000 03917nam a22004575i 4500
001 978-0-387-75481-9
003 DE-He213
005 20161121231208.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387754819
_9978-0-387-75481-9
024 7 _a10.1007/978-0-387-75481-9
_2doi
050 4 _aQA21-27
072 7 _aPBX
_2bicssc
072 7 _aMAT015000
_2bisacsh
082 0 4 _a510.9
_223
100 1 _aSmoryński, Craig.
_eauthor.
245 1 0 _aHistory of Mathematics
_h[electronic resource] :
_bA Supplement /
_cby Craig Smoryński.
264 1 _aNew York, NY :
_bSpringer New York,
_c2008.
300 _aVI, 274 p. 42 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aAnnotated Bibliography -- Foundations of Geometry -- The Construction Problems of Antiquity -- A Chinese Problem -- The Cubic Equation -- Horner's Method -- Some Lighter Material.
520 _aThis book attempts to fill two gaps which exist in the standard textbooks on the History of Mathematics. One is to provide students with material that could encourage more critical thinking. General textbooks, attempting to cover three thousand years of mathematical history, must necessarily oversimplify almost everything, the practice of which can scarcely promote a critical approach to the subject. For this reason, Craig Smorynski chooses a more narrow but deeper coverage of a few select topics. The second aim of this book is to include the proofs of important results which are typically neglected in the modern history of mathematics curriculum. The most obvious of these is the oft-cited necessity of introducing complex numbers in applying the algebraic solution of cubic equations. This solution, though it is now relegated to courses in the History of Mathematics, was a major occurrence in the history of mathematics. It was the first substantial piece of mathematics in Europe that was not a mere extension of what the Greeks had done and thus signified the coming of age of European mathematics. The fact that the solution, in the case of three distinct real roots to a cubic, necessarily involved complex numbers both made inevitable the acceptance and study of these numbers and provided a stimulus for the development of numerical approximation methods. Other unique features include: * a prefatory essay on the ways in which sources may be unreliable, followed by an annotated bibliography; * a modern recounting of a Chinese word problem from the 13th century, illustrating the need for consulting multiple sources when the primary source is unavailable; * the solution of the cubic equation, including multiple proofs that the algebraic solution uses complex numbers whenever the cubic equation has three distinct real solutions; * a critical reappraisal of Horner's Method; The final chapter contains lighter material, including a critical look at North Korea's stamps commemorating the 350th birthday of Newton, historically interesting (and hard to find) poems, and drinking songs or limericks with mathematical themes. The appendix outlines a few, small projects which could serve as replacements for the usual term papers. Craig Smorynski is also the author of "Self-Reference and Modal Logic" and "Logical Number Theory I".
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGeometry.
650 0 _aHistory.
650 1 4 _aMathematics.
650 2 4 _aHistory of Mathematical Sciences.
650 2 4 _aGeometry.
650 2 4 _aAlgebra.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387754802
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-75481-9
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509969
_d509969