- Define rigorously a notion seen in the course; give a geometrical interpretation of it; explain in which fields of application it is found (precise examples).
- Be able to interpret and manipulate a mathematical formula; demonstrate mathematical properties.
- From a problem situation, isolate the data and unknowns; model; represent the situation; solve the problem; interpret the results; judge their plausibility.
- Apply without hesitation the techniques appropriate to the solution of numerical problems related to the subjects taught.
This course addresses mathematics as a discipline serving the biological sciences, and in particular the statistics course. In this sense, it will zoom in on certain mathematical notions used in statistics (sum symbol, matrices, functions of two variables) and will develop its mathematical components.
A supplement to the introduction of differential equations seen in block 1 will also be proposed.
The mathematics covered has a dual purpose: to complement the mathematics of the statistics course and to provide a general mathematical culture to tackle certain problems (e.g. problems of optimisation of functions in two variables or prey/predator systems).
Some elements of mathematical language are introduced to facilitate understanding of statistics courses, such as the sum symbol. We then introduce elements of matrix algebra, including Leslie matrices. The course then moves on to functions of several variables and we tackle optimization problems in two variables. The course concludes with a supplement on differential equations.
1. Sum Symbol
2. Matrix Algebra
3. Functions of Several Variables
4. Introductory to Differential Equations
Exercises are offered for each subject covered, alternating with the theoretical lessons.
The teaching will first of all make sure that the mathematical notions dealt with are related to the statistics course. Once the link is established, mathematical developments will be presented in order to deepen certain notions.
The student will also be required to use their mathematical knowledge in a modelling context. We take the time to introduce each new concept carefully and to explain clearly why things work and how they work. Applications will be provided to enable the student to develop strategies for tackling problems that do not follow a pre-determined 'recipe'. During the tutorials, the student will be asked to interact, to state his or her solution and to compare it with that of another student. The pedagogy used therefore aims to give meaning to learning so that it is transferable.
Group work may also be offered to explore certain subjects in greater depth.
Formula: written examination offered in January and August. The assessment will consist of a written examination which may include both exercises and theory (in particular, proofs of the properties covered).
The difficulty of the exercises will be similar to that of the exercises set in lectures, tutorials and group work.
If they have taken place, group works may be assessed through an oral presentation (possibly outside the exam period) and/or a written examination.
An assessment will be organised in January (first session) and August (second session).
Calculators, and any other electronic devices, are not permitted in the exam.
If the exam is held online (remotely), the proposed format may be updated.
Course syllabus; Biau G., Droniou J., Herzlich M. Mathématiques et statistique pour les sciences de la nature. Modéliser, comprendre, appliquer, EDP Sciences, Collection enseignement sup, Mathématiques, Paris, 2010. Dupiereux E., De la variabilité aux risques d'erreurs. Presses universitaires de Namur, Namur, 2013.
| Training | Block | Credits | Mandatory |
|---|---|---|---|
| Bachelor in Biology | 2 | 3 | Yes |