| Code |
14711
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Basic knowledge of real functions of real variable.
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Mode of delivery |
Face-to-face instruction.
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Work placements |
Not applicable.
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Learning outcomes |
This course has as its main objective the study, though at a basic level, of two fundamental areas of Mathematics, Linear Algebra and Graph Theory, which are an essential tool in the scientific area of Informatics.
Prove elementary results involving sets;
Solve problems using the rules and methods of propositional calculus;
Identify square, rectangular, diagonal and symmetric matrices;
manipulate matrices.
Solve and classify systems of linear equations;
Identify the most important properties of determinants;
Apply determinants to solve systems of linear equations and to obtain the inverse of a matrix;
Classify graphs;
Construct the incidence matrix and the adjacency matrix of a graph.
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Syllabus |
Chapter I – Elements of Logic
1. Propositions and logic operations.
2. Properties of logic operations.
3. De Morgan laws.
4. Conditions.
5. Quantifiers.
6. Second De Morgan laws.
Chapter II – Basic Notions of Sets
1. Intuitive theory of sets
2. Equality of sets.
3. Operations with sets.
Chapter III – Introduction to Linear Algebra
1. Operations with matrices.
2. Elementary operations and condensation.
3. Rank of a matrix.
4. Solving of systems of linear equations.
5. Inverse of a matrix.
6. Determinant of a square matrix.
7. Properties; Algebraic complements.
8. Laplace theorem; Adjoint matrix.
9. Application of determinants in solving systems of linear equations and in obtaining the inverse of a matrix.
Chapter IV - Graphs
1. Graphs and simple graphs
2. Incidence matrix and the adjacency matrix
3. Subgraphs
4. Trees and forests
5. Euler path and Hamilton cycle
6. Applications
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Main Bibliography |
I. Cabral, C. Perdigão, C. Saiago, Álgebra linear: teoria, exercícios resolvidos e exercícios propostos com soluções, Escolar Editora, 2009.
S. Lipschutz, Álgebra linear: resumo da teoria, São Paulo: McGraw-Hill do Brasil, 1972.
D. Cardoso, J. Szymanski e M. Rostami, Matemática Discreta, Escolar Editora, 2009
A. Monteiro e I. Matos, Álgebra um primeiro curso, Escolar Editora, 1995
F. Oliveira, Teoria de Conjuntos intuitiva e axiomática, Escolar Editora, 1982
K. Rosen, Discrete Mathematics and its applications. MCGRAW-HILL EDUCATION - EUROPE
A. Jeffrey, Matrix operations for engineers and scientists, Springer.
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Teaching Methodologies and Assessment Criteria |
The teaching-learning assessment consists of two tests. The final grade is the arithmetic average of the grade obtained in these two tests.
The minimum mark of access to exam is 5 values.
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Language |
Portuguese. Tutorial support is available in English.
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