Mathematical Modeling for Biology
A.Y. 2024/2025
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
The course focuses on basic concepts of Linear Algebra and Theory of Ordinary Differential Equations: e.g., vectors, matrices, linear transformations and solution of linear systems/frequency response or harmonic response of a dynamical system. In particular, we will focus on observed dynamical systems in biological systems: examples of linearization techniques will be considered along with cases of equilibrium and stability studies-always of application interest. The systems studied will be simulated using Python in the tutorials.
Prerequisites for admission
Students should have some background in basic calculus: sets, functions, derivatives, and integrals. We recommend that students review these topics over the summer. However, a brief review of these concepts will be given at the beginning of the course.
Teaching methods
All lectures will be taught in person. The lectures will include discussions between students (in pairs and as a group) and plenty of opportunity for students to ask questions/intervene, as well as the classical format with the lecturer at the board. The Python classes will use suitable online software platforms (e.g. based on Python programming language, such as Jupyter Notebooks) as well as software that the students can install on their own computer.
Teaching Resources
All the useful material will be posted in a dedicated website, e.g. using the UniMi Ariel system. For the Python classes, a good book which is available from the University Library is: https://www.springerprofessional.de/en/a-beginners-guide-to-python-3-programming/17050738?tocPage=1
Assessment methods and Criteria
Grading: The maximum grade for the course is 30/30. Throughout the semester, students will work on three tests, which will be due on a specific date and will be graded and discussed with the instructor during the oral exam. In addition, students will be required to write some programming scripts in Python, also due during the quarter. Finally, an oral exam will be given at the end of the course: each student will prepare a 15-20 minute oral presentation chosen from a list of topics, after which they will answer some questions from the lecturer, during the same oral exam.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 1
MAT/06 - PROBABILITY AND STATISTICS - University credits: 1
MAT/07 - MATHEMATICAL PHYSICS - University credits: 1
MAT/08 - NUMERICAL ANALYSIS - University credits: 1
MAT/09 - OPERATIONS RESEARCH - University credits: 2
MAT/06 - PROBABILITY AND STATISTICS - University credits: 1
MAT/07 - MATHEMATICAL PHYSICS - University credits: 1
MAT/08 - NUMERICAL ANALYSIS - University credits: 1
MAT/09 - OPERATIONS RESEARCH - University credits: 2
Practicals: 16 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Capelli Riccardo
Professor(s)
Reception:
To be scheduled by email
Fifth floor, Tower B, Dipartment of Biosciences