**Quadrimestre 1 - All options**

### General course description

This seminar-modelled course harmoniously integrates lectures, supervised assignments as well as assignments in which students are asked to be proactive. Its interactive character leads students to adopt an efficient and dynamic attitude. It presents an Introduction to discrete mathematics as a conceptual aid in the world of numbers as well as aspects of numerical analysis (this field is presented through simple examples such as those related to problems of approximation by means of rational numbers, and calculations relating to real numbers).

### Learning basic skills

See course book.

### Course Aims

- The ability to express oneself and communicate scientific and technical matters;
- To enhance formalization and modelling skills;
- The acquisition of working methods valid for matters requiring a minimum of abstraction ability;
- Mathematical knowledge linked to the specific needs of computing.

Problem solving is put in the foreground so as to develop the following skills: understanding input, translate this one into a mathematical language in order to solve it in a rigorous way and give an answer expressed in natural language (the parallel between this process and the expected IT process will be established.)

### Course Outline

#### Part 1 : Introduction to Discrete Mathematics

- Basic notions
- Binary, octal and hexadecimal arithmetic
- Basic set theory
- Mathematical logic (
*oriented towards conducting arguments and towards understanding how a computer works*)
- Introduction to set theory
- Introduction to graph theory
- Counting

#### Part 2 : Elements of Numerical Analysis

- Functions: basic notions
- Sequences and series
- Approximation methods

*For more information, students are referred to the course book as well as to the ***schedule** which is handed out to students at the beginning of the year, accompanied by an oral commentary dealing especially with the need to use the schedule to organize personal study.

### Bibliography

- The course book contains a commented bibliography. Nevertheless, one reference work deserves to be mentioned here as it is indispensable to fill any gaps possibly resulting from pre-college education:
**Déledicq A.**, *Maths lycée*, Editions de la Cité (collection manuel+, 1998)