix A. Products of many elements\u003cbr\u003e Appendix B. nth complex roots\u003cbr\u003e Appendix C. How do quaternions represent rotations?\u003cbr\u003e Appendix D. Why are the quaternions so special?\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46001410572568,"sku":"9781108738385","price":33.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781108738385i.jpg?v=1696718324","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/where-do-numbers-come-from-paperback-9781108738385","provider":"Freshly Printed Books","version":"1.0","type":"link"}