Master’s (12 to 36 months) and Doctorate (24 to 84 months)

For both the master’s and doctoral programs, students’ overall performance is evaluated between the first and second semester in a written qualifying examination that includes tests in the following areas: algebra, analysis and geometry/topology.

The main aim of the doctoral program is to produce leaders in mathematical research, most of whom will work as lecturers in universities and research centers or other related areas.

The program aims to generate doctoral theses of sufficiently high quality to be published in the best specialized, internationally renowned journals.

For the second three-year period running, the program was awarded the highest possible score (seven) by CAPES for the period 2004 to 2006.

**Major Area: Algebra
**Lines of Research

- 1. Geometric theory of groups
- 2. Theory of algebras

**Major Area: Analysis
**Lines of Research

- 1. Nonlinear analysis, differential equations and applications
- 2. Functional analysis
- 3. Harmonic analysis

**Major Area: Geometry and Topology**

Lines of Research

- 1. Applications of geometry and topology
- 2. Algebraic geometry
- 3. Riemannian geometry
- 4. Dynamic systems
- 5. Lie theory

**Major Area: Mathematics**

Lines of Research

- 1. Arithmetic of bodies and Galois theory
- 2. Mathematics teaching

**Major Area: Logic and Fundamentals of Mathematics**

Major Area: Partial Differential Equations

Major Area: Functional Analysis

Major Area: Combinatory Topology

Major Area: Lie Theory

Major Area: Stochastic Calculus