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Mathematics II : what biologists might like to know

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Programme Maths M1

Biology Master, ENS
Year : 1 (M1)
Semester : 1 (S1)

Course code :


Course name :

Mathematics II : what biologists might like to know

Coordinator :




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