000 04690nam a22004935i 4500
001 978-0-8176-8268-2
003 DE-He213
005 20140220083227.0
007 cr nn 008mamaa
008 111128s2012 xxu| s |||| 0|eng d
020 _a9780817682682
_9978-0-8176-8268-2
024 7 _a10.1007/978-0-8176-8268-2
_2doi
050 4 _aQA21-27
072 7 _aPBX
_2bicssc
072 7 _aMAT015000
_2bisacsh
082 0 4 _a510.9
_223
100 1 _aKleiner, Israel.
_eauthor.
245 1 0 _aExcursions in the History of Mathematics
_h[electronic resource] /
_cby Israel Kleiner.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2012.
300 _aXXI, 347p. 36 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aA. Number Theory -- 1. Highlights in the History of Number Theory: 1700 BC - 2008 -- 2. Fermat: The Founder of Modern Number Theory -- 3. Fermat's Last Theorem: From Fermat to Wiles -- B. Calculus/Analysis -- 4. A History of the Infinitely Small and the Infinitely Large in Calculus, with Remarks for the Teacher -- 5. A Brief History of the Function Concept -- 6. More on the History of Functions, Including Remarks on Teaching -- C. Proof -- 7. Highlights in the Practice of Proof: 1600 BC - 2009 -- 8. Paradoxes: What are they Good for? -- 9. Principle of Continuity: 16th - 19th centuries -- 10. Proof: A Many-Splendored Thing -- D. Courses Inspired by History -- 11. Numbers as a Source of Mathematical Ideas -- 12. History of Complex Numbers, with a Moral for Teachers -- 13. A History-of-Mathematics Course for Teachers, Based on Great Quotations -- 14. Famous Problems in Mathematics -- E. Brief Biographies of Selected Mathematicians -- 15. The Biographies -- Index.
520 _aThis book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively.  Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work.  Each of the first three parts—on number theory, calculus/analysis, and proof—begins with a survey of the respective subject and is followed in more depth by specialized themes. Among the specialized themes are:  Fermat as the founder of modern number theory, Fermat’s Last Theorem from Fermat to Wiles, the history of the function concept, paradoxes, the principle of continuity, and an historical perspective on recent debates about proof.  The fourth part contains essays describing mathematics courses inspired by history. The essays deal with numbers as a source of ideas in teaching, with famous problems, and with the stories behind various "great" quotations. The last part gives an account of five mathematicians—Dedekind, Euler, Gauss, Hilbert, and Weierstrass—whose lives and work we hope readers will find inspiring. Key features of the work include: * A preface describing in some detail the author's ideas on teaching mathematics courses, in particular, the role of history in such courses; * Explicit comments and suggestions for teachers on how history can affect the teaching of mathematics; * A description of a course in the history of mathematics taught in an In-Service Master's Program for high school teachers; * Inclusion of issues in the philosophy of mathematics; * An extensive list of relevant references at the end of each chapter. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aLogic, Symbolic and mathematical.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aHistory of Mathematical Sciences.
650 2 4 _aMathematics Education.
650 2 4 _aNumber Theory.
650 2 4 _aAnalysis.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aMathematics, general.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817682675
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8268-2
912 _aZDB-2-SMA
999 _c100227
_d100227