Departamento de Matemática

I. ADMISSION

The admission of students to the Graduate Program has the following rules:

1) Applicants to the Master’s Program must have an undergraduate degree in a technological or scientific field or an equivalent academic degree, at the discretion of the Graduate Committee.

2) Applicants to the PhD Program must have a Master’s degree in Mathematics or an equivalent academic degree, at the discretion of the Graduate Program Committee and other academic evaluations.

3) Applications must be submitted online,through the University website .
    a) Every applicant must attach digital copies of their CV, undergraduate degree diploma and undergraduate transcripts.
    b) Applicants to the PhD Program must also attach digital copies of their Master’s degree diploma and of the Master’s transcripts.
    c) Applicants must ask two professors for letters of recommendation. These letters must be sent straight by the professors to the Department.

4) If the Department deems necessary, the applicant will be interviewed by a professor appointed by the Graduate Program Committee.

The registration of the admitted students is done by the university Admission and Registration Department (DAR).

By entering the Graduate Program, the student will have an academic advisor appointed by the Department.

II. CURRICULUM FRAMEWORK

2.1. Graduate Special Courses :

Graduate Special Courses are the selective courses (according to paragraph 3):

1) MAT2215: Linear Algebra (Only for MS students)
2) MAT2220: Algebraic Structures I
3) MAT2229: Computational Linear Algebra
4) MAT2303: Introduction to Probability
5) MAT2447: Scientific Computing and Differential Equations
6) MAT2502: Analysis in one complex variable
7) MAT2620: Real Analysis
8) MAT2621: Measure Theory
9) MAT2622: Functional Analysis
9) MAT2712: Algebraic Topology I
10) MAT2624: Analysis on the Rn Space
11) MAT2712: Algebraic Topology I
12) MAT2812: Differential Geometry on R3
13) MAT2905: Ordinary Differential Equations
14) MAT2907: Partial Differential Equations I

Click here to see the whole list of courses

2.2. Regular Graduate Courses:

Regular Graduate Courses are those with specific syllabus listed in the Graduate Program of the Department, including the Special Courses, but with the exception of Lectures, Seminars and Guided Studies.

III. REQUIREMENTS TO OBTAIN THE TITLE

3.1. Master’s Degree requirements

1) To complete at least 24 credits of the Graduate Program, subject to the following restrictions.
    a) At least 6 of the 24 credits must be earned with Special Courses of the program. To fulfill this requirement, the only valid course credits will be the ones in which the student has a final grade of 7 or higher. The student can be partially or completely exempted to follow the requirement to attend the Special Courses if approved in written exam(s), according to paragraph 3.4
    b) At least 12 of the 24 credits must be earned with Regular Courses of the Graduate Program (including the Special Courses).
c) No more than 6 of the 24 credits can be obtained from Seminars or Guided Studies and from these 6 no more than 4 can be acquired through Guided Studies.
    d) The credit transfer of other Graduate Programs is subject to the rules explained in paragraph 3.3

2) Applicants must pass an English exam, as explained in paragraph 3.5.

3) To present, defend and have approved a Master’s degree dissertation.

3.2. PhD requirements

1)To complete at least 45 credits of the Graduate Program, subject to the following restrictions:
    a) At least 12 of the 45 credits must be earned with Special Courses of the Graduate Program. To fulfill this requirement, the only valid course credits will be the ones in which the student has a final grade of 7 or higher.
At least 9 of the 12 credits of Special Courses should be earned until the end of the first year, subject to the demand of a final grade of 7 or higher. The student who does not meet this requirement will be expelled from the program. The student can be partially or completely exempted to follow the requirement to attend the Special Courses, if he/she passes the written exam(s), according to paragraph 3.4.
    b) At least 21 of the 45 credits must be earned with Regular Courses of the Graduate Program (including the Special Courses).
    c) No more than 8 of the 45 credits can be obtained from Seminars or Guided Studies.
    d) The credit transfer of the Master’s and/or of other Graduate Programs is subject to the rules listed in paragraph 3.3.

2) Pass the Qualifying Examination. The Qualifying Examination consists of an oral test about a subject chosen by the student for his/her thesis. The program and the thesis committee must be approved by the Graduate Committee, at least one month in advance. The board will be composed of three professors, and it also must be approved by the Graduate Committee. The chair must be a professor of the Department. The student must pass the qualifying examination before completing 2 years in the PhD Program, as from the admission date. The student who does not meet these requirements will be expelled from the program.

3)Pass in two foreign language exams, according paragraph 3.5

4) To present, defend and have approved a PhD thesis with original and relevant results in the field of research.

3.3. Credit transfer

The credit transfer of other Graduate Programs (from this or other institution) is subject to the approval of the Graduate Committee which may require the student to take a written test.
The credit transfer for students of the Master’s Program is subject to the following condition:

1) According to Item 37 of the Graduate Programs Regulation of PUC-RIO, the amount of credit transferred from other institutions cannot exceed 1/3 of the mandatory credits of the Master’s degree, in other words, 8 credits, with the exception of the Universities that have specific agreements with PUC-RIO, for which the total of transferred credits cannot pass half of the demanded ones, that is, 12.

The credit transfer for PhD students is subject to the following conditions:

1) A maximum of 25 credits obtained during the Master can be transferred (in this or another institution), at the discretion of the Department’s Graduate Committee.

2) According the Item 38 of the Graduate Program Regulation of PUC-Rio, the amount of credit transferred from other institutions cannot exceed ¾ of the total of credits demanded by the PhD program, that is, 33 credits.

3.4. Exemption of Special Courses

1) The student can ask to be totally or partially exempted to attend a minimal number of Special Courses. The request should be made by the student on the first week of the first semester in the program (Master’s or PhD).

2) The request will be analyzed by the Graduate Program Committee taking into consideration the transcripts of the student and other relevant data. If accepted, the Committee will appoint 1 or 2 Special Courses for evaluation.

3) Each exam is a written test about the topics of the syllabus of the Special Course with a level similar to the one of a Regular Course exam. Each exam will be made and graded by one or two professors nominated by the Committee.

4) The exams will take place within the first month, after the beginning the Graduate Program semester.

5) For each exam passed with grade 7 or higher, the student will be excused from taking 3 credits of Special Courses. The other requirements remain unaltered; in particular, the student will still have the same number of credits to earn, considering that exams do not grant credit.

6) The student who fails an exam will not suffer any penalties. However the exam cannot be redone.

7) If a student passes an exam and, besides it, takes or obtains a course equivalent to the same exam, the first will be annulled.
8) If admitted into the PhD Program, course exemptions granted to the students during the Master’s Program are still valid.

3.5. Foreign Languages Exams

All Graduate students should prove their reading proficiency in English. The PhD students should also prove their English writing proficiency, or should prove their reading proficiency in another language such as: French, German or Russian. The Master’s degree students must pass the English exam within the first year and a half after the beginning of the program. The PhD students should pass the foreign language exams until 3 years; after the beginning of the program.

The PhD students should pass the foreign language exams until 3 years; after the beginning of the program.