Computational mathematics in APP

Description*: The aim of this course is to consolidate the skills acquired in secondary school that are essential for the pursuit of higher studies in science (calculating with powers, manipulating fractions, solving simple equations and inequalities, identifying a situation of proportionality, graphing a function, studying the variations of a function) by solving biomathematical problems. In a teaching context, biomathematics refers to all the mathematical concepts and methods (possibly supported by computer technology) used to study and model biological phenomena. This initial approach to biomathematics will focus on the concept of mathematical function as a model for expressing relationships between quantities, in a quantitative approach to the living world. The mathematical tools used to study functions (graphical representation, notions of limit, continuity and derivative) will be addressed, focusing on real functions of one real variable, in the light of questions about the evolution of biological systems. The linear model, the exponential model, the more elaborate Verhulst model (S-curve) and, finally, the resolution of optimization problems in biological contexts, leading to the determination of function extrema, will be encountered and studied.

The program of this UE will be declined in :

• 2 scientific lectures (1h30 each) shedding light on biomathematical concepts and methods
• 4 cycles, each comprising :

• 2 tutorial sessions of 1h30 devoted to a formative problematic based on a quantitative approach to living organisms
• 1 3-hour tutorial session dedicated to the routinization of mathematical techniques to support problem solving

In addition to the methodological and interpersonal skills objectives (acquisition of cross-disciplinary skills common to the whole APP life sciences bachelor's degree), this course aims to provide the basic computational tools needed to pursue studies in the life sciences, and to introduce students to the field of biomathematics. All the concepts and skills covered in this course have already been encountered in high school (pre-requisites on numbers, proportionality and power functions in junior and senior high school; the notion of derivative and the exponential function in the première mathematics specialization; the notions of limit, continuity and the logarithm function in the terminale complementary mathematics option), with variations depending on the student's profile. The aim of the UE is to enable students to consolidate their high school knowledge and skills, by strengthening the link between mathematical knowledge and knowledge of biology, while at the same time offering rapid access to the contents of the première and terminale for students who have not continued their study of mathematics until the end of high school (subject to greater personal work on the part of the student).

second-level mathematics

100% Continuous assessment :

• 40% Specific knowledge and know-how
• 40% Cross-disciplinary know-how
• 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, the discrete and the continuous
• Cycle 1: the linear model
• Cycle 2: the exponential model
• Second scientific conference: limit, continuity and derivative, tools for studying functions and thinking about the evolution of phenomena
• Cycle 3: the Verhulst model
• Cycle 4: solving optimization problems in biomathematics

Manager*: Thibaut Delcroix, Thomas Hausberger

Administrative contact(s): Sophie Cazanave Pin