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Contribution du cours aux acquis d'apprentissage du programme de bachelier en mathématique. A la fin de cette activité, l'étudiant aura progressé dans :
By the end of the course, the student should have progressed in obtaining the following skills:
- Recognise and understand a basic foundation of mathematics.
- Choose and use the basic tools of calculation to solve mathematical problems.
- Recognise the fundamental concepts of important current mathematical theories.
- Establish the main connections between these theories, analyse them and explain them through the use of examples.
- Identify, by use of the abstract and experimental approach specific to the exact sciences, the unifying features of different situations and experiments in mathematics or in closely related fields (probability and statistics, physics, computing).
- Show evidence of abstract thinking and of a critical spirit.
- Identify, by use of the abstract and experimental approach specific to the exact sciences, the unifying features of different situations and experiments in mathematics or in closely related fields (probability and statistics, physics, computing).
- Show evidence of abstract thinking and of a critical spirit.
- Recognise the key arguments and the structure of a proof.
- Evaluate the rigour of a mathematical or logical argument and identify any possible flaws in it.
- Distinguish between the intuition and the validity of a result and the different levels of rigorous understanding of this same result.
- Write a mathematical text according to the conventions of the discipline.
Acquis d'apprentissage spécifiques au cours. A la fin de cette activité, l'étudiant sera capable de :
By the end of the course, the student should be able to :
- Recognise the concepts, tools and methods in the study of sequences of functions:
' by stating, proving and illustrating existence and global uniqueness conditions,
' by stating different notions of convergence of sequences of functions, and illustrating their connections by proofs and counter-examples,
' by stating, proving and illustrating conditions involving the continuity, differentiability or integrability of sequences and series of functions,
' by applying those notions in the study of Fourier series,
' by stating, proving and illustrating the divergence theorem.
- Solve problems using analytical tools:
' by determining whether a system of equations has a solution, and how the solutions locally depend on some parameter,
' by studying the convergence of a sequence of functions,
' by determining the continuity, differentiability and integrability properties of the limit of a sequence or a series of functions.
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