Any science becomes more mathematical as it matures. Also the field of cognitive neuroscience applies advanced mathematical techniques to investigate the psychological, computational, and neuroscientific bases of human cognition and behaviour.

The data considered in cognitive neuroscience studies are typically of a considerable complexity: multiple time-series of haemodynamic responses recorded in numerous voxels (fMRI, PET) or electrophysiological activity recorded through many electrode channels (EEG) or sensors (MEG). Both the acquisition and analysis of such data rely on sometimes pretty sophisticated quantitative techniques. Also, increasingly, models for the neurocognitive processes underlying these data are specified at a quantitative level.

Consequently, for a basic understanding of data acquisition, analysis and modelling, some minimum amount of mathematical 'literacy' is required. The aim of this course is to provide (or refresh) such a minimal background. Both technical detail and mathematical rigor will be bypassed; instead, focus is on familiarizing the student with the basic mathematical concepts and tools to be encountered in the other courses of the master's programme and possibly to be applied in the second-year research training.

The course also contains numerous exercises with applications of math in the broad field of cognitive neuroscience.  
 

The course will start with general mathematics at –or at least not going far beyond-- a sound secondary school level. Topics here include: (review of) standard functions (algebraic, exponential, logarithmic, trigonometric), differentiation and function extrema, partial derivatives and multidimensional function extrema, integration. Later, more specific topics appear: introduction to differential equations, introduction to complex numbers, to the ideas of Fourier analysis, and to the basics of vector and matrix algebra.