Algebra

Code:

EIC0003

Acronym:

ALGE

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2008/2009 - 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	181	Syllabus since 2006/2007	1	-	5	70	135

Teaching language

Portuguese

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:
At the end of this, students should be capable of:
1) Define vector space, vector subspace and Euclidian subspace;
2) Define linear combination of vectors, linear independence and subspace spanned by a set of vectors;
3) Define a basis and dimension of vector space; obtain the coordinates of a vector with respect to a given basis;
4) Knowing basic matrix operations, properties and operations;
5) Define nonsingular matrix, properties of the inverse of a matrix and calculate the inverse of a matrix;
6) Define determinant of a matrix, properties and calculate it;
7) Analyse and solve linear systems of equations;
8) Define linear transformations, define and calculate kernel and algebraic operations;
9) Define change-of-basis matrix and apply it to problems with vector spaces and linear transformations;
10) Calculate eigenvalues and eigenvectors of linear transformations and knowing properties.

Program

Matrices - Algebraic operations. Transpose of a matrix. Square matrices: definitions and special properties. Inverse of a square matrix. Determinants - Definition and properties. Minors and cofactors. The Laplace theorem. Computation of determinants. The determinant of the inverse of a non-singular matrix. Systems of Linear Equations - Gauss and Gauss-Jordan methods. Cramer´s rule.
Linear Spaces - Definition and properties. Subspaces of a linear space. Dependent and independent sets in a linear space. Bases and dimension. Inner products. Euclidean spaces. Norms and orthogonality. Linear Transformations and Matrices - Definition. Null space and range. Nullity and rank. Algebraic operations. Inverses. One-to-one linear transformations. Matrix representation of linear transformations. Matrices representing the same linear transformation. Similar matrices. Eigenvalues and Eigenvectors - Definition and properties. Linear transformations with similar diagonal matrix representations.

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, J.M.A. César de Sá, A.J. Mendes Ferreira; ALGA - Exercícios Práticos
J.A. Trigo Barbosa; ALGA - Apontamentos Teórico-Práticos

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

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	65,00
Examinations	Exame	4,00		2009-02-20
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Time to study for examination	Estudo autónomo	20	2009-02-20
Time to study for lessons	Estudo autónomo	46	2009-02-20
	Total:	66,00