10 lectures - 32 hours
Basic knowledge on sets, logic, relations, functions, algebraic structures, real and complex numbers
Walter Rudin - Principles of Mathematical Analysis - McGraw-Hill (1976) - Chapters 1-6, 9
Serge Lang - Linear Algebra - Springer (1987) - Chapters I-VI, VIII-XI
Angel de La Fuente - Mathematical Methods and Models for Economists - Cambridge University Press (2000) - § 2.11, Chapter 5
Sets, logic, relations, functions, algebraic structures, real and complex numbers
Definitions, sequences, topology, limits, continuity, completeness, compactness, connectedness
Linear independence, bases, linear transformations, isomorphisms, determinants, systems of linear equations, changes of basis, eigenvalues and eigenvectors, diagonalizability, Jordan normal form, quadratic forms
Differential univariate real functions, partial and directional derivatives, differentiability, homogeneous functions, the implicit function theorem