Basic knowledge of algebra (Algebra 1-4) and analysis (Analisi Matematica 1-4).
Assessment methods and Criteria
The exam consists of a written test and an oral examination in the same session. The written part is made of written exercises (like a computation of the ring of integers, the class group and the group units of a number field). It is not possible to use notes, books or calculators.
Number Theory (first part)
First properties of a number field: norm, trace, discriminant and ring of integers (review of some of the arguments of the Algebra 3 course). Dedekind rings, factorization of ideals and ramification. Theorem of Minkowski. Theorem of Hermite. Theorem of Dirichlet and regulator of a number field. Dedekind ζ function. Class number formula. Other more advanced topics, time permitting.