Mathematics

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.
 

This course brings together as a coherent body of knowledge the game theoretic algorithms and models that underpin several flourishing subjects at the intersection of computer science, economics, e-commerce, and AI.

The course treats multiplicative number theoretic functions, Möbius inversion formula, properties of Euler's totient function, primitive roots and indices, quadratic residues, the Legendre symbol and it's properties, the quadratic reciprocity theorem, representations of integers as sums of squares, number theoretic properties of the Fibonacci sequence, continued fractions, Diophantine approximation.
 

This course provides research training for exchange students. Students work on a research project under the guidance of assigned faculty members. Through a full-time commitment, students improve their research skills by participating in the different phases of research, including development of research plans, proposals, data analysis, and presentation of research results. A pass/no pass grade is assigned based a progress report, self-evaluation, midterm report, presentation, and final report.