1. Understanding of the basic concepts of higher mathematics.
2. Ability to create and develop logical arguments with a clear identification of hypothesis and conclusions.
3. Ability to correctly express oneself in mathematical language.
4. Capacity for abstraction, including logical development of mathematical theories, and relationships between them.
5. Ability to formulate problems in mathematical language, such that their analysis and solution are facilitated.
6. Knowledge of the historical evolution of the fundamental concepts of mathematics.
7. Ability to begin mathematical investigations under the guidance of experts.
8. Ability to formulate optimisation problems, and take decisions and interpret solutions in the light of the individual situations of particular problems.
9. Ability to contribute to the construction of mathematical models from a basis of real situations.
10. Ability to use computational tools of numerical and symbolic calculations for posing and solving problems.
11. Skill in quantitative reasoning.
12. Ability to understand problems and abstract their essential elements.
13. Ability to take qualitative information from quantitative data.
14. Willingness to face up to new problems in different areas.
15. Ability to work with experimental data and contribute to their analysis.
16. Ability to communicate with other non-mathematical professionals, and aid them in the application of mathematics in their respective areas of work.
17. Ability to work in inter-disciplinary teams.
18. Ability to present mathematical reasoning and conclusions clearly and precisely, in an appropriate form for the audience at which they are aimed, both orally and in written form.
19. Basic knowledge of the teaching and learning processes of mathematics.
20. Full understanding of basic mathematics, which are what should be included in pre-university teaching.
21. Ability to participate in the development of pre-university level training programmes in mathematics.
22. Ability to detect inconsistencies.
23. Knowledge of English for reading, writing, and presenting documents in English, as well as for communication with other specialists.