Mathematical Modeling for Biology
A.Y. 2021/2022
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
First semester
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
All lectures will be taught in person in a live class which will be broadcast for students following from home. All lectures will be recorded and made available on Ariel afterwards. 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
Assessment: the maximum course grade is 30/30. Throughout the semester, the students will work on six pieces of summative coursework which will be then marked and discussed with the lecturer (the coursework will contribute 6/30 marks towards the final grade). 6/30 more marks will come from six pieces of Python coursework. The remaining 18/30 marks are attached to an oral examination at the end of the course: each student will prepare a 15-20 minutes oral presentation chosen from a list of topics, after which they will answer a few questions by the lecturer, in the same oral examination.
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Practicals: 16 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Roversi Pietro