Curriculum Structure and Course Details
The curriculum structure of the program is divided into general, specific, and elective courses.
The mandatory courses are distributed as follows:
General:
Real Analysis;
Complex Analysis;
Thesis Preparation and Writing.
Specific:
Algebra;
Numerical Linear Algebra;
Ordinary Differential Equations;
Differentiable Manifolds;
Measure and Integration.
Elective: Functional Analysis;
Rings and Modules;
Partial Differential Equations;
Differential Geometry;
Riemannian Geometry;
Introduction to Algebraic Geometry;
Introduction to Algebraic Topology;
Probability;
Differentiable Manifolds;
Ordinary Differential Equations;
Numerical Differential Equations;
Algebra;
Numerical Linear Algebra;
Seminar I, II, III, and IV;
Topics in Algebra I and II;
Topics in Analysis I and II;
Topics in Geometry and Topology I and II;
Topics in Stochastic Processes I and II;
Topics in Applied Mathematics I and II.
The minimum number of credits required for completion of the Master's degree is 32. The "Disciplina" tab shows the number of credits for each course, typically 60 hours per course equating to 4 credits. Briefly, the mandatory courses total 22 credits (5 courses of 4 credits each plus Thesis Preparation and Writing worth 2 credits), leaving 10 credits to be fulfilled with elective courses and seminars. (For more details on courses, click here).
The curriculum structure of PPGMAT-UFES follows guidelines comparable to top Master's programs in Brazil. Many of our graduates continue their studies in PhD programs at leading national and international institutions, while also providing a solid foundation for those pursuing careers in higher education. Some of our alumni are now teaching in regional educational institutions. For more information on alumni, click here.
In 2018, the program's curriculum was revised to better accommodate graduates from UFES's bachelor's and teaching degrees in Mathematics, as well as those from other institutions. The relationship between courses and research lines is as follows:
Algebra
Algebra
Rings and Modules
Introduction to Algebraic Geometry;
Topics in Algebra I and II
Seminar I, II, III, and IV;
Analysis and Differential Equations Real Analysis
Complex Analysis
Ordinary Differential Equations;
Functional Analysis;
Partial Differential Equations;
Measure and Integration.
Topics in Analysis I and II;
Seminar I, II, III, and IV;
Geometry and Topology
Real Analysis
Ordinary Differential Equations;
Differentiable Manifolds;
Differential Geometry;
Riemannian Geometry;
Introduction to Algebraic Topology;
Topics in Geometry and Topology I and II;
Seminar I, II, III, and IV;
Applied Mathematics and Probability Real Analysis;
Numerical Linear Algebra;
Measure and Integration.
Functional Analysis;
Probability;
Numerical Differential Equations;
Topics in Applied Mathematics I and II.
Topics in Stochastic Processes I and II;
Seminar I, II, III, and IV.
Thus, each research line includes at least one mandatory course. The complete list of courses is available on the Program's website at the following link.
The curriculum matrix consists of two courses per semester structured as follows:
1st year:
1st semester: Real Analysis, Algebra/Numerical Linear Algebra
2nd semester: Complex Analysis, Ordinary Differential Equations/Differentiable Manifolds
2nd year:
1st semester: Measure and Integration, Elective
2nd semester: Thesis, Seminar/Elective
