The PhD program has a normal duration of 3 years, according to the legislation applicable to PhDUNL. However the PhD studies can take up to 4 years, in accordance with the rules of FCT/UNL.

The program, complying 180 credits (ECTS), consists a curricular component and a research project aiming at producing an original thesis.

It involves the following (specialization) areas:
Algebra (ALG),
Geometry (GEO),
Functional Analysis (FA),
Differential Equations (DE),
Numerical Analysis (NA),
Logic and Foundations of Mathematics (LFM).

1st year:
Students must complete 5 courses (UC), each weighting 6 ECTS, and complete the UC Seminar of 3 ECTS, in their specialization area. Typically a student will finish 3 to 4 courses in the 1st semester. The choices of the UC are tailored to each academic pathway and may include courses at masters level.

The available PhD courses, displayed in the official regulations, include:

Abstract Algebra; Universal Algebra; Homotopic Algebra; Advanced Linear Algebra; Semigroup Theory; Numeric Semigroups; Graph Theory; Algebraic Geometry; Functional Analysis; Operator Algebras; Calculus of Variations; Partial Differential Equations; Homogenization Theory; Mechanics of Continuous Medium; Fluid Mechanics; Integral and Differential Equations in Biology; Dispersive non-linear Equations; Holomorphic Dynamics; Finite Elements; Computer Science; Computational Complexity; Mathematical Logic; Rewriting Systems.

A successful accomplishment of the curricular part entitles the student with the FCT-UNL Advanced Studies Diploma in Mathematics.