Università degli Studi di Roma "Tor Vergata"

The final goals are

Linear Algebra

Basic properties of abstract vector spaces and linear transformations. To know how to apply basic properties of matrix algebra with special emphasis on block matrices. To be able to determine eigenvalues and eigenvectors of a matrix. Symmetric matrices. Notions of projections and idempotent matrices. To know how to diagonalize a matrix (under suitable conditions).

Calculus

To be able to evaluate integrals in several variables (by means of Fubini Theorem,). Change of variables in integrals and use of polar coordinates. Evaluation of integral by the derivation under the integral sign technique. To solve simple differential equations.

Optimization

To calculate the Hessian matrix and its eigenvalues. To calculate local minimum and maximum for a several variable function. Lagrangian multipliers to study optimization under costraints. Simple cases of Kuhn-Tucker theorem.

Probability

How the main discrete and (absolutely) continuous distribution arise from real life problems; their properties. Meaning of the basic limit theorems: (weak) law of large numbers and central limit theorem. Geometric meaning of conditional expectation. Multivariate gaussian.

The suggested textbooks are
C.P Simon and L. Blume. Mathematics for Economists. Norton & Company, ii) G. Casella and R.L. Berger. Statistical Inference. Duxbury.

The final goals are

Linear Algebra

Basic properties of abstract vector spaces and linear transformations. To know how to apply basic properties of matrix algebra with special emphasis on block matrices. To be able to determine eigenvalues and eigenvectors of a matrix. Symmetric matrices. Notions of projections and idempotent matrices. To know how to diagonalize a matrix (under suitable conditions).

Calculus

To be able to evaluate integrals in several variables (by means of Fubini Theorem,). Change of variables in integrals and use of polar coordinates. Evaluation of integral by the derivation under the integral sign technique. To solve simple differential equations.

Optimization

To calculate the Hessian matrix and its eigenvalues. To calculate local minimum and maximum for a several variable function. Lagrangian multipliers to study optimization under costraints. Simple cases of Kuhn-Tucker theorem.

Probability

How the main discrete and (absolutely) continuous distribution arise from real life problems; their properties. Meaning of the basic limit theorems: (weak) law of large numbers and central limit theorem. Geometric meaning of conditional expectation. Multivariate gaussian.

The suggested textbooks are
C.P Simon and L. Blume. Mathematics for Economists. Norton & Company, ii) G. Casella and R.L. Berger. Statistical Inference. Duxbury.