Teaching plan for the course unit (Short version)
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General information

 

Course unit name: Mathematics

Course unit code: 360890

Academic year: 2025-2026

Coordinator: Emili Valdero Mora

Department: Department of Economic, Financial and Actuarial Mathematics

Credits: 6

Single program: S

Estimated learning time

Total number of hours 150

 

Face-to-face and/or online activities

60

	-  Lecture with practical component	Face-to-face		30
	-  Problem-solving class	Face-to-face		30

Supervised project

40

Independent learning

50

Learning objectives

Referring to knowledge The course in Mathematics on the Sociology degree aims to equip students with the tools needed to understand the quantitative instruments used in sociological research and to design and organise information effectively. The core objectives of the subject are: Understand and apply the mathematical concepts and tools commonly used in sociology and the social sciences in general. Acquire a solid foundation that enables students to progress with confidence in the quantitative components of the degree. Formalise sociological situations using precise, specialised mathematical language, including matrices, social choice systems, strategies, sets, equilibria, and related structures.

 

 

Teaching blocks

 

1. Markov Chains

*  This block introduces the concept of a stochastic process and of a Markov chain as tools for representing the different states of a system and the probabilities of transition between them. It examines the existence of absorbing states and long-run equilibrium.

2. Game Theory

*  Game theory concerns the study of multi-agent decision problems, including both situations in which explicit agreements between agents or players are possible (cooperative games) and those resolved through individual decision-making without the possibility of establishing binding agreements (non-cooperative games).

This block explains how to formalise real situations as cooperative or non-cooperative games, depending on the context. Students learn to identify the players, the strategies available, the possibilities for cooperation and coalition formation, and the potential outcomes of the interaction. To infer predictable behaviour, we develop the concept of Nash equilibrium for non-cooperative games and the Shapley value for cooperative games. The stability of coalitions that may emerge is also analysed.

 

 

Official assessment of learning outcomes

 

Continuous assessment—the standard mode of evaluation—consists of two, in-person, written mid-term examinations and the submission of other activities completed outside the classroom. Students are informed of the content of each mid-term exam via the Virtual Campus. The exams are closed-book. The out-of-class activities, which must be completed individually, consist of the submission of written practical exercises and a paper on cooperative games. The two mid-term examinations account for 45% and 40%, respectively, of the final grade, while the paper submitted at the end of the course constitutes the remaining 15%. Students who pass the mid-term exams (with a mark equal to or greater than 5 out of 10) are exempt from any further tests on these subjects. Students who fail a mid-term exam must sit an examination covering the same material on the day of the final exam (weighted at 85% of the final grade) and must also submit the cooperative games paper (weighted at 15%). To pass the course by the continuous mode of assessment, students must obtain an overall average mark of 5/10 or higher across the examinations and the paper.   Examination-based assessment Single assessment consists of a final examination, comprising theoretical and practical questions, held on the date set by the Academic Council. The final grade for the course corresponds to the mark obtained on this examination. Repeat assessment takes the form of a final examination with theoretical and practical questions. Repeat assessment dates are established in the Faculty’s academic calendar and coincide with the standard resit period for undergraduate programmes (normally in July). The specific date for the repeat assessment examination for this subject is established by the Academic Council.

Reading and study resources

Check availability in Cercabib

Book

MORROW, James. Game Theory for political scientists. Princeton (N.J.): Princeton University Press, cop. 1994

Catàleg UB  
Versió en línia (1994)  

GARDNER, Roy. Juegos para empresarios y economistas. Barcelona: Antoni Bosch, 1996

Catàleg UB  

RAFELS, C. (coord.). Jocs cooperatius i aplicacions econòmiques. Barcelona : Edicions de la Universitat de Barcelona, 1999

Catàleg UB  

SÁNCHEZ-CUENCA, I. Teoría de juegos. 2a. ed. Madrid : Centro de Investigaciones Sociológicas, 2009

Concise, accessible manual with applications to sociology and political science.

Catàleg UB  
Versió en línia (2009)  

HODGE, Jonathan K. ; KLIMA, Richard E. The Mathematics of voting and elections: a hands-on approach. Providence, R.I.: American Mathematical Society, 2005

Catàleg UB  

TAYLOR, A.D. ; PACELLI, A.M. Mathematics and politics. strategy, voting, power and proof. 2nd ed.. [New York, N.Y.]: Springer, cop. 2008

Catàleg UB  

ADILLON, R. ... [et al.]. Lliçons introductòries de matrius i sistemes d’equacions lineals. Barcelona : Professors del Dept. Matemàtica Econòmica, Financera i Actuarial. Universitat de Barcelona, 2001

Catàleg UB