2024
Computational Algebra
Name: Computational Algebra
Code: MAT14241L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Presentation
In this curricular unit, current computational algebra techniques are acquired, namely Gröbner bases.
Sustainable Development Goals
Learning Goals
O1 - Knowledge: experiencing current techniques in computational algebra, namely Gröbner bases.
O2 - Skills and Competences: developing abstract reasoning and the capacity of finding strategies to solve new problems
O2 - Skills and Competences: developing abstract reasoning and the capacity of finding strategies to solve new problems
Contents
Polynomial rings and ideals.
Monomial orderings in k[x_1,...,x_n].
Monomial ideals and Dickson lemma.
Hilbert basis theorem and Gröbner bases.
Buchberger's algorithm.
Some applications of Gröbner bases.
Rewriting systems. Knuth Bendix algorithm.
Monomial orderings in k[x_1,...,x_n].
Monomial ideals and Dickson lemma.
Hilbert basis theorem and Gröbner bases.
Buchberger's algorithm.
Some applications of Gröbner bases.
Rewriting systems. Knuth Bendix algorithm.
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 between two and six partial tests and quizzes, 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. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral 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 between two and six partial tests and quizzes, 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. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral 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
Certificações
