2024
Introdution to Semigroups
Name: Introdution to Semigroups
Code: MAT14354M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Presentation
In this CU we study finitely generated cancellative monoids as well as numerical semigroups, in particular those that are irreducible.
Sustainable Development Goals
Learning Goals
- Knowledge: having contact with the main objects in the theory of semigroups and experiencing problems in this context, applying general algebraic techniques and creating strategies that are specific to each problem; exploring applications of the theory of semigroups in other fields of Mathematics.
- Skills and Competences: developing abstract reasoning and the capacity of finding strategies to solve new problems.
- Skills and Competences: developing abstract reasoning and the capacity of finding strategies to solve new problems.
Contents
Finitely generated commutative groups.
Finitely generated cancelative monoids.
Numerical semigroups: minimal presentation, cardinality superior limits.
Irreducible numerical semigroups.
Finitely generated cancelative monoids.
Numerical semigroups: minimal presentation, cardinality superior limits.
Irreducible numerical semigroups.
Teaching Methods
Problem-solving sessions, where students are invited to work on their own or in small groups, with some moments of exposition or discussion involving the whole class.
The evaluation may be either continuous, done through two or three oral presentations, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.
The evaluation may be either continuous, done through two or three oral presentations, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.
