Mathematics

This course covers the concepts of complex numbers, systems of linear equations, vector space in Cn, matrix algebra, eigenvalues and eigenvectors, orthogonality, and normal matrices.

Systems biology is a new approach to biological and biomedical research based on a more holistic perspective and relies on the use of mathematical and computational models, with complementing experiments in the lab.  This course provides an overview of systems biology and its building blocks, experimental approaches, and a variety of mathematical models and tools. Students are introduced to the mathematical basis of dynamic systems, networks, and constraint-based modeling.  Examples used in the course include cancer metabolism (molecular modeling), neuroscience (tissue-level modeling), and diabetes (whole-body level modeling). Practical skills are trained by carrying out computer experiments. 

The course provides rigorous theoretical foundation for key concepts appearing in Analysis: open sets, closed sets, continuous maps, continuity, differentiability, Riemann integral. This is done in the context of sets on the real line and of functions of one variable.

Students learn elementary yet important mathematical concepts and techniques that have a wide range of applications in natural and social sciences. The focus is on calculus skills required for further study in life sciences, earth sciences, and economics, amongst others. Topics include basic and discrete mathematics, matrices, graphs and derivatives, functions of multiple variables, and optimization and basic integration, with applications to probability distributions.