1. Students will acquire competencies in:
a. Identifying adequate research topics;
b. Selecting and defining research problems, including appropriate parameters;
c. Preparing a research project for a doctoral thesis;
d. Organizing and conducting research appropriately;
e. Write a research article and a doctoral thesis;
f. Write a proposal for funding a research project;
g. Knowing the main literature and conferences related to the research in complex systems.
These competencies will allow developing research in complex systems studies domains, according to the normal procedures in this scientific domain.
2. Defining and presenting the Plan of the Doctoral Thesis, to be followed until the conclusion of the work.

1. Introduction
1.1. Critical and scientific thinking
1.1.1 Empiricism: the use of empirical evidence
1.1.2 Rationalism: the practice of logical reasoning
1.1.3 Scepticism: sceptical attitude
1.2 Types of research - empirical vs. non-empirical, Social and Human Sciences vs. "Hard" Sciences
1.3 Interdisciplinary research
2. Reviewing of literature
3. Defining the problem
3.1 Formulating the problem
3.2 Identifying variables
4. Examples of research
5. Writing
5.1 a research article
5.2 a doctoral thesis
6. Research project
6.1 Funding projects in complex systems research
6.2 Contents of a proposal
6.3 Case study
7. Literature and conferences
7.1 Main sources of literature
7.2 Main conferences
7.3 Organization of workshops and activities developed by the doctoral programme students

Continuous Assessment:
- Project (90%) - Research project describing the doctoral research work.
- Participation in class (10%).

Students will acquire competencies in:
1. using theoretical concepts and tools from Mathematics for the study of complex systems, according to the state of the art in the domain;
2. using theoretical concepts and tools from Network Theory for the study of complex systems, according to the state of the art in the domain;
3. using theoretical concepts and tools from Physics for the study of complex systems, according to the state of the art in the domain;
4. using theoretical concepts and tools from Biology for the study of complex systems, according to the state of the art in the domain.
These competencies will allow developing interdisciplinary research in complex systems observed in nature.

1. Mathematics: differential equations; order vs. chaos; non-linearity and feedback; linear and non-linear dynamics; determinism vs. previsibility; Rössler's attractor; the butterfly effect; strange attractors; Lorenz equations; bifurcation diagrams; fractal structures; Cantor, Koch, Sierpinski, Mandelbrot.
2. Network Theory: essential concepts; relational structures; complex simplices; hypergraphs; poliedral connectivity; q-transmition; incidence matrices; system time and events; applying hypernetworks.
3. Physics: statistical mechanics; order, disorder, equilibrium point and fractal geometry; patterns and auto-organised structures; reaction-diffusion; stationary patterns through the Turing mechanism; Ockham's razor; sand piles; percolation.
4. Biology: auto-organization; evolutionary biological systems; positive and negative feedback; stigmergy; epidemiology and pandemic propagation.

Continuous Assessment:
- Exercises (90%) - Exercises regarding the subjects presented in class.
- Participation in class (10%).

Students will acquire competencies in:
1. Preparing and writing a scientific article.
2. Organizing a workshop internal to the doctoral programme.
3. Presenting and discussing the article in the workshop.

1. Preparing and writing a scientific article.
2. Organizing a workshop internal to the doctoral programme.
3. Presenting and discussing the article in the workshop.

Continuous Assessment:
- Scientific article:
* text (50%)
* presentation (30%)
- Organisation of the workshop (20%).

Students will acquire competencies in:
1. using theoretical concepts and tools from Economics for the study of complex systems, according to the state of the art in the domain;
2. using theoretical concepts and tools from Sociology for the study of complex systems, according to the state of the art in the domain;
3. using theoretical concepts and tools from Anthropology for the study of complex systems, according to the state of the art in the domain;
4. using theoretical concepts and tools from Psichology for the study of complex systems, according to the state of the art in the domain;
5. using theoretical concepts and tools from Social Networks for the study of complex systems, according to the state of the art in the domain;
6. using theoretical concepts and tools from Data Processing for the study of complex systems, according to the state of the art in the domain.

1. Economics: John Reed; Brian Arthur; Hayek; methodological individualism, reductionism; economics based on computational artificial agents.
2. Sociology: Norbert Elias. Social structures vs. levels of analysis. Raimond Boudon.
3. Anthropology: cultural diversity, ethnocentrism; primitive societies, evolution; actual societies, functionalism.
4. Psychology: Bibb Latané, Social Impact Theory. James Davies. Social decision schemas. Piaget: genetic psychology. Keith Sawyer: individualism vs. holism. Max Weber. Holism: Durkheim, social facts. Vigotsky. Functionalism. Socio-culturalism. Fodor and Davidson.
5. Social Networks: six degrees of separation (Erdos); random graphs; small world effect; Watts and Strogatz; scale-free; hub effect; Mateus effect.
6. Data Processing

Continuous Assessment:
- Exercises (90%) - Exercises regarding the subjects presented in class.
- Participation in class (10%).

1. Follow the state of the art in Complexity Sciences.
2. Present the doctoral thesis research work.

1. Participation at the International Cycle of Conferences in Complexity Sciences, at the ISCTE-IUL and the FCUL, related to topics previously presented at this doctoral programme.
2. Organisation of a workshop in the domain of the doctoral thesis.
3. Presentation of the thesis research work at the workshop.
4. Conception and presentation of the doctoral thesis.

1. Participation at the International Cycle of Conferences in Complexity Sciences - 5%
2. Organisation of a workshop in the domain of the doctoral thesis and presentation of the thesis research work at the workshop - 5%
3. Doctoral thesis - 90%