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| 001 | 2301855 | ||
| 003 | BD-DhUL | ||
| 005 | 20140822130151.0 | ||
| 008 | 980401s1999 maua b 001 0beng | ||
| 010 | _a 98017834 | ||
| 020 | _a0817640401 (alk. paper) | ||
| 020 | _a3764340401 (alk. paper) | ||
| 035 | _a(OCoLC)ocm38992931 | ||
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_aDLC _cBD-DhUL _dBD-DhUL _dOrLoB-B |
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_aeng _hger |
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| 043 | _ae-gx--- | ||
| 050 | 0 | 0 |
_aQA29.R425 _bL3813 1999 |
| 082 | 0 | 0 |
_a510.92 _221 _bLAB |
| 100 | 1 | _aLaugwitz, Detlef. | |
| 240 | 1 | 0 |
_aBernhard Riemann, 1826-1866. _lEnglish |
| 245 | 1 | 0 |
_aBernhard Riemann, 1826-1866 : _bturning points in the conception of mathematics / _cDetlef Laugwitz ; translated by Abe Shenitzer with the editorial assistance of the author, Hardy Grant, and Sarah Shenitzer. |
| 260 |
_aBoston : _bBirkhäuser, _cc1999. |
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| 300 |
_axvi, 357 p. : _bill. ; _c24 cm. |
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| 504 | _aIncludes bibliographical references (p. [341]-349) and index. | ||
| 505 | 0 | 0 |
_g0. _tIntroduction -- _g1. _tComplex Analysis. _g1.1. _tThe genesis of complex analysis up to Riemann's time. _g1.2. _tThe dissertation of 1851. _g1.3. _tThe elaborations. _g1.4. _tThe zeta function and the distribution of primes -- _g2. _tReal Analysis. _g2.1. _tFoundations of real analysis. _g2.2. _tTrigonometric series before Riemann. _g2.3. _tRiemann's results. _g2.4. _tTrigonometric series after Riemann. _g2.5. _tA self-contained chapter: Gauss, Riemann, and the Gottingen atmosphere -- _g3. _tGeometry; Physics; Philosophy. _g3.1. _tGeometry. _g3.2. _tPhysics. _g3.3. _tOn philosophy -- _g4. _tTurning Points in the Conception of Mathematics. _g4.1. _tThe historians' search for revolutions in mathematics. _g4.2. _tTurning point in the conception of the infinite in mathematics. _g4.3. _tTurning point in the method: Thinking instead of computing. _g4.4. _tTurning point in the ontology: Mathematics as thinking in concepts. _g4.5. _tThe ontology and methodology of mathematics after Riemann. _g4.6. _tConcluding remarks. |
| 520 | _aThis book, originally written in German and presented here in an English-language translation, is the first attempt to examine Riemann's scientific work from a single unifying perspective. Laugwitz describes Riemann's development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. | ||
| 520 | 8 | _aDavid Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle - for mathematics and physics alike - to be a matter of "understanding the world through its behavior in the infinitely small.". | |
| 520 | 8 | _aThis remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann's work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics. | |
| 600 | 1 | 0 |
_aRiemann, Bernhard, _d1826-1866. |
| 650 | 0 |
_aMathematicians _zGermany _vBiography. |
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| 650 | 0 |
_aMathematics _zGermany _xHistory _y19th century. |
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_aAUTH _bTOC |
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