LCMath PhD Program Lisbon/Carnegie-Mellon in Mathematics

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1 LCMath PhD Program Lisbon/Carnegie-Mellon in Mathematics Main goals In the context of the cooperation program established between the Portuguese Government and Carnegie Mellon University (CMU), a specific project between this University and the University of Lisbon (UL), the Technical University of Lisbon (UTL) and the New University of Lisbon (UNL) is proposed. The purpose of this project, involving the Department of Mathematical Sciences of CMU, the Department of Mathematics of the School of Sciences of UL (FCUL), the Department of Mathematics of the Technical Superior Institute of UTL (IST- UTL) and the Department of Mathematics of the School of Sciences and Technology of UNL (FCTUNL), is to develop advanced programs of research and education in specific areas of mathematics of common interest and expertise. Namely, it is intended: i) to reinforce the scientific and learning capabilities in Portugal, as well as to promote the internationalization of the graduate programs of the aforementioned Portuguese Public Universities, ii) to stimulate mobility and scientific interaction of graduate students, researchers and post-docs between the cited Institutions, iii) to attract to the involved Universities strongly motivated students who are able to integrate advanced research programs in Mathematics and applications, iv) to optimize resources, promoting a program that involves all public universities in Lisbon. Primary goal Without excluding other possible programs within the context of items i)-iv) above, the priority goal is to establish a program of graduate studies in Mathematics. Taking into account the stated goals, our aim is to create an internationally attractive graduate program, which should be settled along the following guidelines: 1) In order to ensure that this is a top quality program, a student enrolled in it must satisfy the requirements from all of the Universities involved. Therefore, upon completion of these requirements, both CMU and the Portuguese Universities, will confer to the student a degree in Mathematics (dual degree). 1

2 2) There is a long history of scientific interactions between the Department of Mathematics of CMU and their Portuguese counterparts, namely in the areas of Applied Mathematics, Calculus of Variations and Partial Differential Equations. These are areas where good intelectual matching between members of CMU and members of the Portuguese Universities is possible and therefore, in order to promote good scientific collaborations and top research work, these areas should be preferred, at least at an initial stage. Other areas of possible interest are, for example, Mathematical Finance, Stochastic Analysis, Logic and Discrete Mathematics. Ideally, the program could be expanded to include these areas in the future. 3) The student should be involved in research activities as soon as possible, so that he/she can benefit the most from the matching between researchers. 4) The research activity resulting from this program should be monitored by the research centers from the aforementioned Universities to which the involved researchers belong. Program Description a) The program, whose typical duration is four to five years, will consist of up to two years of courses, followed by up to three years of thesis preparation with possible advanced coursework. Taking into account the desired mobility of both graduate students and researchers, the student is expected to spend the first year in Lisbon, the second and third years at CMU and the fourth year in Lisbon. In year five, the time spent in each country will be decided on an individual basis, depending on the demands of the research schedule. b) A student may apply to LCMath if he/she meets one of the following conditions: (i) to have concluded the primeiro ciclo in Mathematics or any collateral area, with a minimum of 35 ECTS in Mathematics, in any European university in accordance with the Bolonha Process, and the equivalent of 60 ECTS in a segundo ciclo in mathematics or collateral area; (ii) the equivalent to the previous points in the context of the CMU curriculae, namely, a degree in Mathematics or collateral area, like Physics or Engineering; (iii) to have other degrees that are considered equivalent. c) Applicants should submit three letters of recommendation, the results of TOEFL and GRE general and subject tests, and their transcript to both the CMU and the Portuguese selection committees. A student will be accepted into the program if he/she meets the requirements of both committees. In this case, he/she will be assigned an advisor from the Portuguese team and one from CMU. These need not be his/her future scientific advisors, but will be practical advisors who will follow the student s progress and will provide guidance within the first years of the program. 2

3 d) In the first year the student will be in Portugal, where he/she will be enrolled in about 5 courses, totaling 60 credits (ECTS), at the Portuguese Universities. These courses, taught in English, will be selected, among those available at the graduate level by the student under the supervision of his/her Portuguese practical advisor. Possible examples of admissible courses, whose syllabus are to be accepted by the faculty of CMU s Department of Mathematical Sciences, are Functional Analysis, Ordinary and Partial Differential Equations, Measure and Integration and Numerical Analysis. During the first year students may also have access to CMU courses through teleconferences. e) The courses completed in year 1 will be considered towards the requirements of the CMU Master of Science Degree as well as the Portuguese degree of Mestre em Matemática or other academic diplomas, awarded by the Portuguese Universities. f) During the second year the student will attend courses at CMU, under the guidance of his/her CMU practical advisor. The syllabus of these courses should be accepted by the Portuguese team. By the end of this second year, the student should have acquired a level of knowledge that will enable him/her to begin research work. This basic knowledge will be tested no later than the beginning of the third year, by means of a qualifying exam. g) The student is now in position to select a scientific advisor from CMU and one from Lisbon. If different from the practical advisor(s), the latter cease(s) his (their) functions. The student spends year three at CMU working on his/her PhD dissertation under the supervision of his/her CMU scientific advisor. h) During his/her stay at CMU the student is expected to be a teaching assistant during one semester. To this extent, he/she will be required to attend the International Teaching Assistant s Workshop at the Department of Mathematical Sciences, and pass the corresponding ITA test. i) Since one of the main goals of the program is to reinforce research interactions between Portuguese and CMU faculty, during this third year the Portuguese advisor should join his/her student at CMU for a period of up to a semester s length, in order to engage in a research collaboration with his/her CMU colleagues. j) The student spends year four in Portugal under the guidance of his/her Portuguese advisor. The thesis should be completed during years four or five. After year four the time remaining to finish the thesis can be spent in either country in accordance with the requirements of the research schedule. The CMU advisor is expected to visit Portugal for a short term during this phase of the program. l) The student s progress will be reviewed anually by CMU s Graduate Student Retention Committee and its Portuguese counterpart. Under exceptional conditions, the program can be extended to a sixth year, if both scientific advisors recommend it. 3

4 m) The defense of the thesis can take place, either in presence of the full committee or by teleconference, at any of the Universities to which the scientific advisors belong. The committee should include at least two tenure track faculty members from CMU s Mathematical Sciences Department and at least two faculty members from the Mathematics Departments of the referred Lisbon Universities. In any case, the number of members of the thesis committee from CMU s Mathematical Sciences Department should equal the number of members from the Portuguese Universities. Both scientific advisors are required to sit on the committee. n) Each of the three Portuguese Institutions will, in turn, be in charge of student registration, records and other secretarial work, including internet support, for a period of three years. o) A student enrolled in this program, will be considered a graduate student of both CMU and the Portuguese Universities. Namely, he/she will be provided with office space and will have access to the libraries, computer facilities, and so on, at all of the participating schools. p) In recognition of completion of the course of studies, the aforementioned Universities will confer to the student two degrees in Mathematics: PhD in Mathematics conferred by CMU and Doutor em Matemática conferred by the Portuguese Universities in association (joint degree), in the terms of article 42 o of Decreto-Lei 74/2006 of March 24 (in case one of these Portuguese Universities is unable to confer the degree, it will be awarded by the others). Resources and measure of success An effort should be made to recruit and attract international students to the program, namely by publicizing it appropriately. In order for such a program to be viable, it is necessary that scholarships are made available for the selected students, covering up to 5 years of studies in Portugal and in the USA. The number of students in the program should be proportional to the number of CMU s and Portuguese faculty involved. Taking this into account, we expect to have, enrolled in all years of the program, around 8 to 10 students. We foresee that more faculty will join the program, so that, at a later stage, around 16 students will be enrolled. In any case, the number of students under CMU s advisory guidance, should be at most one half of the total number of students in the program. In accordance with the previously listed goals, financial aid should also be secured to allow for short term visits of the scientific advisors. The advantages of these visits are twofold. On one hand, they enable a closer monitoring of the student s progress by both advisors simultaneously and, on the other hand, they reinforce the scientific ties between the researchers. For this to be possible, it is crucial that the teaching and administrative duties of the Portuguese advisors involved in this program match those of their American counterparts. Therefore, we suggest that the teaching load of these faculty members, 4

5 during the year of their scheduled visit to CMU, should be half of the usual and concentrated in one semester. The entity financing the program would reimburse the Portuguese Universities accordingly. This entity would monitor the progress and scope of the program as well as the work of all of the involved parties. 5