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, such as Sociology and Political Science. These disciplines were cultivated in the past using almost always qualitative techniques and statistical analysis. Currently, the literature uses rather massively also some non-trivial mathematical models in the analysis of socio-political scenarios. 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, to see how they can be used for the construction of models, and to use these models to support 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 quantitative and qualitative approaches to the study of Dynamic Systems do constitute a powerful tool for the analysis of socio-political questions.

The approach privileges intuition rather than formal mathematical rigor. Special attention is given to 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.)
• Individual assignments

Together with frontal lectures, students are offered R&E sessions (R = Review; E = Exercises) in which they choose topics they would like to be re-explained or on which they would like to see exercises. In addition, students can see more exercises worked out in detail during the TA sessions.

Students are warmly encouraged to make regular use of instructors' office hours throughout the entire academic year.

The same syllabus and exam rules apply to first year students as well as students who have not passed the exam yet.

Assessments are divided into two blocks.

Block 1 - It consists of three individual assignments to be submitted on Blackboard. Due dates will be communicated during the semester. As a general rule, the first assignment will be at the end of linear algebra, the second assignment will be at the end of Calculus, and the last one will be one week before the end of the course. Once available on Blackboard, students will have 5 days to complete and submit their work.

In each assignment students will be asked 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.

Each assignment will be evaluated with a grade from 0 to 3. These points will remain valid during the whole a.y.

Block 2 – It consists of a written exam divided into two partial written exams that will be scheduled during the course. The first written partial exam will concern the program covered from the beginning of the course until the point reached at the time of the first partial; the second written partial exam will concern the remaining of the program.

General info

• All exams are written.

• The exam can be taken via two partial exams or via a general exam.

• In order to take an exam, a registration is needed; students who do not register in time will not take the exam.

• During the exam only the use of pen and paper will be allowed; calculators, mobiles, books, notes, etc. are not allowed.

Both partial and general exams will follow the same rules and will have the same structure.

Partial exams: The first written partial exam will be on October, 21. It will be possible to take the second partial exam alternatively on December, 12 2022 or (exclusive) on January, 23 2023.

The first partial exam will be evaluated with a score from 0 to 100 points, while the second partial exam will be evaluated with a score from 0 to 120 points.

The overall grade will be given by (1) the sum of the points earned in the two partials divided by ten and (2) the points earned through the assignments. The overall grade will be rounded to the nearest integer. An overall grade greater than or equal to 18 will be considered as a “passing” grade. An overall grade of 31 will be an honor grade (30 e lode).

General exam: The general exam will concern the entire program of the course and will consist of the two partial exams administered at the same time. The general exam will be evaluated with a score from 0 to 220 points.

The overall grade will be given by (1) the sum of the points earned in the general exam divided by ten and (2) the points earned through the assignments. The overall grade will be rounded to the nearest integer. An overall grade greater than or equal to 18 will be considered as a “passing” grade. An overall grade of 31 will be an honor grade (30 e lode).

• L. PECCATI, M. D'AMICO, M.CIGOLA, Maths for Social Sciences, Springer, New York, 2018.

• Exercises available on BBoard.