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# Algebra

 Code: EIC0003 Acronym: ALGE

Keywords
Classification Keyword
OFICIAL Mathematics

## Instance: 2018/2019 - 1S

 Active? Yes Responsible unit: Mathematics Section Course/CS Responsible: Master in Informatics and Computing Engineering

### Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEIC 165 Syllabus since 2009/2010 1 - 4,5 56 121,5

### Teaching Staff - Responsibilities

Teacher Responsibility
António Joaquim Mendes Ferreira
Ana Maria Azevedo Neves

### Teaching - Hours

 Lectures: 2,00 Recitations: 2,00
Type Teacher Classes Hour
Lectures Totals 1 2,00
António Joaquim Mendes Ferreira 2,00
Recitations Totals 6 12,00
Mariana Rita Ramos Seabra 1,25
Luís Filipe Gomes Pereira 2,50
Albertino José Castanho Arteiro 1,00
Ana Maria Azevedo Neves 3,25
António Joaquim Mendes Ferreira 4,00

### Teaching language

Suitable for English-speaking students

### Objectives

SPECIFIC AIMS: This discipline has two main objectives: the promotion of logical reasoning and methods of analysis and the introduction and theoretical development of a set of concepts that will be fundamental to support the study of other disciplines along this course of studies.

### Learning outcomes and competences

LEARNING OUTCOMES: Learning Outcomes: At the end of the semester, students should be: 1. capable of analysing and solving systems of linear equations; 2. acquainted with basic matrix operations and its properties; 3. capable of defining a non-singular matrix and be acquainted with the properties of an inverse matrix and its calculation; 4. capable of defining the determinant of a matrix and be acquainted with its properties and calculation; 5. capable of defining vector space, vector subspace and Euclidian space; 6. capable of defining linear combination of vectors, linear independence/dependence vectors and subspace; 7. capable of defining and determining a base and the dimension of a vector space; be capable of obtaining the components of a vector in relation with its base; 8. capable of defining a linear transformation and calculate and characterize its kernel; be acquainted with algebraic operations and define and calculate inverse transformation; 9. capable of using a matrix to represent a linear transformation and operate linear transformations using matrix algebra; 10. capable of defining a change of base matrix and apply it to problems of change of base that involve elements of a vector space and linear transformations; 11. capable of defining similar matrices and be acquainted with their properties; 12. capable of calculating eigenvalues and eigenvectors of linear transformations and to be acquainted with their properties, and if possible identify a diagonal matrix representation for a linear transformation.

Presencial

### Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic knowledge of systems of equations and vector algebra

### Program

Definition of vector space Vector subspaces Linear dependence and independence Bases and dimension Components Inner product Euclidian spaces Norms and orthogonality Linear spaces of matrices Product of matrices Transposed matrix Inverse matrix Square matrix Orthogonal matrix Similar matrices Change of bases matrices Determinants Condensation method and Laplace theorem Inversion of matrices using a determinant Systems of linear equations Gaussian method of elimination Cramer’s rule Linear transformation Kernel Algebraic operations with linear transformations Injective linear transformations Matrix representation of a linear transformation Isomorphism between linear transformations and matrices Eigenvalues and eigenvectors of linear transformations Characteristic polynomial Conditions for the existence of diagonal matrix representation and linear transformation

### Mandatory literature

Anton, Howard; Elementary linear algebra. ISBN: 0-471-44902-4
Apostol, Tom M.; Calculus. ISBN: 84-291-5001-3
Barbosa, José Augusto Trigo; Noções sobre matrizes e sistemas de equações lineares. ISBN: 972-752-069-3 972-752-065-0
J.A. Trigo Barbosa; ALGA - Apontamentos Teórico-Práticos
J.A. Trigo Barbosa, J.M.A. César de Sá, A.J. Mendes Ferreira; ALGA - Exercícios Práticos
José Trigo Barbosa; Noções sobre Geometria Analítica e Análise Matemática, 2017

### Complementary Bibliography

Luís, Gregório; Álgebra linear. ISBN: 972-9241-05-8
Ribeiro, Carlos Alberto Silva; Álgebra linear. ISBN: 972-8298-82-X
Monteiro, António; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8

### Teaching methods and learning activities

Theoretical classes: detailed exposition of the program of the discipline illustrated by application examples. Theoretical-practice classes: application of the theoretical concepts in the resolution of several exercises that can be found in the proposed literature.

### Evaluation Type

Distributed evaluation without final exam

### Assessment Components

Designation Weight (%)
Exame 100,00
Participação presencial 0,00
Total: 100,00

### Amount of time allocated to each course unit

Designation Time (hours)
Estudo autónomo 66,00
Frequência das aulas 56,00
Total: 122,00

### Eligibility for exams

According to General Evaluation Rules of FEUP

### Calculation formula of final grade

Students have to attend to three mini-tests. Final mark will be based on the average mark of the three exams. The dates of the mini-test and the final exam have not yet been set. The exams are closed book exams.

### Examinations or Special Assignments

Students have to attend to three mini-tests. Final mark will be based on the average mark of the three exams. The dates of the mini-test and the final exam have not yet been set. The exams are closed book exams.

Not applicable

### Special assessment (TE, DA, ...)

Although working students are exempt from classes, they must do the mini-tests

### Classification improvement

After the normal exam season, students who have failed one or more mini-tests, can make another mini-test(s), at the "recurso" test.

### Observations

Students are not allowed to use a graphics calculator on the exam.