The objective of the course is to present mathematical tools and results that constitute the analytical foundations underlying modern economics and finance. These contents will be used throughout the PhD courses.

General characterization





Responsible teacher

Marta Faias


Weekly - Available soon

Total - Available soon

Teaching language



Available soon


1.    Aliprantis D. and K. Border, Infinite Dimensional Analysis, Springer-Verlag, 1999.
2.    Billingsley P., Probability and Measure, NY:Wiley, 1995.
3.    Kolmogorov A. and S. Fomin, Introductory Real Analysis, Dover (a better translation into Brazilian Portuguese is available in the library: Elementos da teoria das funções
e da análise funcional), 1970.
4.    Rudin W., Principles of Mathematical Analysis, 1976.
5.    Simon C. and L. Blume, Mathematics for economists, 1994.
6.    Stokey N. and R. Lucas, Recursive Methods in Economic Dynamics. Harvard University Press, 1989.

Teaching method

The professor gives the course by lectures, where she explains all topics referred to in the syllabus and solves some relevant examples. Problems are provided to students to be worked outside the classroom with prior knowledge acquired during the course. Solved problems are also provided. Students still have the so-called office hours where they can clarify their doubts with the teacher.

Evaluation method

Midterm (40%). Final exam (40%.), Problem sets (20%)

Subject matter

1.    Differential equations
2.    Dynamic optimization in discrete-time and introduction to continuous time
3.    Elements of set theory and topology of metric spaces
4.    Fixed-point theory
5.    Measure theory and probability theory


Programs where the course is taught: