A Unique Mathematical Tour
Authors
Description
The book is not an elementary introduction to singularity theory, nor is it a specialized treatise containing many new theorems. The purpose of this short book is to invite the reader on a mathematical tour. We will pay a visit to Hipparchus, Newton and Gauss, as well as to many contemporary mathematicians. We played around with a little bit of algebra, topology, geometry, complex analysis, combinatorics, and computer science. We hope that motivated undergraduate students and mathematicians with more advanced knowledge will enjoy some of these panoramas.
Target audience
Higher education
Name: A Unique Mathematical Tour
Author(s): e Étienne Ghys
Pages: 346
Publication: IMPA, 2021
ISBN: 978-65-990528-9-7
Edition: 1
Foreword
Script
Intersecting polynomials
Patterns and Permutations: Donald Knuth
Separable permutations
Hipparchus and Schröder
De methodis serierum et fluxionum: Newton’s method
De methodis serierum et fluxionum: Newton’s series
A little formal algebra
Gauss and algebraic curves
Proof of Gauss’s claim about singularities
De seriebus divergentibus: Euler, Cauchy and Poincaré
Convergence: Cauchy
Möbius and its track
Necklaces of Möbius
Singularity Resolution
The 3-dimensional sphere and the Hopf fibration
The cusp and the clover
Victor Puiseux, finally!
Jack Milnor and his fibering
The Hipparchus–Schröder–Tamari–Stasheff associate
Jim Stasheff and the spaces of ties
Operads
Operads singulares
Gauss is back: curves in the flat
Analytical String Diagrams: An Algorithm
Analytical String Diagrams:
Entanglement graphs
Gauss and the number of intertwining
Kontsevich is back: a universal invariant
Afterword
Thanks
Image credits