Computational mathematics in PPA

Description* : This course aims to consolidate the skills acquired in high school that are essential for the pursuit of higher education in science (calculating with powers, manipulating fractions, solving simple equations and inequations, identifying a situation of proportionality, graphing a function, studying the variations of a function) through the resolution of biomathematical problems. In a teaching context, biomathematics is understood to mean all the mathematical concepts and methods (possibly equipped with computer technology) that allow the study and modeling of biological phenomena. This first approach to biomathematics will focus on the concept of mathematical function as a model for expressing relationships between quantities, in a quantitative approach to life. The mathematical tools that allow the study of functions (graphical representation, notions of limit, continuity, derivative) will be approached, restricting themselves to real functions of a real variable and in the light of a questioning on the evolution of biological systems. The following will be encountered and studied, in order: the linear model, the exponential model, the more elaborate Verhulst model (S-curve) and finally the resolution of optimization problems, arising from biological contexts, leading to the determination of the extrema of functions.

The program of this EU will be broken down into:

• 2 scientific conferences of 1h30 to clarify the concepts and methods of biomathematics
• 4 cycles, each including :

• 2 tutoring sessions of 1h30 devoted to a formative problematic which finds its source in a quantitative approach of the living
• 1 session of 3 hours dedicated to the routinization of mathematical techniques that are used to solve problems

In addition to the methodological and life skills objectives (acquisition of transversal competences common to the whole life sciences degree in APP), this course aims to provide the basic computational tools necessary to pursue studies in life sciences and to introduce the field of biomathematics. All the notions and abilities worked on in this course have already been encountered in high school (the prerequisites on numbers, proportionality and power functions in junior high and high school; the notion of derivative and the exponential function in the mathematical specialty of the first year of high school; the notions of limit, continuity and the logarithm function in the mathematical option of the last year of high school), with variations according to the profile of the students The ambition of this course is to allow students to consolidate their high school knowledge and skills, by reinforcing the articulation between mathematical knowledge and knowledge in biology, while offering a quick access to the contents of the first and the last year of high school to students who would not have continued their study of mathematics until the end of high school (subject to a more important personal work of the student).

second level mathematics

100% Continuous assessment:

• 40% Specific knowledge and know-how
• 40% Cross-cutting skills
• 20% Know-how

Syllabus: The EU will follow the following progression:

• Opening scientific conference: quantitative approaches in life sciences and mathematical language - numbers, functions as models, discrete and continuous
• Cycle 1: the linear model
• Cycle 2: the exponential model
• Second scientific conference: limit, continuity and derivative, tools to study functions and think about the evolution of phenomena
• Cycle 3: The Verhulst Model
• Cycle 4: Solving optimization problems in biomathematics

Person in charge* : Thibaut Delcroix, Thomas Hausberger

Administrative contact(s): Sophie Cazanave Pin