BMAT 12A03 - Mathematics - Advanced level

This course has two aims. First, to provide students with the mathematical tools required for the second semester economics course and for the quantitative social science courses. Second, to make them autonomous learners: able to understand and assimilate new mathematical methods, both now and in the future.

To achieve these aims, the course will be built around a dialogue between mathematical concepts and their applications in the quantitative social sciences. Theoretical lectures will be kept to a minimum, and students will be engaged in active work as much as possible. Each concept will be linked to concrete situations in which it is used. For example, the introduction of a new notion will be motivated by the desire to understand or model a phenomenon drawn from the social sciences. A concept may be introduced through an exercise and then formalised afterwards in a summary handout. Students will then work through a variety of exercises drawn from different contexts. The course is organised around two fundamental themes that serve as prerequisites and essential tools for the economics courses: the manipulation of algebraic expressions and the study of functions (of one or several variables). A geometric approach to functions and to differentiation is particularly important. Exercises will draw on these two themes as often as possible, and will adopt varied perspectives in order to foster a deep understanding of the concepts involved.

This course is made up of two parts: 12 hours of pre-term teaching during the first two weeks of the academic year, followed by 24 hours over the course of the semester. The programme has been split into two so as to allow for a change of teacher between the two parts. Concepts are not compartmentalised between the pre-term and the semester: they are introduced during the pre-term and then consolidated during the semester. The 12 hours of pre-term teaching will be used to review foundational material. It includes, in particular

● Review and further topics on functions

● Sequences

● Systems of linear equations The 24 hours term module includes, in particular

• Integration

● Matrices

● Further topics in differentiation and optimisation

● Graphs and networks

There will be multiple assessments throughout the semester.