This cycle focuses on the preparation of the doctoral thesis project and includes the following components:

Elective Courses and Second-Year Research Seminar:
These activities are aimed at developing the thesis project or strengthening the student’s training within their research area. They are carried out under the supervision of a faculty advisor.

Thesis Project (Oral Qualification Exam):
This consists of a literature review and research proposal within the chosen area. The thesis project is developed through the elective courses and research seminar.

The thesis project defense must be completed by the fifth semester of the program before an ad-hoc committee appointed by the Academic Committee.

This cycle is dedicated to the development of the Doctoral Thesis, an individual and original research work expected to lead to at least one publication in a peer-reviewed journal and contribute significantly to the field of mathematics. Thesis development begins after the project is approved and extends from the fifth to the eighth semester.

Once the thesis is completed and approved by the thesis advisor, the Academic Committee will appoint a Thesis Committee, composed of the advisor, co-advisor (if applicable), two external experts with recognized expertise in the area, and the Program Director or their representative.

Once accepted, the student may schedule the Final Examination, a public event where the thesis is presented and defended before the Thesis Committee.

Additional Graduation Requirements

Language Proficiency Test: Students must demonstrate proficiency in technical English through an oral presentation of a research topic before a committee appointed by the Academic Committee. This test must be completed within the first three years of the program.