School of Science - UG Booklet

Program Overview Physics encompasses everything from the tiniest elementary particle to the ultimate fate of the universe, and provides the foundation for all modern science and engineering. The BSc in Physics program gives students depth and breadth in their studies. Students will learn about exciting topics ranging from quantum computing, superconductivity and nanotechnology to quarks and black holes. The program prepares students for science-related careers, or for further studies in physics and related fields. PHYSICS (PHYS) MATHEMATICS (MATH) The BSc in Physics program offers two options: Program Highlights • Honors Physics Option - This option is intended for students planning to enter graduate school after their undergraduate studies at HKUST. The curriculum provides a strong foundation of courses and requires students to complete a research project and thesis in their final year. • Physics and Mathematics Option - This option is tailor-made for students with a strong interest in both physics and mathematics. It is particularly useful for students who plan to pursue future studies in theoretical physics. Student Sharing HKUST has provided me with various research opportunities, which allow me to explore different fields, including optical microscopy, nonlinear dynamics analysis, and astronomical instrumentation. I also got the precious chance to work with a Physics Nobel Prize Laureate for the astronomical instrumentation project. These experiences have trained me as a future scientist. Program Overview Mathematics permeates almost every discipline of science and technology. It is not only a tool for understanding the abstract models of real-world phenomena while solving practical problems, but it is also the language of commerce, engineering and other sciences such as biology, physics and computing. The BSc in Mathematics program is unique among all universities in the territory. It offers seven tracks: Program Highlights • Applied Mathematics Track • Computer Science Track • Financial and Actuarial Mathematics Track • General Mathematics Track • Pure Mathematics Track • Pure Mathematics (Advanced) Track* • Statistics Track The Pure Mathematics (Advanced) Track is specially designed for mathematically gifted students. Students in this track will study a series of mathematics courses at a deeper level, which better prepares students to pursue postgraduate studies. * Student Sharing I have joined research projects supervised by computer science and math professors and worked alongside postgraduate students. As a sweet bonus, I got the internships opportunities in Indonesia and Hong Kong. Overall, the math program and the university have given me the tools required for my early career, and I only need to utilize them! Extended Major Options Students can opt for an Extended Major in Artificial Intelligence (AI) or Digital Media and Creative Arts (DMCA). Extended Major is not a standalone major, but is adhered to a certain majors as expanded choices, enabling students to keep abreast of emerging technology and innovation that are shaping our society in a multi-faceted way. On top of expertise in mathematics or physics, the students with an Extended Major will acquire multidimensional visions and knowledge of emerging technologies (AI or DMCA), and can apply innovative technological skills to solve real-world problems in the area of their expertise. Upon fulfilment of the curriculum requirement, the students will be awarded one of the following degrees: • BSc in Mathematics with an Extended Major in Artificial Intelligence • BSc in Mathematics with an Extended Major in Digital Media and Creative Arts • BSc in Physics with an Extended Major in Artificial Intelligence 1.3. Transition Maps 13 1.3. Transition Maps Let M⊂R3 be a regular surface, andFα(u1,u2) : Uα →MandFβ(v1,v2) : Uβ →Mbe two smooth local parametrizations of Mwith overlapping images, i.e. W:=Fα(Uα) ∩ Fβ(Uβ) =∅. Under this set-up, it makes sense to define the maps F−1 β ◦Fα andF−1 α ◦Fβ. However, we need to shrink their domains so as to guarantee they are well-defined. Precisely: (F−1 β ◦Fα) : F−1 α (W) →F−1 β (W) (F−1 α ◦Fβ) : F−1 β (W) →F−1 α (W) Note that F−1 α (W) and F−1 β (W) are open subsets of Uα and Uβ respectively. The map F−1 β ◦Fα describes a relation between two sets of coordinates (u1,u2) and(v1,v2) of M. In other words, one can regardF−1 β ◦Fα as a change-of-coordinates, or transition map and we can write: F−1 β ◦Fα(u1,u2)=(v1(u1,u2), v2(u1,u2)). 12 13