NUMERICAL SYSTEMS AND GALOIS THEORY
Learning outcomes of the course unit
To introduce ordered fields different from the subfields of the real fields, to generalize the concept of absolute value of the real field, to deepen field theory as studied by the theory of Galois fields, to solve equations in the field of p-adic numbers, Galois’ criterion for solvability by radicals, separability, Abel's theorem about the general equation of degree n.
Course contents summary
The course deals the following main topics:
Ordered fields , equations in the field of p-adic numbers, Galois’ criterion for solvability by radicals, teorema di Abel sull’equazione generale di grado n, separability.
B.L. Van Der Waerden “Modern algebra” Springer
The preferred teaching tool for the development of such knowledge are the lectures. The note taking is seen as part of the learning process.
Assessment methods and criteria
The assessment of learning is done in classic way, through the evaluation of an oral interview. In the colloquium, the student must be able to independently conduct demonstrations related to the intrinsic properties of the studied structures using an appropriate algebraic language and a proper mathematical formalism.