Geodesic
Let's get acquainted with mapping degree!
The Teaching of Mathematics, XIV (2011) no. 2, p. 119

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Given a continuous map $f : M\rightarrow N$ between oriented manifolds of the same dimension, the associated {t degree} $deg(f)$ is an integer which evaluates the number of times the domain manifold $M$ "wraps around" the range manifold $N$ under the mapping $f$. The mapping degree is met at almost every corner of mathematics. Some of its avatars, pseudonyms, or close relatives are "winding number", "index of a vector field", "multiplicity of a zero", "Milnor number of a singularity", "degree of a variety", "incidence numbers of cells in a $CW$-complex", etc. We review some examples and applications involving this important invariant. One of emerging guiding principles, useful for a mathematical student or teacher, is that the study of mathematical concepts which transcend the boundaries between different mathematical disciplines should receive a special attention in mathematical (self)education.
Classification : 1AMS5501 97I60 2ZDMI65
Keywords: Mapping degree, winding number. 
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     author = {Rade T. \v{Z}ivaljevi\'c},
     title = {Let's get acquainted with mapping degree!},
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Rade T. Živaljević. Let's get acquainted with mapping degree!. The Teaching of Mathematics, XIV (2011) no. 2, p. 119 . http://geodesic.mathdoc.fr/item/TM2_2011_XIV_2_a6/