Guia docente 2013_14 Escola de Enxeñaría Industrial

Contents

Topic	Sub-topic
Preliminaries	The field of the real numbers. The field of the complex numbers: structure and properties.
Matrices, determinants and systems of linear equations.	Definition and types of matrices. Operations with matrices. Elementary transformations, rank. Inverse and determinant of a square matrix. Discussion and resolution of systems of linear equations
Vectorial spaces and linear applications.	Definition of vectorial space. Subspaces. Linear independence, base and dimension. Coordinates, change of base. Basic notions on linear applications.
Eigenvalues and eigenvectors.	Definition of eigenvalue and eigenvector of a square matrix. Diagonalization. Applications of the eigenvalues.
Vectorial spaces with scalar product and quadratic forms.	Vectorial spaces with scalar product. Associated norm and properties. Orthogonality. Gram-Schmidt orthogonalization process. Orthogonal diagonalization. Quadratic forms.
Descriptive statistics and regression.	Concept and uses of the statistics. Variables and attributes. Types of variables. Representations and charts. Position and dispersion measures. Analysis of bivariate data. Linear regression. Correlation.
Probability.	Concept and properties. Conditional probability and independence of events. Bayes Theorem.
Discrete random variables and continuous random variables.	Concept of random variable. Types of random variables. Distribution function. Discrete random variables. Continuous random variables. Characteristics of a random variable. Main distributions: Binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Normal. Central Limit Theorem.
Statistical inference.	General concepts. Sampling distributions. Point estimation. Confidence intervals. Tests of hypotheses.