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