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Curves and singularities

Grant number: 22/11895-8
Support Opportunities:Scholarships in Brazil - Program to Stimulate Scientific Vocations
Effective date (Start): January 03, 2023
Effective date (End): February 22, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Maria Aparecida Soares Ruas
Grantee:Odete Lara Melo Budtinger
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Classical differential geometry is the object of study of the undergraduate course in Mathematics. The approach of geometry topics in R3 through the singularity theory allows a very rich study of the geometric properties of curves, families of curves and surfaces, which successfully complements the classical approach. On the other hand, the introduction of the theory of singularities in order to study the generic properties of curves and surfaces does not require much prior knowledge and is therefore quitesuitable for undergraduate students. (AU)

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