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In this class we shall make a transition from a very geometric notion of
symmetry of two dimensional objects and wall patterns to a very algebraic notion of a group.
The main theme can be expressed with a quote from Sophie Germain:
L'algèbre n'est qu'une géométrie écrite;
la géométrie n'est qu'une algèbre figurée.
(Algebra is nothing but written geometry;
Geometry is nothing but pictured algebra.)
We shall touch upon a curious similarity between mathematicians and biologists: namely,
their urge to classify things. In particular, we shall discuss why an algebraist may consider
a wall pattern made of Escher's Clowns to be the "same" as the one made of simple triangles.
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