ENS ÉDITIONS
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COM.ONIXSUITE.9782847889406
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ENS Éditions
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284788940X
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9782847889406
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9782847889406
DG
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002
<TitleType>01</TitleType>
<TitleText>Hors Collection</TitleText>
<TitleType>01</TitleType>
<TitleText textcase="01">A singular mathematical promenade</TitleText>
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GCOI
29021100476860
1
A01
Étienne Ghys
Ghys, Étienne
Étienne
Ghys
<p>Étienne Ghys is a CNRS Senior Researcher at École normale supérieure de Lyon.</p>
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eng
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306
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MAT027000
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ENS Internet -site
Sciences
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<p>A stroll in the mathematical world. This is neither an elementary introduction to the theory of singularities, nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit of algebra, topology, geometry, complex analysis, combinatorics, and computer science. Hopefully some motivated undergraduates and some more advanced mathematicians will enjoy some of these panoramas.</p>
<p></p>
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The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit of algebra, topology, geometry, complex analysis, combinatorics, and computer science.
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<p>Preface<br />
Road map<br />
Intersecting polynomials: Maxim Kontsevich<br />
Patterns and permutations: Donald Knuth<br />
Separable permutations<br />
Hipparchus and Schroeder<br />
De methodis serierum et fluxionum: Newton's method<br />
De methodis serierum et fluxionum: Newton's series<br />
Some formal algebra<br />
Gauss on algebraic curves<br />
Proof of Gauss's claim on singularities<br />
De seriebus divergentibus: Euler, Cauchy and Poincaré<br />
Convergence: Cauchy<br />
Moebius and his band<br />
Moebius necklaces<br />
Resolution of singularities<br />
The 3-sphere and the Hopf fibration<br />
The cusp and the trefoil<br />
Victor Puiseux, at last!<br />
Jack Milnor and his fibration<br />
The Hipparchus-Schroeder-Tamari-Stasheff associahedron<br />
Jim Stasheff and loop spaces<br />
Operads<br />
Singular operads<br />
Gauss is back: curves in the plane<br />
Analytic chord diagrams: an algorithm<br />
Analytic chord diagrams: interlace graphs<br />
Gauss and linking<br />
Kontsevich is back: universal invariant<br />
Postface<br />
Acknowledgments<br />
Image Credits</p>
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<p>A stroll in the mathematical world. This is neither an elementary introduction to the theory of singularities, nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit of algebra, topology, geometry, complex analysis, combinatorics, and computer science. Hopefully motivated undergraduates and more advanced mathematicians will enjoy some of these panoramas.</p>
<p></p>
35
<p>A stroll in the mathematical world. This is neither an elementary introduction to the theory of singularities, nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit of algebra, topology, geometry, complex analysis, combinatorics, and computer science. Hopefully some motivated undergraduates and some more advanced mathematicians will enjoy some of these panoramas.</p>
06
03
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ENS Éditions
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