This is a first graduate course on Mathematics for Economists. It assumes knowledge of the elementary techniques of Mathematics that are used in Economics, although they will be revisited and deepened throughout the course.

The objective is to provide a mathematical background for advanced courses on Economic theory. The student should learn and manage the main mathematical tools which are widely applied in the different areas of Economics. Regarding the general competences and skills, the student will develop the ability to: - Use the main tools that are needed in the analysis of economic problems. - Address economic problems with precision and rigour by means of mathematical models. - Analyze and solve the above mentioned models. - Interpret the solutions and apply them to a real context appropiately. On the other hand, regarding the specific competences, the student will be able to: - Perform operations with vectors and matrices and solve systems of linear equations. - Understand the fundamental concepts involved in the calculus of real-valued functions (with emphasis in differentiability). - Describe the qualitative properties of real-valued functions (with emphasis in convexity). - Articulate the different notions in a topology defined in a metric space. - Pose and solve static and dynamic optimization problems.

1. Matrix and Vector Algebra. Operations with matrices, determinants and Inverse Matrices. Systems of Linear Equations. Eigenvalues and Diagonalization. Quadratic forms. 2. Topology. Interior, Closure and Boundary. Compact sets. Convergent sequences and Limits. 3. Functions of One Variable. Properties. Monotonicity , continuity and differentiation. 4. Multivariable Calculus. Continuity and Differentiation. Implicit Function Theorem. 5. Convexity. Linear functionals and hyperplanes. Separating theorems. 6. Multivariable Optimization. The Lagrange Multiplier method. The Kuhn-Tucker Theorem. 7. Dynamical Systems. Difference Equations.

Students are expected to try to solve the problems and be ready to discuss them in class. Homeworks will be assigned on a regular basis, and will be solved in the classroom. Quizzes based on the classroom material will be held in class. There will be three office hours every week (voluntary).