Mathematics II : what biologists might like to know
Biology Master, ENS
Year : 1 (M1)
Semester : 1 (S1)
Course code :
UNBIO1-050 (T105)
Course name :
Mathematics II : what biologists might like to know
Coordinator :
ECTS :
6
Keywords :
Fourier transform, dynamical systems, Markov chains, stochastic differential equations, partial differential equations.
Prerequisites for the course :
Mathematics I : What a biologist should know (L3)
Course objectives and description :
This course is a follow up to Mathematics I : "what a biologist should know" (L3). It is especially adapted to students interested in mathematical modeling in ecology/evolution/genetics and neurobiology. The program includes : Fourier transform, dynamical systems and chaos, continuous-time Markov chains and infinitesimal generators, diffusions and stochastic differential equations, partial differential equations, interacting particle systems. Teaching relies more heavily than in Math I on computer simulations and on individual work. It is supported by computer-based sessions.
Assessment / evaluation :
two-people computer projects
Course material (hand-outs, online presentation available, …) :
not applicable
Suggested readings in relationship with the module content (textbook chapters, reviews, articles) :
– Elements of Mathematical Ecology by Mark Kot
– Modelling Populations in Space and Time, by Eric Renshaw
– Mathematical Biology, by James Murray
– A Biologist’s guide to mathematical modeling in ecology and evolution, by S. Otto and T. Day
– Theoretical Neuroscience, by P. Dayan and Abbott
– Dynamical Systems in Neuroscience : The Geometry of Excitability and Bursting, by E. Izhikevich
– Spiking Neuron Models, by W. Gerstner et W. M. Kistler