Curriculum Proposal – Master’s Program

Master’s Program

The Master’s program has a duration of two years. It is recommended for students with an undergraduate degree in Mathematics or related areas. The aim of the program is to provide training for those wishing to pursue a doctoral degree and invest in research and for those seeking to work as professors in higher education institutions. Upon completion of the program, the students receive the degree of:

“Master in Mathematics”

The degree is granted in one of the following areas of concentration:

Applied Mathematics
Geometry and Topology

The curriculum structure of the Master’s program is as follows:
I – Structure

The Master’s curriculum is composed of:

a) Regular courses, divided into four groups, as listed below.
b) Mandatory “Teaching Practicum” (4 credits), consisting of didactic activities supervised by a professor (called a tutor), in which the student teaches classes in undergraduate courses.
c) “Mathematics Colloquium” (2 credits). The course consists of lectures given by local or invited researchers and is offered whenever possible.
d) Master’s thesis (6 credits).

II – Requirements

To obtain the degree of Master in Mathematics, the student must meet the following requirements, in addition to the provisions set out in the Program Bylaws.

a) Obtain approval in 2 required courses, 1 elective course from each group (1, 2, 3 and 4), and 1 elective course chosen between groups 2, 3 or 4.
b) Exemption from one or more of the courses in item “a” above may be requested, provided that the student took a compatible undergraduate course and obtained grade 7.0 or higher.
c) In any case, attend and obtain approval in at least 6 (six) regular courses of the program.
d) Obtain approval in the Teaching Practicum.
e) Enroll and obtain approval in the Mathematics Colloquium in three semesters throughout the program.

Cases not covered here will be decided by the Program’s Delegated Council.

III – Regular Courses

The regular courses listed below are offered according to the following:
a) The Advanced Calculus course is offered in the first semester and the Functional Analysis course in the second semester.b) Courses from Group 1 and Group 2 are offered in the first semester and courses from Group 3 are offered in the second semester.
c) Courses from Group 4 may be offered in the first or second semester, according to the necessity.


The Program’s Bylaws establish that:

Art. 50. Throughout the first academic year, proof of foreign language proficiency (English, French, German or Spanish) will be required. The Master’s program requires proficiency in one foreign language, and the doctoral program requires proficiency in two foreign languages.


List of courses

Mandatory (6 credits each)

MTM410018 Advanced Calculus

MTM410029 Functional Analysis

Group 1
MTM410019 Linear Algebra
MTM410024 Computational Linear Algebra

Group 2
MTM410034 Ordinary Differential Equations
MTM410020 Complex Variable

Group 3
MTM410035 Partial Differential Equations
MTM410028 Numerical Analysis I
MTM331200 Linear Programming
MTM410027 Measure and Integration
MTM330400 Algebraic Structures
MTM410026 Topology
MTM331000 Differential Geometry
MTM410057 Dynamical Systems
MTM410056 Non-Linear Programming
MTM410071 Finite Groups and their Representations
MTM410073 Mathematical Methods for Statistics

Group 4
MTM410039 Operator Algebras
MTM410051 Differentiable Manifolds
MTM410052 Algebraic Topology
MTM410053 Probability and Markov Processes
MTM410055 Symbolic Dynamics
MTM410064 Ergodic and Information Theory
MTM410038 Distribution Theory and Sobolev Spaces

MTM410037 Numerical Analysis II
MTM410036 Introduction to Hopf Algebras

MTM410030 Theory of Non Commutative Rings
MTM410048 Corings and Comodules
MTM410040 Convex Analysis
MTM410082 Fibers in Differentiable Manifolds
MTM410068 Commutative Algebra
MTM410066 Introduction to Regularization Theory
MTM410070 Introduction to Category Theory
MTM410081 Mathematical Modeling Biomathematics

Specialized Topics

  1. Computer Resources
    Master’s students have access to a computer laboratory. The graduate program also has a few laptops that can be borrowed for certain periods.

Since 2016, there is a room dedicated to postdoctoral researchers and another to the visiting faculty. All faculty rooms, and the computer lab, are connected to the internet.

  1. Library

All students enrolled, as well as the university staff, have access to the central and branch libraries. In spite of a relatively small bibliographical collection in the area of ​​Mathematics, this collection is incremented annually with the suggestions of our faculty. Access to journals is also available through the Capes online publication website.