Graduate and Research Central Coordination Office (CCPG)

Graduate Program in Mathematics

General Information

Program Overview

The Mathematics Department of PUC-Rio was founded in 1966. In 1968, the Bachelor program was created and, in 1972, the Licentiate. 1969 saw the birth of the Master’s course and 1974, that of the Doctorate. As of 2015, the Department has granted 266 Master's and 93 Doctoral degrees.

The Mathematics Department is the structural unit at PUC-Rio that concentrates all academic and administrative teaching and research activities pertaining to mathematics. Consequently, every mathematics discipline offered at the University, at both the undergraduate and graduate levels, are under its responsibility. With this spirit of integration, the Mathematics Department offers disciplines to students from diverse Engineering, Chemistry, Physics, Informatics, Administration, Economics and Architecture courses, beyond students from the Mathematics course itself.

The Mathematics Department is composed of researchers with national and international recognition, whose scientific production is published in world-class international journals. Eleven of its seventeen faculty members are CNPq Research Productivity Grant holders, seven of these in level 1. Moreover, the Department has three full members and one affiliated member of the Brazilian Academy of Science, three Scientists from Our State and two Young Scientists from Our State by FAPERJ. Exchanges with numerous universities in Brazil and abroad abound and the quality of the Mathematics Graduate Program is widely recognized by the academic community.

History

In 1966, the Mathematics Institute of the Catholic University, IMUC, became an autonomous entity. Until 1965, it was a teaching sector of the PUC-Rio Physics Institute. In 1968, IMUC was divided into two Departments: Mathematics and Informatics. That same year saw the implantation of the Bachelor program in Mathematics, followed by that of the Licentiate in 1972.

The Department’s Graduate Program was founded with the creation of its Master’s course in 1969, the establishment of its Doctoral course followed in 1973, both with options in Pure and Applied Mathematics. As of 2005, the Department has granted 194 Master’s and 55 Doctoral degrees. Among its Master’s degree holders, 22 pursed their Doctoral degree at the Department.

Objectives

The Graduate Program of the Mathematics Department aims to offer its students a solid and ample education, training high-level researchers and professionals capable of working in activities that demand high mathematical qualifications.

An important aspect of the Program is its close relationship between pure and applied mathematicians, besides its relationship with researchers from other sciences, which is stimulated by the University itself, with its especially active technological and economic areas. In view of this multidisciplinarity, the Program offers a flexibility of choice in students’ and their advisors’ discipline subjects, without nevertheless neglecting the main disciplines that form the backbone of the course.

Concentration areas and lines of research

Concentration area: Pure and Applied Mathematics

Lines of research

1. Analysis and Partial Differential Equations
2. Combinatorics
3. Computer Graphics
4. Mathematical Physics
5. Algebraic Geometry
6. Differential Geometry
7. Probability and Stochastic Processes
8. Dynamic Systems
9. Topology

Course Recognition

Master’s and Doctoral Degrees

Recognition:
CAPES (Coordination for the Improvement of Higher Eduction Personnel; from Brazilian Ministry of Education) evaluation: grade 6 (in a 3 to 7 scale) for the 2010-2012 period.
Approved by the CNE/CES MEC n.288/2015 of July 08, 2015.
Granted degrees: Master in Mathematics and/or Doctor in Science-Mathematics

Requirements for obtaining the Master’s and Doctoral degrees

Master

1. Completion of a minimum of 24 Graduate Program credits, subject to the following restrictions:
   • At least 6 of these 24 credits must be obtained from the Graduate Program’s Fundamental Disciplines, and the student must obtain a final grade equal to or higher than 7 in these disciplines in order to validate their credits. The student may be partially or completely exempted from the requirement of following the Fundamental Disciplines in case of approval in a written exam, as shown below in the “Exemption of Fundamental Courses” paragraph.
   • At least 12 of these 24 credits must be obtained from the Graduate Program’s Regular Disciplines (including the Fundamental ones).
   • No more than 4 of these 24 credits can be earned from Seminars or Guided Studies.
   • Credit transfer from other Graduate Programs is subject to the rules explained below in  the “Credit Transfer” paragraph.
2. Approval in English Language Exam, as written in the “Foreign Languages Exam” paragraph.
3. Presentation, defense and approval of a Master ’s dissertation.

Doctor

1. Completion of at least 45 Graduate Program credits, subject to the following restrictions:
   1. At least 12 of these 45 credits must be obtained from the Graduate Program’s Fundamental Disciplines,  and the student must obtain a final grade equal to or higher than 7 in these disciplines in order to validate their credits. At least 9 of these 12 Fundamental Courses credits should be earned until the end of the first year, and their validation are subject to the requirement of obtaining a final grade equal to or higher than 7. The student who does not meet this requirement will be expelled from the program. The student may be partially or completely exempted from the requirement of following the Fundamental Disciplines in case of approval in a written exam, as shown below in the “Exemption of Fundamental Courses” paragraph.
   2. At least 21 of these 45 credits must be obtained from the Graduate Program’s Regular Disciplines (including the Fundamental ones).
   3. 45 credits, at least 21 must be graduate Regular disciplines (including Essentials).
   4. No more than 8 of these 45 credits can be earned from Seminars or Guided Studies.
   5. Credit transfer from the Master’s course and/or from other Graduate Programs is subject to the rules explained below in  the “Credit Transfer” paragraph.
2. Approval in the Qualifying Examination.
   The Qualifying Examination consists of an oral test on the chosen subject of the student's thesis.
   The program and the board of the exam must be approved by the Graduate Committee, at least one month in advance.
   At least two of the three members of the board of the exam must be professors from the Mathematics Department. The board director must be a Mathematics Department professor.
   The student must be approved in the Qualification Examination before completing 2 years since the admission date to the Doctoral course. The student who does not meet this requirement will be expelled from the program.
3. Approval in two foreign language exams, as written in the “Foreign Languages Exam” paragraph.
4. Presentation, defense and approval of a Doctoral thesis containing original and relevant results on the field of research.

Credit Transfer

The credit transfer from other Graduate Programs (this or other institutions) is subject to approval from the Graduate Committee and may depend on a written test.

Credit transfer for Master’s course students is subject to the following condition:

1. According to Item 37 of the PUC-Rio Graduate Programs Regulation, the amount of credits transferred from other institutions cannot exceed 1/3 of the total credits demanded for the Master’s degree, in other words, a maximum of 8 credits, excepting Universities that have specific agreements with PUC-Rio, for which the total of transferred credits cannot pass half of the compulsory ones, in other words, 12 credits maximum.
2. Regulation strict sense of graduate Program at PUC-Rio, the total harnessed credits by other institutions may not exceed 1/3 of total credits required for the Master’s course, or Education institutions with the PUC-Rio keep specific agreement, for which the total availed credits may not exceed half of the required credits, or that is 12 credits.

Credit transfer for Doctoral course students is subject to the following conditions:

1. Up to 25 credits obtained from the Master’s course (at PUC-Rio or at another institution) can be transferred, at the discretion of the Department's Graduate Committee.
2. According to Item 38 of the PUC-Rio Strictu Sensu Graduate Programs Regulation, the amount of credits transferred from other institutions cannot exceed 3/4 of total credits required for the Doctoral course, in other words, a maximum of 33 credits.

Exemption from Fundamental Disciplines

1. The student can ask for total or partial exemption from the Fundamental Courses. The request must be made by the student on the first week of the first semester in the program (Master’s or Doctoral courses).
2. The request will be analyzed by the Graduate Committee taking into consideration the student’s academic transcripts and other relevant data. In case of acceptance, the committee will appoint 1 or 2 Fundamental Disciplines as for evaluation.
3. Each exam is a written test about subjects corresponding to the Fundamental Disciplines syllabus, in a difficulty level comparable to the regular course. Each exam will be made and graded by one or two professors chosen by the Committee.
4. The Exams will take place within the first month after the beginning of the Graduate Program semester.
5. For each exam in which the student obtains a grade higher than or equal to 7, he or she will be dispensed from taking 3 credits of Fundamental Courses. Other requirements remain unaltered; in particular, the student will still have the same number of credits to earn, since exams do not grant credits.
6. The student who fails an exam will not suffer any penalties. However the exam may not be redone.
7. If the student is approved in some exam and, besides it, takes or obtains a course equivalent to the same exam, the first will be annulled.
8. Credit transfers obtained by a student in the Master’s course are posteriorly valid in the student’s Doctoral course.

Foreign Language Exams

All Graduate students must demonstrate reading proficiency English. Doctoral students must also demonstrate English writing proficiency, or prove reading proficiency in a second language such as: French, German or Russian. The Master’s course students must be approved in the English exam within the first year and a half after the beginning of the program. Doctoral students must be approved in the foreign language exams up to three years after the beginning of the program.

Admission and Enrollment

The selection of Graduate students has the following  rules:

1. Master’s Program applicants must be holders of an undergraduate degree in a technological or scientific field or possess an equivalent academic degree, at the discretion of the Graduate Committee.
2. Doctoral Program applicants must possess a Master’s degree in Mathematics or an equivalent academic degree, at the discretion of the Graduate Committee and other regulatory instances.
3. Applications must be submitted online, through the University website:
   1. All applicants must attach digital copies of their curriculum vitae, undergraduate diploma and undergraduate transcripts.
   2. Applicants to the Doctoral course must also attach digital copies of  their Master's diploma and Master’s transcripts.
   3. The candidate must ask two professors for reference letters, which should be sent from the professors directly to the Department.
4. If the Department deems necessary, the applicant will be interviewed by a professor appointed by the Graduate Committee.
   Enrollment of successful applicants is done at the University’s Admission and Registration Department (DAR).
   Upon entrance to the program, the student shall have an academic advisor appointed by the Department.

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