Course 2019-2020 a.y.

The course is composed of two modules:

1. Mathematical Reasoning: provides students with the nuts and bolts of mathematical logic, covering some key methods of proof.
2. Reasoning about mathematical models: investigates, through examples, the virtues and limitations of axiomatizing social scientific concepts.

• Understand the idea of formal languages, formal proofs and logical consequence
• Undersand the notion of algorithmic procedure
• Grasp the logical distinction between “truth” and “rational opinion”.
• Recognise fallacies in logical and elementary probabilistic reasoning.
• Identify the critical elements in the mathematical modelling of informal concepts.
• Develop strong analytic skills

• Formalise expressions in natural language.
• Decide algorithmically the validity/invalidity of suitable natural language arguments.
• Assess critically the meaning of axiomatisation in economics and the social sciences.
• Read original research in the methodology of the social sciences.

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

The learning experience in this course includes, in addition to lectures and class discussions, exercises and individual assignments:

• For each topic covered in class, students are given an exercise set which (i) helps them consolidate their understading (ii) trains them to solve exam problems.  Exercises are discussed in class, if needed in dedicated sessions.
• On a selection of particularly important and cross-disciplinary topics, projects are assigned to individuals who have an interest in broading their knowledge and "joining the dots". Projects are given on a voluntary basis (they are not assessed formally) and allow particularly motivated students to acquire some degree of indepencence in the pursuit of their academic interests.

We run two partial exams (50% each of the final grade), one in the mid-term break to assess students on Part I of the course content, and a final exam to assess students on Part II of the course content (see section 2.b) Students scoring less than 17/30 to the first partial will not be admitted to the second partial, and will be required to sit the general final exam.

In order to evaluate the acquisition of the aforementioned learning outcomes, the assessment of attending students comprises two partial examinations using a mix of open-ended and multiple-choice questions.  Closed-ended questions are used to test the basic knowledge acquired of the course material. Open-ended questions are used to assess the ability to recognise fallacies in logical and elementary probabilistic reasoning and to identify the critical elements in the mathematical modelling of informal concepts.  Finally, open-ended questions are used to test the analytic skills acquired through the course.

General final exam (100% of the final grade) In order to evaluate the acquisition of the aforementioned learning outcomes, the assessment of attending students comprises two partial examinations using a mix of open-ended and multiple-choice questions.  Closed-ended questions are used to test the basic knowledge acquired of the course material. Open-ended questions are used to assess the ability to recognise fallacies in logical and elementary probabilistic reasoning and to identify the critical elements in the mathematical modelling of informal concepts.  Finally, open-ended questions are used to test the analytic skills acquired through the course.

A full set of lecture notes with exercises are provided for this course. Reference for further readings are also included.