Mathematics

The course examines fundamental concepts of mathematical modeling and discrete and continuous dynamical systems, with applications across science and technology, including biology, physics, and economics. Students develop both conceptual understanding and practical skills in constructing and analyzing mathematical models of real-world phenomena. Topics include difference equations, ordinary differential equations, stability analysis, phase portraits, bifurcations, and an introduction to fractals and complex dynamics (Julia and Mandelbrot sets). 

This course introduces students to a variety of applicable mathematical methods for solving real-world problems. It is intended for students interested in how further mathematics can be used to solve hands-on problems. The economically-minded will be interested in optimizing based on constrained resources, and computer scientists will be interested in the various network algorithms explored. Physicists will find the material at the end of the course indispensable for solving classical problems. The game theory section of the course includes a discussion of the assumptions made about how rational agents act, which may interest psychologists and philosophy students.

This undergraduate research course provides opportunities to conduct independent research under the supervision of a faculty member at the Chinese University of Hong Kong. Participants are expected to devote approximately 20 hours per week to their research project, with the exact time commitment determined in consultation with the faculty supervisor. The course requires the completion of an original research paper. It develops research methods, analytical thinking, academic writing, and the ability to communicate research findings effectively through scholarly papers and reports. As an independent research program, the course emphasizes initiative, self-directed learning, and regular consultation with the faculty supervisor throughout the research process.

This course studies fundamentals in algebra. Topics include field theory, dedekind domains, finite group representations, and lie algebras.