30319 - QUANTITATIVE METHODS FOR SOCIAL SCIENCES (MODULE I - MATHEMATICS)

During the last decades an important evolution has been registered in the study of Social Sciences, like, for instance, Sociology and Political Science. These disciplines were cultivated in the past using almost always qualitative techniques and statistical analysis. At present the literature uses rather massively also some non-trivial mathematical models in the analysis of socio-political questions. Some examples are Arab Springs, Grexit, political consensus dynamics and connection between tools and objectives in political choices. The well-known UK program “Q-Step”, supporting the introduction of quantitative courses in programs oriented to Social Sciences, constitutes another relevant signal of the aforementioned evolution. The mission of this course is to introduce some mathematical tools useful in Social Science and to see how they can be used for the construction of models and how these models can help the understanding of socio-political issues.

The structure course contains three pillars:

1. The first one is a quick introduction to Linear Algebra and to its application in Politics. Several models are presented, together with their implementation with a scientific software.
2. The second pillar is a crash-introduction to Differential and Integral Calculus, with various applications in Economics, NGO management. Basic applications to Statistics are presented too.
3. The last pillar of the course consists in seeing how the quantitative and the qualitative  approaches to the study of Dynamic Systems do constitute a powerful tool for the analysis of socio-political questions.

The approach privileges intuition and not formal mathematical rigor. Special attention is put on model construction.

• Describe problems of interest using mathematical notions.
• Explain how mathematics allows for deducing hidden consequences from the available information.
• Illustrate the concrete implications for social sciences of what can be mathematically deduced.

• Formulate a description of a real problem using models.
• Analyze models through the mathematical tools the course provides (Linear Algebra, Calculus and Dynamic Systems).
• Interpret the mathematical results in the terms of the starting problem.
• Analytically manipulate simple examples.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)

Together with frontal lectures the students are regularly offered R&E sessions (R = Review; E = Exercises) in which students choose topics they would like to be re-explained or on which they would like to see exercises. This opportunity is offered also in extra-sessions for small groups. In the R&E sessions the topics to be covered are freely chosen by students.

The exam consists of three parts:

1. Written exam: 14 points
2. Modeling: 3 points
3. Oral exam: 14 points

• The written exam assesses the ability to analyze a concrete problem, to describe it through a mathematical model, to manipulate the model in order to get results of concrete interest and to explain them.
• The modelling part assesses the ability of modeling a concrete situation for an assigned mathematical tool. Students may take this part by doing three homeworks (1 point each) assigned during the course and/or by doing an optional written part during the written exam. Students may take the optional written part even to improve the results they have already obtained through the homeworks.
• The oral exam assesses the knowledge acquired by students about the mathematical tools the course covers, through definitions, main properties, and significant theorems.

• L. PECCATI, M. D'AMICO, M.CIGOLA, Maths for Social Sciences, Springer, New York, 2018. 
• Mathcad files, available on Bboard.