This PhD program in Applied Mathematics (MAP-PDMA) is intended to foster the development of applied or applicable mathematics, conferring the degree of doctor of philosophy to motivated students from different scientific backgrounds.

# About MAP-PDMA...

The MAP-PDMA is a PhD joint program of the Universities of Minho (Department of Mathematics and Applications), Aveiro (Department of Mathematics) and Porto (Faculties of Sciences, Economics, Engineering and Biomedical Sciences) with the collaboration of the University of Beira Interior.

The MAP-PDMA is intended for promoting the development of mathematics, applicable or applied, in a broad sense through the granting of a PhD degree to motivated students of varied, but adequate, backgrounds.

The teaching staff consists of mathematicians of the four universities and several research centers with an academic diversity that offers a wide range of applications. This diversity in academic origin provides a wide range of applications that can be exploited at thesis level, as well as a considerable variety of taught courses.

The student enrolling in the MAP-PDMA can choose from a list of taught courses aimed at providing the necessary basis for their research. The courses can be chosen to fill gaps of previous academic curricula, to direct the students to a specific line of research and/or to provide information to guide them in their choice of research area. The courses available vary each year depending on the teaching staff’s availability and on the demand of students. Classes will be taught in English, except if all students are Portuguese fluent speakers.

**Goals**

The primary overall goal consists in endowing students with scientific autonomy in the field of Applied Mathematics and its applications in four large domains: Mathematics, Engineering, Economy and Health.

This context is twofold:

- formulate and solve novel applied mathematical problems arising in those domains;
- identify mathematical challenges in these domains and, in order to address them, extend the current body of applied mathematics.

**Admission Requirements**

Will be admitted graduate students (pre-Bologna) or possessing a 2nd cycle of studies (post-Bologna) in Mathematics, Engineering, Physics, Astronomy, Chemistry, Economics or related fields, if the training is considered appropriate to the course objectives.

**MAP-PDMA Structure**

The MAP-PDMA PhD program corresponds to 240 ECTS lasting four academic years on a full time basis and includes

- A curricular part corresponding to 60 ECTS to be completed in the first year of the program. It consists of a Seminar and a Research Project, both mandatory, and optional courses, being possible the frequency of courses from other doctoral programs (from Universities of Porto, Aveiro or Minho) subject to authorization by the Scientific Committee.
- The development of an original thesis in Applied Mathematics and specially prepared for this purpose.

The MAP-PDMA PhD structure of the 1st year, with 60 ECTS, is organized as follows: Seminar (9 ECTS) and Research Project in Mathematics (21 ECTS), both mandatory, and specialized optional courses in (i) Mathematics and Applications (24-30 ECTS), and/or (ii) from any 3rd cycle of studies at UM, UA and UP (0-6 ECTS).

Each student must choose the optional courses as follows:

- Choose two from four Structural Courses of 6 ECTS each, in the 1st semester, namely, “Advanced Topics in Algebra, Logic and Computation”, “Advanced Topics in Analysis and Optimization”, “Advanced Topics in Dynamics and Geometry” and “Advanced Topics in Probability and Statistics”,
- Complete the remaining credit with optional courses with 3 or 6 ECTS each.

The choice of all optional courses is subject to approval by the Scientific Committee.

The remaining 180 ECTS correspond to the 2nd, 3rd and 4th years which are dedicated to research and writing of the thesis.

The approval in optional courses and Seminar, corresponding to 39 ECTS, confers the award of “Diploma of Advanced Studies in Applied Mathematics”.