Mathematical modeling for Biology

A.Y. 2020/2021
Overall hours
MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Learning objectives
The main objective of the course is to provide the basic mathematical tools needed to properly describe some fundamental mechanism in biological phenomena. Therefore, the course mainly focuses on the modelling aspects of Mathematics; it does not deeply enter into the technical details of the proofs, but rather aims at highlighting the meaning of the mathematical concepts and their usefulness in studying Life Science problems. To reach this goal the course is organised into a set of traditional lessons, strictly linked to lab sessions where the students have the opportunity to experience the features of the provided tools, through the use of suitable software platforms (e.g. based on Python programming language).
Expected learning outcomes
At the end of the course, the students will have a basic knowledge of some fundamental tools to describe several biological phenomena. In addition, they will have acquired the ability to develop and implement simple quantitative models through the use of suitable software platforms.
Course syllabus and organization

Single session

Lesson period
First semester
The lectures will be held online on the Zoom platform and will be delivered both synchronously (at set times) and remotely (in case of unavoidable commitments of the teacher, participation in telematic congresses, meetings, etc.).
Tutorials will include both pen and paper exercises and computer simulations and will be held online on the same platform.
Course syllabus
The course will mainly focus on the basic concepts of Linear Algebra and Ordinary Differential Equation Theory. Concerning Linear Algebra, vectors, matrices and linear transformations will be first studied; afterwards, the problem to solve linear systems and elementary spectral analysis will be faced. Concerning Ordinary Differential Equations, the focus will be in the study of dynamical systems involved in biological phenomena; in particular, linearization techniques, as well as equilibria and their stability, will be considered in connection with specific example of applicative interest. All the mathematical concepts will be also illustrated in the lab lessons.
Prerequisites for admission
Students should have a preliminary knowledge of basic Calculus: sets, functions, derivatives an integrals. However, at the beginning of the course, a quick review of these concepts will be provided.
Teaching methods
The lectures will have both the classical format with lessons given by the teachers at the blackboard (or at the whiteboard), and the lab lectures delivered by using suitable software platforms (e.g. based on Python programming language).
Teaching Resources
All the useful material will be posted in a dedicated website, e.g. using the UniMi Ariel system.
Assessment methods and Criteria
Learning assessment will be through an oral exam at the end of the course. The exam aims at assessing how deeply the student has acquired the mathematical concepts developed during course, as well as her/his ability to applied them in simple situations of biological interest.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 16 hours
Lessons: 40 hours
Educational website(s)