Admission Requirements
Some basic experience with programming and the Linux terminal is helpful. The key skills will be introduced in a preparatory afternoon.
Basic knowledge of differential equations is required.
Description
Biological systems are so complex, that biologists often need to call in the help from mathematicians and computational scientists. These questions constitute a rich source of applied mathematical problems, for which often a range of mathematical and computational techniques need to be combined with one another. Mathematical insight into dynamical systems, pattern formation, complex networks, multiscale dynamics and parallel processing turn out to be a tremendous help while trying to ‘make sense of life’.
This course will in particular introduce you to the mathematical modeling of healthy and diseased multicellular organisms, like plants and animals, including ourselves. A key question is how cells cooperate to create biological structure, and how this biological structure feeds back on gene expression. The focus will be on how to sharpen one’s intuition on the emergence of biological systems and patterns by using and further developing a variety of continuous and discrete mathematical models of biological systems.
Mathematical techniques include ordinary-differential equations, partial-differential equations, cellular automata, Hamiltonian systems, and in many cases combinations of those. This course will cover a range of multicellular phenomena, including development of animals and plants, blood vessel networks, bacterial pattern formation and diversification, and tumor growth and evolution.
Course Objectives
At the end of the course the Ba3 student can propose a conceptual biological model based on experimental observations
At the end of the computer practicals run simulations of the model implementation
At the end of the computer practicals the Ba3 student can implement a simple model using existing software
At the end of the computer practicals the Ba3 student can critically interpret the model simulation and compare it with biological data
At the end of the course the Ba3 student can update a conceptual model based on discrepancies with biological data
At the end of the course the Ba3 student can interpret and critically evaluate published mathematical biology models
At the end of the course the Ba3 student can propose a simple new experiment to test a model prediction
At the end of the course the Ba3 student can develop a basic mathematical model based on previous models and new experimental observations and present it in an oral and written report.
Timetable
In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.
Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.
Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Mode of instruction
The course consists of a series of lectures, practical assignments using biological modeling environments, and a final project.
Assessment method
The final grade consists of practicals (20%), and an examination of two parts: (1) a final product (a small research project and a short presentation performed in a team of two, 40%) and a written exam (40%). To pass the course, the grade for the (retake) exam should be at least 5.5, the grade for the final product at least 5.5, and the (unrounded) weighted average of the three partial grades at least 5.5. No minimum grade is required for the practicals in order to take the exam or to pass the course. The deadline for the project report is December 20th, followed by a retake opportunity January 31st. The practicals consists of 5 computer lab assignments, of which the lowest grade is dropped.
Reading list
Handouts of slides, partial lecture notes and research papers will be provided during the course.
Registration
As a student, you are responsible for enrolling on time through MyStudyMap.
In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
Prof. dr. Roeland Merks: merksrmh@math.leidenuniv.nl
Students of the minor Quantitative Biology can also contact Dr. Sander Hille: shille@math.leidenuniv.nl
Remarks
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.