30319 - QUANTITATIVE METHODS FOR SOCIAL SCIENCES (MODULE I - MATHEMATICS)
Course taught in English
Go to class group/s: 23
Class-group lessons delivered on campus
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:
- 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.
- 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.
- 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
- Online lectures
- Exercises (exercises, database, software etc.)
- Individual assignments
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 assessment procedure for this course reflects its crucial education goal: “how mathematics can be used to model and analyze problems in Social Sciences”.
Such a goal requires a twofold skill:
- - given a mathematical tool, imagine where it could be applied;
- – given a concrete problem, find and use an appropriate mathematical tool.
The assessment is divided into two blocks, aligned with the distinction above.
Block 1 - It consists of three assignments, the first one, at the end of the presentation of linear algebra, the second one, at the end of Calculus, the last one, one week before the end of the course.
Each assignment will ask the student to describe concrete situations that can be credibly described and analyzed through an assigned mathematical tool.
Students will be provided with a scheme for their presentation.
Presentations must be uploaded via Blackboard in 5 days.
Each assignment is evaluated with a grade from 0 to 5.
These points are valid during the whole a.y.
At any oral exam, students can ask to avoid the use of the accumulated points: they will get a question, whose answer will be evaluated with a grade from 0 to 6.
Block 2 – It is an oral exam, to be taken at any of the scheduled sessions. This oral exam consists of two questions, one about the first part of the course (Linear Algebra and/or Calculus), the other about the second part of the course (Dynamic Systems). Each answer is worth 8 points.
- L. PECCATI, M. D'AMICO, M.CIGOLA, Maths for Social Sciences, Springer, New York, 2018.
- Exercises available on BBoard.