# Mathematics I

**Auditing and Taxation**

6 ECTS; 1º Ano, 1º Semestre, 30,0 T + 45,0 PL

**Lecturer**

- José Manuel Borges Henriques Faria Paixão

- Cristina Maria Mendes Andrade

**Prerequisites**

Knowledge of algebraic calculus.

**Objectives**

At the end of this module the students will be able to analyse, interpret and formulate problems in Linear Algebra and project analysis, and have obtained the mathematical foundations that will allow the extrapolation of mathematical problems to economic and social problems.

**Program**

PROJECT ANALYSIS WITH NETWORKS: 1. Introduction to Microsoft Project 2. CPM and PERT 3. Financial analysis

LINEAR ALGEBRA: 1.Matrices(definition, types of matrices, matrix arithmetics, rank of a matrix, Gaussian elimination and systems of linear equations); 2. Determinants (definition, properties, Laplace expansion, the adjoint and inverse matrices, Cramer's rule and systems of linear equations)

**Evaluation Methodology**

Continuous Assessment: written test (70%)(mínimum grade 6) and project with Microsoft Project (30%).

Exams assessment: Closed-book written test graded from 0 to 20.

**Bibliography**

- Anton, H. (2010). *Elementary Linear Algebra*. USA: John Wiley & Sons

- Strang, G. (2009). *Linear Algebra and its Applications*. USA: Wellesley Cambridge Press

- Amaral, I. e Ferreira, M. (2008). *Algebra Linear: Matrizes e Determinantes*. (Vol. 1). Portugal: Edições Sílabo

**Method of interaction**

Lectures designed to introduce concepts and discuss their applications. Practical lessons are designed develop autonomy in problem solving some of them with Microsoft Project.

**Software used in class**

Microsoft Project