Cellular functions

Abstract

In most fields of mathematics, we study some class of objects and also the functions appropriate to the objects of study. In linear algebra, the objects studied are vector spaces and the corresponding functions, called linear transformations and usually represented by matrices, are those which preserve the vector space structure. In geometry, we study isometries, such as rotations: functions that do not change the geometric properties of length, angle measure, area, and volume. In abstract algebra, the objects of study are groups and the appropriate functions are homomorphisms, which preserve the algebraic properties of the groups. The best possible homomorphism is an isomorphism; isomorphic groups are essentially identical algebraically.

“On a dit souvent que la géométrie est l’art de bien raisonner sur les figures mal faites.”

Henri Poincaré