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
You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.
MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).
For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.
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 homework (20%), a final product (a small research project and a short presentation performed in a team of two, 40%) and a written (retake) exam (40%). To pass the course, the grade for the (retake) exam should be at least 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 homework in order to take the exam or to pass the course. The deadline for the project report is December 31st, followed by a retake opportunity January 31st. The homework counts as a practical and there is no retake for it; the homework consists of 5 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
From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.
Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.
Contact
Prof. dr. R.M.H. Merks - merksrmh@math.leidenuniv.nl
For minor students: please contact Sander Hille shille@math.leidenuniv.nl
Remarks
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