Dr I-Hsun NI, Senior Lecturer
DEPARTMENT OF MATHEMATICS
IV. Statistics Option Core courses
MATH 101 Multivariable Calculus MATH 11 1 Linear Algebra Required courses
MATH 201 MATH 241 MATH 243 MATH 301 (1) MATH 311 MATH 341 MATH 342 MATH 343 COMP 102 Elective courses
Elective WDes
Introduction to Analysis Probability
Statistical Inference Real Analysis Algebra I
Stochastic Modelling Regression Analysis Data Analysis
Computer and Programming Fundamentals I
Minimum Minimum no. of courses total credits
(2) MATH Mathematics elective 4 16
ENGG Engineering elective 1 3
(3) FREE Free elective 5 15
(4) H&SS Humanities and Social Science elective 4 12 (5) SB&M Business and Management elective 2 6 Additional requirement
(6) LANG 001 Language Skills Enhancement l 10-3-1 :O]
Notes:
(1) The course may be replaced by MATH 303, MATH 304 or MATH 321.
(2) MATH 231 is a recommended elective; however, it may be replaced by another approved MATH elective. For the remaining MATH electives, two must be statistics courses chosen from MATH 346, MATH 347, MATH 541, MATH 542, MATH 543, MATH 544, MATH 545, MATH 546, MATH 645, ISMT 355, ISMT 359 or ISMT 659.
Department of Mathematics
(3) At leastthree of thesecourses must be non-mathematics electives totalling at least 12 credits.
(4) Of these courses, at least one course in Humanities and one in Social Science are required.
(5) ECON 11011 1111 91 is a recommended elective. Students entering with grade B or above in AL Economics take ECON 191; those with grades C to E in AL Economics take ECON 11 1 ; all other students can choose to take either ECON 110orECON 111.
(6) Students admitted without grade C or above in AS Use of English will be required to take and pass this course during the first semester of attendance.
A minimum of 100 credits is required for the BSc programme in Mathematics - -Statistics Option. Students must take additional course(s) andlor elective(s) of higher- than-required credit value to meet this minimum total of 100 credits.
Recommended Pattern of Study for the Statistics Option 1 st year Fall C MATH 101, MATH 11 1 ;
R MATH 241;
E ECON111;
0 LANG 001 (Total: 16 credits)
Spring R MATH 201, MATH 243, COMP 102;
E ECON 112, H&SS (Total: 18 credits) 2nd year Fall R MATH 301, MATH 342;
E ENGG, FREE (non-math), H&SS (Total: 17 credits) Spring R MATH 341, MATH 343;
E MATH 231, FREE (non-math), H&SS (Total: 18 credits) 3rd year Fall R MATH 31 1;
E MATH (statistics), FREE, FREE (non-math), H&SS
(Total: 17 credits) Spring E MATH (statistics), MATH, FREE, FREE (non-math)
(Total: 14 credits) C = core course; R = required course; E = elective course; 0 = other course
Minimum Basic Graduation Requirements for the BSc Programme in Mathematics
Students will be awarded the BSc degree in Mathematics without an option designation if they fail to meet the requirements specifiedforthe option in which they are officially registered, but have completed all of the following requirements satisfactorily:
(1) a minimum of 36 credits in non-Mathematics courses; these credits must include:
(a) a minimum of 12 credits in Humanities and Social Science courses, with at least one course in Humanities and one in Social Science; and
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(b) a minimum of 6 credits in Engineering courses, and 6 credits in Business and Management courses;
(2) a minimum of 10 courses in Mathematics which must include:
(a) MATH 101, MATH 11 1, MATH 201 and MATH 301 ; (b) one of MATH 303, MATH 304, MATH 31 1 or MATH 321 ; and (c) at least two more MATH courses at 300-level or higher;
(3) a minimum total of 100 credits.
Postgraduate Programmes and Research
Major research areas planned include almost all the major pure and applied mathematical branches. At present five major areas of research are emphasised:
analysis, algebra and geometry, scientificcomputation, fluid mechanics, and probability and statistics.
1. Analysis
Analysis includes harmonicanalysis, real analysis, complex analysis, functional analysis, differential equations and other related fields, with emphasis on complex analysis. Most activities in applicable mathematics are in the area of analysis or related to analysis. The study of theoretical science and engineering relies heavily on applied analysis.
2. Algebra and geometry
Algebra and geometry include number theory, Lie theory, algebraic and geo- metric topology, and algebraic geometry. Interactions between various areas are emphasised. Current research includes linear forms in p-adic logarithms and the applications, self-dual codes and lattices, Lie algebras and vertex oDerator alaebras, algebraic K-theory, intersection homology, low dimensional topology, Goup actions on manifolds, stratified spaces, stable vector bundles over algebraic surfaces and Donaldson theory, fundamental groups of algebraic varieties, and knot theory.
3. Scientific computation
Over the past two decades, scientific computation has become an independent approach to studying science and technology, complementing the long-estab- lished theoretical and experimental approaches. With the advent of parallel computers and development of new algorithms, it plays an even more important role in future. Scientific computation in the Mathematics Department means not only large scale computation of solutions to problems in science, engineering and business and management but also developing algorithms that are reliable, accurate and economical. Current research areas include shock-capturing schemes, parallel algorithms, symbolic computation, numerical linear algebra, numerical solutions to elliptic and hyperbolic partial differential equations, and computational quantum mechanics:
here
are also joint research projects with other departments in the University and other institutions in and outside Hong Kong.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
Department of Mathematics
mathematics. Current research areas include two-phase flow, water wave motion, fluid dynamics of typhoon, fluid dynamics of combustion, rotating flow, high speed flow, bubble dynamics, flow instability, bifurcation, chaos and turbulence.
5. Probability and Statistics
Probability and statistics are subjects that study random phenomena. Random- ness arisesfrequently in diverse disciplines, rangingfrom economics to biology.
Probability and statistics have direct applications in fields such as econometrics, finance, medical sciences and control engineering. Current faculty research interests include time series; spatial statistics; linear models and stochastic control, calculus, and differential equations.
Master of Science (MSc) Programme in Mathematics
The MSc programme emphasises course work to strengthen students' general background in mathematics and mathematical sciences. It can be a terminal dearee or a preliminary degree leading to the PhD, and requires a research project in add%ion 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 credits 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 : 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) Programme 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 ora 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 must submit their theses to the Department and, subsequently, to present and defend them. A student who has performed unsatisfactorily will be asked to re-submit the thesis. 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 normally at least 18 are mathematics courses at the postgraduate level.
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Research : 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) Programme in Mathematics
The aim of the PhD degree programme is to prepare students to become research scholars in an academic or industrial environment. The programme provides a broad background in mathematics and mathematical sciences, and 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. The doctoral thesis must be an original contribution to the field. 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: undertake course work and conduct thesis research. They are also encouraaed to teach a course at the undergraduate level. The passing standard in a graded course is C and the overall averagemust be B or above: students must pass
5
comprehensive/qualifying examination-and, in the final stage of the programme, Dresent and defend theirtheses after submitting them to the Department. Astudent who has performed unsatisfactorily will be asked t6 re-submit the thesis. The result of the second attempt of the thesis defence will be either Pass or Fail.Specific programme requirements are:
1 . 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.
2. Candidacy examinations:
a. Pure Mathematics
To become PhD candidates, students must first pass a qualifying oral examination (normally no later than by the end of the second year) on two of the three subject areas: analysis, algebra, and geometry; and at a later date another oral examination on a major area excluding the two areas covered in the first oral examination.
b. 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 theoretical 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.
Department of Mathematics
3. Thesis : Original research work and its successful presentation and defence before a thesis examination committee.
Faculty Research Interests
Professor Din-Yu HSIEH, Acting Head of Department Waves and stability, asymptotic methods, two-phase flows.
Professor Grafton Wai-How HUI, Associate Dean of Science
Theoretical and computational fluid dynamics; nonlinear water wave theory; nonlinear partial differential equations.
Professor Ronnie LEE
Low-dimensional topology, guage theory, cohomology of discrete groups.
Professor Chung-Chun YANG
Complex analysis, value-distribution theory.
Professor V. I. ARNOLD, Visiting Professor
Dynamical systems, topology, singularities, simplectic geometry, partial differential equations.
Dr Ngai-Hang CHAN, Reader
Time series, spatial statistics, econometrics, asymptotic inference.
Dr Vladimir A. VLADIMIROV, Reader
Fluid dynamics, rotating flow, hydrodynamic stability.
Dr Kun-Rui YU, Reader
Transcendental number theory, diophantine approximations.
Dr Kwing-Lam CHAN, Senior Lecturer
Computational physics, fluid dynamics, atmospheric dynamics, astrophysics, cosmol- ogy.
Dr Yue-Kuen KWOK, Senior Lecturer
Computational fluid dynamics, numerical analysis, geophysics Dr Der-Chen E. CHANG, Visiting Senior Lecturer
Fourier analysis on Euclidean spaces, and several complex variables.
Dr Yue-Fan DENG, Visiting Senior Lecturer
3D parallel fluid dynamics computation, parallel computational electromagnetics, number theory problems.
Dr Gopal K. BASAK, Assistant Professor
Asymptotics of Markov processes, stochastic differential equation, stochastic model- ling, classification, estimation, probability.
Dr Jeffrey R. CHASNOV, Assistant Professor
Turbulence simulation and theory, nonlinear dynamics, scientific computation.
School of Science DeDartment o f Mathematics
Dr Bei-Fang CHEN, Assistant Professor
Discrete mathematics, combinatorics, geometric probability, computational geometry.
Dr Kani CHEN, Assistant Professor
Survival analysis, bootstrap, sequential analysis, empirical process, stochastic model- ling, missing data and EM algorithm.
Dr Yik-Man CHIANG, Lecturer
Ordinary differential equation in the Complex plane, geometric function theory.
Dr Jimmy Chi-Hung FUNG, Lecturer
Computational fluid dynamics, turbulence, environmental studies.
Dr Walter G. GALL, Assistant Professor
Bifurcation, scientific computation, symmetry and nonlinear stability.
Dr Guo-Qiang GE, Assistant Professor Algorithms, number theory.
Dr Ji-Shan HU, Lecturer Applied analysis.
Dr Jing-Song HUANG, Lecturer Representation theory, Lie theory.
Dr Bing-Yi JING, Lecturer
Bootstrap analysis, blockwise bootstrap, Kernel density estimation, edgeworth and saddlepoint approximations, empirical likelihood, nonparametric tilting, linear models, robust statistics, permutation and randomisation tests.
Dr Bao-Qin LI, Lecturer
Complex analysis and harmonic analysis.
Dr Kin-Yin LI, Assistant Professor
Complex function theory, Hilbert space operator theory, functional analysis.
Dr Wei-Ping LI, Lecturer Algebraic geonetry.
Dr Shiu-Hong LUI, Assistant Professor Bifurcation theory, numerical analysis.
Dr Jian-Min MAO, Assistant Professor
Nonlinear dynamics, chaotic behaviour, Hamiltonian bifurcation theory; mathematical physics; scientific computation.
Dr Guo-Wu MENG, Assistant Professor Algebraic topology, differential topology.
Dr Mo MU, Assistant Professor
Numerical analysis, parallel computing, numerical solution to PDEs, numerical linear algebra, mathematical software.
Dr Tai-Man TANG, Lecturer
Partial differential equations, functional analysis.
Dr Charles H. TONG, Assistant Professor
Numerical linear algebra, numerical methods for partial differential equations, parallel numerical algorithms, scientific computing in general.
Dr Allanus Hak-Man TSOI, Assistant Professor
Stochastic analysis, point processes, stochastic filtering and control, probability in finance.
Dr Rongguang WANG, Lecturer
Differential geometry, partial differential equations, topology.
Dr Xiao-Ping WANG, Lecturer
Nonlinear partial differential equations, computational and applied mathematics.
Dr Man-Yu WONG, Assistant Professor
Statistical inference, generalised linear model, biological statistics, medical statistics.
Dr Li-Xin WU, Lecturer
Numerical analysis, computational fluid dynamics.
Dr Xiao-Ping XU, Lecturer
Self-dual codes and lattices, Lie algebras and vertex operator algebras, discrete groups, Hamiltonian operators and related algebraic structures. Yang-Baxter equa- tions.
Dr Min YAN, Lecturer
Algebraic topology, geometric topology.
Dr Yong-Chang ZHU, Lecturer
Infinite dimensional Lie algebras, Hopf algebras and Quantum groups, vertex operator algebras, conformal field theory.
Dr Konstantin I. IL'IN, Research Associate Stability theory, fluid dynamics.
Dr Yuan-Wei QI, Lecturer
Differential equations, scientific computation.
School o f Science Department of Pbysics