# Mathematics and algorithms

## Presentation

Programme (detailed contents):

Logic, reasoning methods, sets, binary relations, applications, finite sets and enumeration, real numeric sequences

Foundations for algorithms: control structures, variables, function and procedure definition

Organisation:

Lectures with handouts.

Tutorial classes must be prepared by students. Extra exercises for personal work are provided.

With practical sessions using the Ada language,

students may use concepts learnt in lectures and tutorials.

Main difficulties for students:

Handle abstract concepts. Build rigorous statements or proofs. Apply correctly theorems or typing rules by checking the hypotheses.

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

- concepts of algorithm and typing (assigning by type).
- Logic and the main reasoning methods.
- Set theory and operations on sets
The student will be able to:
- Rigorously prove mathematical statements.
- Handle abstract sets.
- Design an algorithm to solve a simple problem and translate it into the Ada
language.

## Needed prerequisite

Common sense, rigour.

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...