Face-to-face , first term, 30 hours of theory and 15 hours of exercises.

First term
Friday from 11:00 to 13:00 at 109 Marais 100

French

The aims of this course are:

- to situate, in anthropological and historical perspectives, various concepts and results of the construction of mathematical thinking;
- to develop the student's ability to apply basic mathematical techniques to issues of social sciences, using a formalisation, deduction and formal language tool.
- to develop the analysis of structures which enable to understand theoretical developments in social sciences. Structure analysis being one of the major constituents of mathematics;
- to provide the students with the necessary mathematical tools to follow the subsequent courses resorting to statistical techniques and data analysis.

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Mathematics being primarily and generally a reasoning method, they enable to analyse relations between entities at a level of abstraction, a rigor and efficiency that is not always possible with ordinary language. This course will be considered at different levels, addressing the idea of mathematics as construction of knowledge, development of a tool and analysis of structures. It will be different from other mathematics courses due to its constant interaction with social themes.

Course outline:

Chapter 1: A bit of Social Choice Theory (and an impossibility theorem)
Chapter 3: Structures and (thinking) Mathematics;
Chapter 2: Logic and valid reasoning;
Chapter 4: Shapley value in a cooperative game
Chapter 5: Matching

Lecture and tutorials

Written examination. Calculators are prohibited.
It consists of four parts in order to cover all of the subject matter (including exercise sessions).

The references included here are the sources that have guided the preparation of certain parts of the course.

Balinski M., Le suffrage universel inachevé, Belin, 2004. (Surtout les pages 283-311).

Freund M., Logique et Raisonnement, Ellipse, 2011.

Gura E.-Y. and Maschler M. B., Insights into Game Theory -- An alternative mathematical experience, Cambridge University Press, 2008.

Hudry O., Votes et paradoxes~: les Èlections ne sont pas monotones !, Mathématiques et Sciences humaines / Mathematics and Social Sciences, n∞ 163, 2003, p. 9-39.

Lucas Th., Berlanger I. et De Greef I., Initiation à la logique formelle, Ed. de Boeck, 2003.

Taylor A.D. and Pacelli A.M., Mathematics and Politics -- Strategy, Voting, Power and Proof, Second Edition, Springer, 2008.

Other references are available in the course notes.

A copy of the slides designed to be complete during the lecture, will be available.

Additional notes (incorporating more mathematical developments and readings) are also available at the reprography service.