A Singular Mathematical Promenade

Abstract

This is neither an elementary introduction to singularity theory 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 and computer science. Hopefully, some motivated undergraduates and some more advanced mathematicians will enjoy some of these panoramas.

300 pages, 500 figures

Cited by in corpus (9)

• The combinatorics of plane curve singularities. How Newton polygons blossom into lotuses
• Differential Geometric Foundations for Power Flow Computations
• Measuring the local non-convexity of real algebraic curves
• Poincaré-Reeb graphs of real algebraic domains
• Permutations encoding the local shape of level curves of real polynomials via generic projections
• Decomposition in Coxeter-chambers of the configuration space of $d$ marked points on the complex plane
• Combinatorial study of morsifications of real univariate singularities
• On the enumeration of closures and environments with an application to random generation
• Topologie et dénombrement des courbes algébriques réelles singulières