Doctoral Degree in Computational Algebra

Entidade parceira: Universidade Aberta

General Objectives of the Course

The PhDCA aims at developing the area of computational algebra in the Lusophone space. This is a growing subject in advanced countries and has been explicitly recommended for development by an international mathematical panel hired by the Portuguese government to assess/advise the development of Science in Portugal. Moreover, the online teaching techniques developed in the last two decades, in particular in the Open University pedagogical model, allow the creation of high quality teaching teams, as we can bring together internationally recognized researchers wherever in the world they are located. This PhD program aims at taking advantage of these possibilities and put a group of national and international researchers, very active and recognized in the field of Computational Algebra, in contact with students from the Portuguese-speaking world (and elsewhere) interested in this topic. Thus, the course aims at educating professionals with a solid training in computational algebra who might become members of research centers in order to enhance scientific research.

Admission Requirements

According to Decree-Law No. 74/2006 of 24 March, in its current wording, and as specified in ``Despacho (extrato)’’ nº 5442/2013 of April 23, are entitled to apply to the PhDCA:
a) those holding an MSc degree or legal equivalent, in the areas of Mathematics or ICT;
b) those holding a faculty degree or legal equivalent, in the areas of Mathematics or ICT, provided it is recognized by the scientific council of the host institution that their scientific curriculum attests capacity to carry out the PhD program;
c) exceptionally, those possessing a scientific curriculum that the Scientific Council of the host institution recognizes as proof of the ability to successfully complete the PhD program.

Candidates should check the admission requirements available on this site, in addition to the information provided here.

Professional Goals

The students of the program typically already have a job, the majority as professional programmers. The basic purpose of the PhDCA is not, therefore, to create a new type of jobs (although that may come to happen). The real purpose is to atract professional programmers and mathematicians with an interest in scientific research. So a group of highly qualified researchers may eventually be formed, able to produce computational tools in the fields of automatic theorem proving and symbolic computation for the general mathematical community. Participation in research projects, spin-off creation and new scientific jobs will be the natural result of the activities carried out by this group.

Mode of Study

Distance learning in online collaborative learning system, in virtual class, asynchronous; the contact hours with teaching staff occur primarily through an e-learning platform.

Teaching / Evaluation language(s)

Portuguese and English

Examination Regulations, Assessment and Grading

Coursework assessment has a continuous component, based on discussions held online, in virtual classes. The final evaluation is of an individual nature, and consists of a take-home exam lasting 48 hours, which accounts for 30% of the final grade. The assessment is in accordance with “Regulamento Pedagógico da Universidade de Coimbra” (“Regulamento” nº 321/2013 of August 23; The method of evaluation of each course is described in the corresponding course form (FUC). The final grade of a course is given on a 0-20 scale.

Learning Objectives and Intended Skills

It is expected that at the conclusion of the PhDCA the student is able to:
1- Understand the main results, models and computational tools associated with the theory of groups, semigroups, logic, loops, etc., as well as understand their potential, and analyze and formulate open problems having in mind implementation/exploitation of knowledge in the design of new computer tools.
2- Develop independently, critically and imaginatively, projects of new computational packages for GAP systems (Groups, Algorithms, and Programming; GAP – or for prover9/Mace4.
3- Manage processes of change resulting from the introduction of new technologies and techniques, both at a theoretical level (discovery of new theorems/algorithms) and at a computational level (introduction of new IT tools).

Course Coordinator(s)

Alfredo Manuel Gouveia da Costa

ECTS Departmental Coordinator(s)

Daniel Alexandre Peralta Marques Pinto

Recognition of Prior Learning

Done in accordance with the regulations of both HEI, requiring a solid background in Mathematics, capable of guaranteeing ability to enroll this PhD program. Among the legislation in force, we point out the “Regulamento de Creditação de Formação Anterior e de Experiência Profissional da Universidade de Coimbra” (

Qualification Requirements and Regulations

The legal framework for the qualification is established by the decrees: Decree-Law no 74/2006, 24th March, in its current wording.

Graduation Requirements

: The PhDCA program includes 2 semesters of coursework in an e-learning system, comprising 6 mandatory courses, and 6 semesters dedicated to developing a PhD thesis. Approval in the coursework of this study program requires approval in each of the six courses with grade 10 points or more in a 0-20 scale. In the PhD thesis the student must present original work of high quality produced under the supervision of one or two professors associated with the PhDCA. The work developed must be suitable for publication in international peer-reviewed journals. After completion of the thesis, the student must submit to a public defense of it. The approval of the thesis completes the requirements for the student to be awarded the degree of Doctor in Mathematics. The diploma conferring this degree will be issued jointly by both HEI.

Access to Further Studies

Not applicable.

Study Programme

Computational Algebra

Academic year

Course Type
3rd Cycle Studies

DGES Code: PA36

Qualification Awarded: Doutor

Duration: 4 Year(s)

ECTS Credits: 240.0

Annual Fee: 2000.0


Call for Applications


1st Semester
Start date: 14-09-2020
End date: 19-12-2020
2nd Semester
Start date: 08-02-2021
End date: 22-05-2021


Agência de Avaliação e Acreditação do Ensino Superior
2016-10-19 a 2022-10-18
Direcção Geral de Ensino Superior