A numerical semigroup is a subset of ${\mathbb N}$ closed under addition, containing the zero element, and with finite complement in ${\mathbb N}$. Even though the concept is easy to understand, there are many pro\-blems related to numerical semigroups that remain unsolved. Probably, the most popular of them is the Frobenius problem, which consists in finding a formula for the largest integer not belonging to a numerical semigroup in terms of its generators. In this three session course we will overview the basics and tools used in the study of numerical semigroups, as well as several interconnections with other branches of mathematics. Most of the contents are meant to be understood by any student with a course in elementary mathematics.

Main topics:

1. Three ways to define a numerical semigroup. Generalities.

2. Big families.

3. Numerical semigroups and Diophantine inequalities.

Este curso está estruturado em três sessões de 1 hora:

2006-04-07 (duas sessões) 14:30 - 15:30 e 16:00 -- 17:00

2006-04-10 (uma sessão) 17:00 -- 18:00