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MATHEMATICAL SCIENCES OPTION IN BUSINESS AND MANAGEMENT
4. Fluid mechanics
Fluid mechanics is the study of the motion of liquids and gases with direct application to industry and environmental research. It is particularly rich in nonlinear problems and is a major source of ideas and techniques in applied mathematics. Current research areas include two-phase flow, water wave motion, fluid dynamics of typhoon, high speed flow, bubble dynamics, flow instability, biurcation, chaos and turbulence.
Master of Science (MSc) in Mathematics
The MSc programme emphasises course work to strengthen students' general background in mathematics and mathematical sciences. It can be a terminal degree or a preliminary degree leading to the PhD, and it requires a research project in addition to a programme of courses. The duration of the programme normally ranges from 18 months to three years for full-time studies, and it may be extended to five years for part-time studies.
In fulfilling the degree requirements, students are expected to attend and present seminars, undertake course work and complete an assigned project. The minimum number of credii needed to fulfil the degree requirements is 30, as follows:
Courses: 24 credits in mathematics or related fields, of which at least 18 credits are mathematics courses at the postgraduate level
Research: An approved MSc project (6 credits)
The passing standard in a graded course is C and the overall average obtained must be B or above.
Master of Philosophy (MPhil) in Mathematics
The MPhil programme aims to strengthen students' general background in mathematics, and mathematical sciences, and to expose the student to the environment and scope of mathematical research. It can be a terminal degree or a preliminary degree leading to the PhD, and requires research leading to a thesis as well as a course programme. The duration of the programme normally ranges from 18 months to three years for full-time studies, and may be extended to five years for part-time studies.
Students with a first degree in an area other than mathematics may be required to take additional courses.
In the final stage of the programme, students are required to submit their theses to the Department and, subsequently, to present and defend them. Any student who has performed unsatisfactorily will be asked to re-submit thesis as recommended by the examination committee. The result of the second attempt of the thesis defence will be either Pass or Fail.
Specific programme requirements are :
Courses: 24 credits in mathematics or related fields; of which at least 18 are mathematics courses at the postgraduate level.
Research: An approved MPhil thesis; and presentation and oral defence of the thesis.
The passing standard in a graded course is C and the overall average obtained must be B or above.
Doctor of Philosophy (PhD) in Mathematics
The aim of the PhD degree programme is to prepare students to become research scholars either in an academic or industrial environment. The programme, besides providing broad background in mathematics and mathematical sciences, aims to enable students to do independent and original research. Students have three options from which to choose their major concentration: pure mathematics, applicable mathematics, and mathematical sciences. A doctoral thesis representing an original contribution to the field is a requirement forthe degree. The duration of the programme normally ranges from four to eight years from the first degree, with a reduction of 18 months if a relevant master's degree is earned prior to entering the PhD programme. Students with a first degree in an area other than mathematics may be required to take additional courses.
In fulfilling the degree requirements, students are expected to attend and present seminars, undertakecourseworkandconductthesis research. They are also encouraged to teach a course at the undergraduate level. The passing standard in a graded course is C and the overall average must be B or above. Students must pass a comprehensive1
School of Science
qualifying examination as specified below. In the final stage of the programme, students are required to submit their theses to the Department and, subsequently, to present and defend them. Any student who has performed unsatisfactorily will be asked to re-submit the thesis as recommended by the examination committee. The result of the second attempt of the thesis defence will be either Pass or Fail.
Specific programme requirements are :
Courses: 36 credits in mathematics or related fields, of which at least 24 credits are mathematics courses at the postgraduate level. For students from other institutions with an MSc or MPhil degree, up to 18 credits can be transferred to fulfil the credit requirements, subject to departmental approval.
Candidacy examinations:
1. Pure Mathematics
To become PhD candidates, students must first pass an oral qualifying examina- tion (normally no later than by the end of the second year) on two of the three subject areas: analysis, algebra, and geometry; and then at a later date, another oral examination on a major area excluding the two areas in the first oral examination.
2. Mathematical Sciences and Applicable Mathematics
To become PhD candidates, students must submit a thesis proposal, and pass an oral examination on the thesis proposal and two minor subjects. For mathematical sciences students, one of the minor subjects should be in theoreti- cal mathematics. For applicable mathematics students, one of the minor subjects should be in science. The oral examination should normally take place by the first half of the third year.
Thesis:
Original research work and its successful presentation and defence before a thesis examination committee.
Faculty Research interests
Professor Din-Yu HSIEH, Head of Depaflment
Waves and stability, asymptotic methods, two-phase flows.
School o f Science
Professor Grafton Wai-How HUI
Theoretical and computational fluid dynamics; nonlinear water wave theory;
nonlinear partial differential equations.
Professor Chung-Chun YANG
Complex analysis, value-distribution theory.
Professor Wu-Chung HSIANG, Adjunct Professor
Algebraic topology, differential topology, algebraic K-theory.
Professor James Sai-Wing WONG, Adjunct Professor Ordinary differential equations.
Professor Wing-Hung WONG, Visiting Professor
Statistical computation, image rectoration, semiparametric models, sliced re- gression.
Dr John D. BUCKMASTER, Reader
Combustion theory, fluid dynamics, asymptotics.
Dr Ngai-Hang CHAN, Reader
Time series, spatial statistics, econometrics, asymptotic inference.
Dr Kunrui YU, Reader
Transcendental number theory, diophantine approximations.
Dr Der-Chen E. CHANG, Visiting Senior Lecturer
Fourier Analysis on Euclidean spaces, and several complex variables.
School of Science
Dr Gopal K. BASAK, Lecturer
Asymptotics of Markov processes, Stochastic differential equation, Stochastic modelling, classification, estimation.
Dr Jeffrey R. CHASNOV, Lecturer
Numerical simulation of turbulent flow; homogeneous turbulence; stably-strati- fied flows; rotating fluids; convection; large-eddy simulation; parallel computation.
Dr Bei-Fang CHEN, Lecturer
Discrete mathematics, combinatories, probability.
Dr Yik-Man CHIANG, Lecturer
Ordinary differential equation in the Complex plane, geometric function theory.
Dr Kwai-Man FAN, Lecturer Algebraic geometry.
Dr Jimmy Chi-Hung FUNG, Lecturer
Computational fluid dynamics, turbulence, environmental studies.
Dr Walter G. GALL, Lecturer
Bifurcation, scientific computation.
Dr Guo-Qiang GE, Lecturer Algorithms, number theory.
Dr Bi-Zhong HU, Lecturer
Compact polyhedra with nonpositive curvature.
School of Science
Dr Ji-Shan HU, Lecturer Applied analysis.
Dr Jing-Song HUANG, Lecturer
Representation theory, Lie theory.
Dr Yue-Kuen KWOK, Lecturer
Computational fluid dynamics, numerical analysis, geophysics.
Dr Kin-Yin LI, Lecturer
Complex function theory, Hilbert space operator theory, functional analysis.
Dr Wei-Ping LI, Lecturer Algebraic geometry.
Dr Shiu-Hong LUI, Lecturer
Bifurcation theory, numerical analysis.
Dr Jian-Min MAO, Lecturer
Nonlinear dynamics, chaotic behaviour, Hamiltonian bifurcation theory; math- ematical physics; scientific computation.
Dr Guo-Wu MENG, Lecturer
Algebraic topology, differential topology.
Dr Mo MU, Lecturer
Numerical analysis, parallel computing, numerical solution to PDEs, numerical linear algebra, mathematical software.
School of Science
Dr Yuan-Wei QI, Lecturer
Differential equations, scientific computation.
Dr Tai-Man TANG, Lecturer
Partial differential equations, functional analysis.
Dr Charles H. TONG, Lecturer
Numerical linear algebra, numerical methods for partial differential equations, parallel numerical algorithms, scientific computing in general.
Dr Allanus Hak-Man TSOI, Lecturer
Stochastic analysis, stochastic differential geometry.
Dr Xiao-Ping WANG, Lecturer
Nonlinear partial differential equations, computational and applied mathematics.
Dr Man-Yu WONG, Lecturer
Statistical inference, generalised linear model, biological statistics, medical statistics.
Dr Li-Xin Wu, Lecturer
Numerical analysis, computational fluid dynamics.
Dr Xiao-Ping XU, Lecturer
Selfdual codes and lattices, Lie algebras and vertex operator algebras.
Dr Min YAN, Lecturer
Algebraic topology, geometric topology.
School of Science
Dr Yue-Fan DENG, Visiting Lecturer
3D parallel fluid dynamics computation, parallel computational electromagnetics, number theory problems.
Dr Delin CHU, Visiting Scholar
Parallel algorithms, computational fluid dynamics.