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/