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Code: | M3010 | Acronym: | M3010 | Level: | 300 |

Keywords | |
---|---|

Classification | Keyword |

OFICIAL | Mathematics |

Active? | Yes |

Responsible unit: | Department of Mathematics |

Course/CS Responsible: | First Degree in Mathematics |

Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|

L:B | 0 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |

L:CC | 1 | Plano de estudos a partir de 2014 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:F | 2 | study plan from 2017/18 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:G | 0 | study plan from 2017/18 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:M | 31 | Plano estudos a partir do ano letivo 2016/17 | 2 | - | 6 | 56 | 162 |

3 | |||||||

L:Q | 0 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |

Teacher | Responsibility |
---|---|

Manuel Augusto Fernandes Delgado | |

Maria Zélia Ramos Alves da Rocha |

Theoretical and practical : | 4,00 |

Type | Teacher | Classes | Hour |
---|---|---|---|

Theoretical and practical | Totals | 1 | 4,00 |

Manuel Augusto Fernandes Delgado | 2,00 | ||

Maria Zélia Ramos Alves da Rocha | 2,00 |

Study constructive methods of numerical resolution of the following problems of Linear Algebra: systems of equations, inverse of matrices and determinants, focusing on the aspects of conditioning and stability, convergence, error control, construction of algorithms, implementation and experimentation in computer in the MATLAB language and processing of study cases.

Students should acquire knowledge on some basic concepts of Computational Algebra, as well as to have contact with Gröbner basis.

Students should acquire the knowledge of the fundamental methods of Numerical Linear Algebra in their theoretical, practical, computational and experimental aspects.

It is expected that the student has good knowledge of abstract algebra. In particular the student should know the division algorithm for polynomials in one variable, the Euclidean algorithm and how to calculate the greatest common divisor of two polynomials in one variable.

Fundamental notions of Linear Algebra.

Basic notions of any programming language.

- Motivation: affine varieties and polynomial ideals.
- Gröbner bases: polynomial ideals, monomial orders and multivariate division with remainder, monomial ideals and Hilbert basis theorem, Gröbner bases and S-polynomials, Buchberger's algorithm.

- Introduction to MATLAB
- The MATLAB environment. Random, Hilbert and Pascal matrices, the command
*gallery*. Linear algebra: norms, condition numbers, the operator \, Gauss and Cholesky factorizations, the*lu*and*chol*commands. Programming. Graphs. - Numerical resolution of linear systems, inverse of matrices and determinants: vector and matrix norms, matrix series, conditioning, condition numbers, triangular systems and inverses, direct methods of Gauss and Cholesky; iterative methods of Jacobi and Gauss-Seidel.

Cox David; Ideals, varieties, and algorithms. ISBN: 0-387-97847-X ((4th edition))

Brezinski Claude; Méthodes numériques directes de l.algèbre matricielle. ISBN: 2-7298-2246-1

Gathen Joachim von zur; Modern computer algebra. ISBN: 0-521-82646-2

The course material and examples will be presented by the teacher. Some time is to be reserved for the resolution of exercises by the students with the advice of the teacher.

In the theoretic-practical classes are presented the contents of the syllabus with illustrative examples followed by the resolution of theoretical, practical and computational exercises implemented in the MATLAB language.

SageMath

Singular

Physical sciences > Mathematics > Computational mathematics

designation | Weight (%) |
---|---|

Exame | 50,00 |

Teste | 50,00 |

Total: |
100,00 |

designation | Time (hours) |
---|---|

Estudo autónomo | 106,00 |

Frequência das aulas | 56,00 |

Total: |
162,00 |

Numerical Linear Algebra module: exam.

Computational Algebra module: exam.

Numerical Linear Algebra module: exam.

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Page created on: 2019-09-18 at 13:34:50

Page created on: 2019-09-18 at 13:34:50