30563 - MATHEMATICAL MODELLING FOR NEUROSCIENCE

This course integrates aspects of elementary calculus, linear algebra, basic stochastic processes, and Python programming. While not obligatory, familiarity with these tools can greatly enhance the learning process. Such familiarity encourages a deeper engagement with the course material, enabling students to grasp concepts more effectively.

This course delves into the biological basis of cognitive functions such as perception and learning. It introduces theoretical models while highlighting the significance of experimental findings in shaping scientific inquiries. Additionally, it integrates specialized mathematical tools, encompassing data analysis and modeling, for comprehensive examination. These elements constitute the foundation of neuroscience, enabling students to bridge theoretical frameworks with empirical evidence. This connection equips them with the ability to interpret, analyze, and model intricate biological phenomena, preparing them for advanced studies in neuroscience.

• Principles of neural coding
• Biophysics governing neurons and synapses
• Modeling individual neuron activity
• Dynamics of networks of neurons
• Learning in neural circuits

• Grasp fundamental neurobiological concepts
• Interpret experimental findings obtained through recent technologies
• Comprehend phenomenological models describing neurobiological processes
• Understand mechanistic models explaining the neural underpinnings of brain functions
• Explore normative models outlining the principles guiding neurobiological processes

• Interpret experimental data derived from neurobiological recordings
• Calculate response dynamics within single neuron, synapse, and neural network models
• Analyze learning and learning dynamics in neural models

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

• Face-to-face lectures focus on the theoretical, methodological, and computational aspects of the topics covered by the course.
• During hands-on exercise sessions, online lectures, and group projects, the primary focus will be guiding students through accessing, analyzing, and interpreting modern neuroscience datasets. These datasets encompass large-scale recordings from awake behaving animals, aiming to deepen understanding through practical application and collaborative exploration.

• 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.