1. Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications 4

2. Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas. 4

3. Evaluate and use new information within the field in a systematic approach. 3

4. Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field; research, conceive, design, adapt and implement an original subject. 3

5. Critical analysis, synthesis and evaluation of new and complex ideas. 3

6. Gain advanced level skills in the use of research methods in the field of study. 3

7. Contribute the progression in the field by producing an innovative idea, skill, design and/or practice or by adapting an already known idea, skill, design, and/or practice to a different field independently. 2

8. Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals. 1

9. Demonstrate leadership in contexts requiring innovative and interdisciplinary problem solving. 2

10. Develop new ideas and methods in the field by using high level mental processes such as creative and critical thinking, problem solving and decision making. 3

11. Investigate and improve social connections and their conducting norms and manage the actions to change them when necessary. 3

12. Defend original views when exchanging ideas in the field with professionals and communicate effectively by showing competence in the field. 2

13. Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level. 2

14. Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements. 2

15. Demonstrate functional interaction by using strategic decision making processes in solving problems encountered in the field. 2

16. Contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values. 2

1. Develop the ability to use critical, analytical, and reflective thinking and reasoning 3

2. Reflect on social and ethical responsibilities in his/her professional life. 3

3. Gain experience and confidence in the dissemination of project/research outputs 2

4. Work responsibly and creatively as an individual or as a member or leader of a team and in multidisciplinary environments. 2

5. Communicate effectively by oral, written, graphical and technological means and have competency in English. 2

6. Independently reach and acquire information, and develop appreciation of the need for continuously learning and updating. 5

1. Develop abstract mathematical thinking and mathematical intuition. 3

2. Demonstrate a broad understanding of several areas of advanced mathematics and of their interrelations. 4

3. Have knowledge of the fundamental and advanced concepts, principles and techniques from a range of topics. 4

4. The ability to tackle complex problems, reveal structures and clarify problems, discover suitable analytical and/or numerical methods and interpret solutions. 3

5. Analyze problems of the area of specialization, plan strategies for their solution, and apply notions and methods of abstract and/or applied mathematics to solve them. 2