**1st module**

**Prof. Marco Andreatta**

**A.A. 1998/99**

**PROGRAMME**

The pourpose of the course is to give a unitary presentation of
many central and fundamental results of mathematics; this is done with
an historical approach, starting from "ancient" theorems and proofs , with
the pourpose to be selfcontained and complete (that is to supply all the
neccessary proofs).

Among the considered themes we recall: the theorem of Pithagora and
some fundamental results of the Greek mathematics, polynomial equations,
solvability of polynomial equations of degree ? 4 and their formulas, elementary
problems in number theory, the last Fermat theorem for n ? 4, analytic
and projective geometry, differential geometry and non euclidean geometries
, elliptic functions, complex numbers in algebra, geometry and analysis,
curves in mechanics, algebraic curves....

**REFERENCE TEXTS**

J. STILLWELL, MATHEMATICS AND ITS HISTORY, SPRINGER-VERLAG