30563 - MATHEMATICAL MODELLING FOR NEUROSCIENCE

Not required

Brain functions, such as perception and learning, emerge from biological processes unraveling at different temporal and spatial scales. The purpose of this course is to present theoretical models that have been developed to explain these processes. Particular emphasis will be put on experimental results, which will be used to motivate the study of specific theoretical questions, and on the mathematical tools that have been developed to analyze them.

Biophysics of neurons and synapses

• Dynamics of networks of neurons

• Neural encoding and decoding of information

• Learning and memory in neural circuits

Understand basic neurobiological concepts

• Understand experimental results obtained with recently developed technologies

• Understand phenomenological, mechanistic and normative models of neurobiological processes underlying brain functions

• Compute response dynamics in single neuron, synapses, and neural networks models

• Interpret experimental data obtained in neurobiological recordings

• Analyze learning in simple neural network models

• Face-to-face lectures
• Exercises (exercises, database, software etc.)
• Individual assignments

Throughout the course, home assignments will be given to test the students’ understanding of the concepts taught in class, and to deepen the knowledge of the field.

• The written exam will test the students’ understanding of the concepts taught in class.

• The group assignment will test the students’ ability to apply these concepts to specific

  neurobiological problems.

• Grading scheme:

  •  General written exam: 50% of the final grade. 

  • Group assignment: 50% of the final grade.

The recommended textbook is:

• L. F. Abbott and P. Dayan, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, The MIT Press, 2005. Additional relevant references will be provided during the course.