Credits: 7.5

Type: bridging

Objectives:

To provide a solid grounding in the study of number theory, including the treatment of classical problems from a modern perspective as well as the consideration of their applications.

Knowledge:

• Arithmetic of number fields.
• Quadratic fields and binary quadratic forms.
• Cyclotomic fields.
• Riemann's zeta function.
• Dedekind's zeta function.
• Distribution of prime numbers.

Subject-specific competences:

• To assimilate the basic facts of the arithmetic of number fields and, more specifically, quadratic and cyclotomic fields.
• To be able to work with Riemann's zeta function and Dedekind's zeta function.
• To be able to apply algebraic and analytic methods to the study of prime numbers and Diophantine equations.
• To handle specific bibliography and software.