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003			MiTN
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906			_a6 _bcbc _ccopycat _d2 _eepcn _f20 _gy-gencatlg
925	0		_aacquire _b2 shelf copies _xSel/rjc, 2016-02-02
948			_au609357
955			_txn11 2016-03-11 copy 2 added
008			150112s2015 enka b 001 0 eng d
010			_a 2015930555
020			_a9780198702597
020			_a0198702590
020			_z9780191007064 _q(PDF)
020			_z0191007064 _q(PDF)
020			_z9780191007071 _q(ePub)
020			_z0191007072 _q(ePub)
035			_a(OCoLC)ocn907194512
040			_aBTCTA _beng _cBTCTA _erda _dBDX _dERASA _dCDX _dYDXCP _dOCLCO _dOCLCF _dOCLCO _dIQU _dOCLCO _dZCU _dDLC
042			_alccopycat
050	0	0	_aQA241 _b.C6945 2015
082	0	4	_a512.7 _223
100	1		_aCorry, Leo, _d1956-
245	1	2	_aA brief history of numbers / _cLeo Corry.
250			_aFirst edition.
264		1	_aOxford, United Kingdom ; _aNew York, NY, United States of America : _bOxford University Press, _c2015.
300			_axiii, 309 pages : _billustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
504			_aIncludes bibliographical references (pages 295-301) and indexes.
505	0		_aThe system of numbers : an overview: From natural to real numbers ; Imaginary numbers ; Polynomials and transcendental numbers ; Cardinals and ordinals -- Writing numbers : now and back then: Writing numbers nowadays : positional and decimal ; Writing numbers back then : Egypt, Babylon and Greece -- Numbers and magnitudes in the Greek mathematical tradition: Pythagorean numbers ; Ratios and proportions ; Incommensurability ; Eudoxus' theory of proportions ; Greek fractional numbers ; Comparisons, not measurements ; A unit length ; Appendix 3.1: The incommensurability of 2 -- ancient and modern proofs ; Appendix 3.2: Eudoxus' theory of proportions in action ; Appendix 3.3: Euclid and the area of the circle -- Construction problems and numerical problems in the Greek mathematical tradition: The arithmetic books of the elements ; Geometric algebra? ; Straightedge and compass ; Diophantus' numerical problems ; Diophantus' reciprocals and fractions ; More than three dimensions ; Appendix 4.1: Diophantus' solution of Problem V.9 in Arithmetica -- Numbers in the tradition of medieval Islam: Islamicate science in historical perspective ; Al-KhwaÌrizmiÌ and numerical problems with squares ; Geometry and certainty ; Al-jabr wa'l-muqaÌbala ; Al-KhwaÌrizmiÌ, numbers and fractions ; AbuÌ KaÌmil's numbers at the crossroads of two traditions ; Numbers, fractions and symbolic methods ; Al-KhayyaÌm and numerical problems with cubes ; Gersonides and problems with numbers ; Appendix 5.1: The quadratic equation. Derivation of the algebraic formula ; Appendix 5.2: The cubic equation. Khayyam's geometric solution -- Numbers in Europe from the twelfth to the sixteenth centuries: Fibonacci and Hindu-Arabic numbers in Europe ; Abbacus and coss traditions in Europe ; Cardano's Great art of algebra ; Bombelli and the roots of negative numbers ; Euclid's Elements in the Renaissance ; Appendix 6.1: Casting out nines -- Number and equations at the beginning of the scientific revolution: VieÌte and the new art of analysis ; Stevin and decimal fractions ; Logarithms and the decimal system of numeration ; Appendix 7.1: Napier's construction of logarithmic tables -- Number and equations in the works of Descartes, Newton and their contemporaries: Descartes' new approach to numbers and equations ; Wallis and the primacy of algebra ; Barrow and the opposition to the primacy of algebra ; Newton's Universal arithmetick ; Appendix 8.1: The quadratic equation. Descartes' geometric solution ; Appendix 8.2: Between geometry and algebra in the seventeenth century : the case of Euclid's Elements -- New definitions of complex numbers in the early nineteenth century: Numbers and ratios : giving up metaphysics ; Euler, Gauss and the ubiquity of complex numbers ; Geometric interpretations of the complex numbers ; Hamilton's formal definition of complex numbers ; Beyond complex numbers ; Hamilton's discovery of quaternions -- "What are numbers and what should they be?" : understanding numbers in the late nineteenth century: What are numbers? ; Kummer's ideal numbers ; Fields of algebraic numbers ; What should numbers be? ; Numbers and the foundations of calculus ; Appendix 10.1: Dedekind's theory of cuts and Eudoxus' theory of proportions ; Appendix 10.2: IVT and the fundamental theorem of calculus -- Exact definitions for the natural numbers : Dedekind, Peano and Frege: The principle of mathematical induction ; Peano's postulates ; Dedekind's chains of cardinal numbers -- Appendix 11.1: The principle of induction and Peano's postulates -- Numbers, sets and infinity : a conceptual breakthrough at the turn of the twentieth century: Dedekind, Cantor and the infinite ; Infinities of various sizes ; Cantor's transfinite ordinals ; Troubles in paradise ; Appendix 12.1: Proof that the set of algebraic numbers is countable -- Epilogue: Numbers in historical perspective.
520			_aThe world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the. -- _cSource other than Library of Congress.
650		0	_aNumber theory _xHistory.
650		7	_aNumber theory. _2fast _0(OCoLC)fst01041214
655		7	_aHistory. _2fast _0(OCoLC)fst01411628
596			_a1
903			_a32843
999			_c32843 _d32843