CENTRAL AND INTERDEPARTMENTAL RESEARCH UNITS
LANGUAGE CENTRE
LANG 001 Language Skills Enhancement I [0-3-1 :O]
A general integrated-skill course in English for academic purposes. A study of the language of description, definition, temporal and sequential relationships, comparison and contrast, classification, cause and effect, and argumentation. Graded either P, IP or F.
LANG 002 Language Skills Enhancement II [O-3-1:0]
A general integrated-skill course in English for academic purposes, revising and supplementing the language study areas of LANG 001, with a special emphasis on oral presentation and self-access learning. Graded either P, IP or F.
LANG 003 Language Skills Enhancement Ill [O-3-1:0]
A general integrated-skill course in English for academic purposes, further revising and supplementing the language study areas of LANG 001 and LANG 002. Graded either P or F.
LANG 01 1 Putonghua I [O-3-1 :O]
Basic knowledge of Putonghua phonology in comparison with Cantonese phonology;
extraction of salient points from Putonghua discourse; effective conversation in Putonghua. Students must be able to read Chinese characters. Graded either P or F.
LANG 012 Putonghua II [O-3-1 -:O]
Comparison of Putonghua phonology with Cantonese phonology; understanding the gist of Putonghua discourse in various contexts; carrying out extended conversations in Putonghua. Graded either P or F. Prerequisite: LANG 01 1
LANG 013 Putonghua Ill [O-3-1:0]
Expert mastery of Putonghua phonology in comparison with Cantonese phonology; full comprehension of Putonghua discourse in various contexts; conversation and presen- tations in Putonghua. Graded either P or F. Prerequisite: LANG 01 2
LANG 101 Business Communication [O-3431
Restricted to students in the School of Business and Management. Focuses on the processes and skills of effective oral presentation, negotiation, and report writing in business situations where English is the medium of communication.
LANG 103 Technical Communication [0-3-0:3]
Restricted to students from certain departments in the Schools of Engineering and Science. Focuses on developing the skills of practising oral and written reports relevant to the students' various disciplines.
Undergraduate Course Descriptions
LANG 1 1 1 Basic Business Putonghua [O-3-1 :O]
Restricted to students in the School of Business and Management. Focuses on communicative skills required in business situations such as making appointments, participating in meetings and attending recruitment interviews. Students must be able ~ - -
to read Chinese characters.
LANG 112 Advanced Business Putonghua [O-3-1 :O]
Restricted to students in the School of Business and Management. Focuses on the Putonghua communicative skills required in linguistically demanding business situa- tions such as conducting meetings, giving interviews, negotiations and making presen- tations. Prerequisite: LANG 11 1
LANG 204 Advanced English Reading-Writing for Business [O-3-1:2]
Students
For SBM students only. Focuses on developing reading and writing skills relevant to the study of business. The material used will draw heavily on business magazines. Can be taken concurrently with LANG 205. Grades will be awarded as Pass or Fail.
LANG 205 Advanced English Reading-Speaking for Business [O-3-1:2]
Students
For SBM students only. Focuses on developing reading and speaking skills in the context of business-related topics. The material used will draw heavilv on ~ublications related to business. Can be taken concurrently with LANG 204. ~ r a d e s will'be awarded as Pass or Fail.
LANG 301 Oral Business Communication i n Putonghua [I -2-1 :3]
Restricted to MBA students. Focuses on Putonghua phonology, the processes and skills of effective oral presentation, negotiation and interviews in business situations.
DEPARTMENT OF MARKETING
MARK 212 Marketing Management [4-0-0:4]
Introduction to marketing from the perspective of the decision-maker; controllable variables (product, price, promotion and distribution), uncontrollable variables (compe- tition, law, society, technology, and economy), consumer behaviour and marketing research.
MARK 222 Marketina Research rd-n-n-AI L . "
".-,
Basic research tools aniprocedures used in marketing research, and strategic uses of marketing research information in managerial decision making. Prerequisite: MARK 212
MARK 241 Promotion and Advertising Management [4-0-0:4]
Major aspects of promotion, with emphasis on advertising: setting of advertising objectives, strategies, tactics, choice of media, budget determination and measuring advertising effectiveness. Prerequisite: MARK 21 2
MARK 242 Consumer Behaviour [4-0-0:4]
Psychological concepts such as perception, learning and motivation, sociological concepts such as reference groups, family and culture and theories of purchase decision processes underlying consumer buying behaviour. Prerequisite: MARK 212
Undergraduate Course Descriptions
MARK 243 Global Marketing [4-0-0:4]
Understanding the formulation of intemationaVmultinationa1 marketing strategy; factors influencing international trade, assessment of market potential, threats and opportuni- ties in the international market environment, global marketing activities. Prerequisite: - MARK 21 2
MARK 321 Strategic Marketing [4-0-0:4]
Developing a comprehensive and integrated framework for directing and managing the marketing functions of a company; methods to analyse marketing opportunities, assess competitive advantages and forecast market changes. Prerequisites: MARK 212,222, and 242
MARK 329 Special Topics [2-4 credits]
Selected topics in current marketing thought and practices; topics vary from semester to semester. Prerequisite: MARK 212
DEPARTMENT OF MATHEMATICS
MATH 001 Calculus I [3-1-0:4]
Calculus of one variable: limits and continuity; differentiation; L'Hospital's rule; maxima and minima; implicit differentiation; elementary transcendental functions; antiderivatives and integrals; techniques of integration; improper integrals. Exc1usions:C or above in either AL Pure Mathematics or AL Applied Mathematics Prerequisite: HKCEE Additional Mathematics, or AS ~ a t h e m a t i k and Statistics, or AS
tr plied
Mathematics, or grade D or E in either AL Applied Mathematics or AL Pure MathematicsMATH 002 Calculus II [3-1-0:4]
Infinite series and Taylor's series. Calculus of several variables: parametric curves and vectors: oartial differentiation: aradients: constrained maximum/minimum problems;
multiple integrals; line and &+ace integrals; the Green's, divergence, and Stokes' theorems. Exclusions: MATH 100, MATH 101 Prerequisite: MATH 001 or AL Applied
Mathematics or AL Pure Mathematics
MATH 005 Algebra and Calculus I [3-1441
Review of as~ects of alaebra and analvtic aeometrv essential to the study of calculus.
lntroduction of basic concepts of functiok, limiis, continuity and derhatives with applications to management; social science and biomedical science. Applications to odimisation. Exclusions: C or better in HKCEE Additional Mathematics: AS Mathemat- ids and Statistics; AL Pure Mathematics; MATH 001
Reference: Geoffrey C. Berresford, Calculus with Applications to the Management, Social, Behaviorial, and Biomedical Sciences
MATH 006 Algebra and Calculus II [3-1-0:4]
Continuation of
MATH
005: an introduction to elementary integration theory and related techniaues. functions of several variables and partial derivatives with applications.~ x c l u s ~ o n s ~ C or better in HKCEE Additional 'Mathematics; AS
at he ma tics
and Statistics; AL Pure Mathematics; MATH 001; MATH 002 Prerequisite: MATH 005 Reference: As for MATH 005MATH 100 Introduction to Multivariable Calculus [2-1-0:2]
Differentiation in sewera1 variables, with applications in approximation, maximum and minimum and geometry. Integration in several variables, with application to physics and
Underwaduate Course DescriDtions
vector analysis. Exclusions: MATH 002, MATH 101 Prerequisite:MATH 001 or AL Pure Mathematics or AL Applied Mathematics
Reference: Thomas and Finney, Calculus and Analytic Geometry
MATH 101 Multivariable Calculus [3-1-0:4]
Sequences, series, gradients, chain rule. Extrema, Lagrange multipliers; line 'ntegrals, multiple integrals. Green's theorem, Stroke's theorem, divergence theorem; change of variables. ~xclusions: MATH 002, MATH 100 prerequisite: MATH 001 or AL pure Mathematics or AL Applied Mathematics
Reference: Lang, Calculus of Several Variables
MATH 110 Concepts in Mathematics [2-0-0:2]
Expository lectures and discussion on basic mathematical concepts and ideas, histori- cal developments in various areas of mathematics, and selected trends and advances in mathematical sciences. Graded either P or F. Prerequisite: MATH 002 or AL Mathematics
MATH 11 1 Linear Algebra [3-1-0:4]
Matrix; system of linear equations; vector space; linear independence; linear transfor- mation; determinant; eigenvector and eigenvalue; inner product; orthogonality; sym- metric matrix; quadratic form. Exclusions: MATH 1 13, MATH 152 Prerequisite: MATH 001 or AL Pure Mathematics or AL Applied Mathematics
References: D.C. Lay, Linear Algebra and its Applications, and S.H. Friedberg, A.J. lnsel and L.E. Spence, Linear Algebra
MATH 113 Introduction to Linear Algebra [2-1-0:2]
Systems of linear equations; vector spaces; linear transofrmations; matrix representa- tion of linear transformations; linear operators, eigenvalues and eigenvectorsi similarity invariants and canonical forms. Exclusions: MATH 1 1 1. MATH 152 Prereauisite:MATH 001 or AL Pure Mathematics or AL Applied ~ a t h e m a i c s
Reference: A. C. Baker and H. L. Porteous, LinearAlgebra and Differential Equations
MATH 132 Discrete Structures [3-1-0:4]
Logic: propositions, axiomatisation of propositional calculus, deduction theorem, com- pleteness and soundness. Combinatorics: permutations and combinations, generating functions. Set theory: basic operations on sets, relations, countable and uncountable sets. Prerequisite: MATH 001 or AL Pure Mathematics or AL Applied Mathematics MATH 150 Introduction to Ordinary Differential Equations [2-1-0:2]
First order equations; second order equations; Laplace transform method; numerical solution of initial value problems; boundary-value problems. Exclusion: MATH 151 Prerequisite: MATH 001 or AL Pure Mathematics or AL Applied Mathematics Reference: Boyce and DiPrima, Elementary Differential Equations and Boundary
Value Problems
MATH 151 Differential Equations and Applications [3-1-0:4]
First and second order differential equations, higher order equations, Laplace transform method; series solutions; Sturm-Liouville equation; Bessel functions and Legendre polynomials; numerical solution of initial and boundary value problems. Exclusion:
MATH 150 Prerequisite: MATH 001 or AL Pure Mathematics or ALApplied Mathematics Reference: Boyce and DiPrima, Elementary Differential Equations and Boundary
Value Problems
Undergraduate Course Descriptions
MATH 152 Applied Linear Algebra and Differential Equations [3-1-0:4]
Linear dependence; norms; solution of linear systems; orthogonal projections;
eigenvalues and eigenvectors; singular value decomposition; iterative solutions; sys- tems of first order linear equations; partial differential equations and Fourier series.
Exclusions: MATH 1 1 1, MATH 1 13 Prerequisite: MATH 151
References: Ben Noble and James Daniel, Applied Linear Algebra, and
Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems
MATH 201 Introduction t o Analysis [3-1-0:4]
[Previous Course Code: MATH 1021 Limits; sequences and series of numbers;
continuity; differentiation; Riemann integral; sequence and series of functions; uniform convergence. Prerequisite: MATH 101
Reference: Battle and Sherbert, lntroduction to Real Analysis
MATH 225 Mathematical Logic [3-1441
Propositional and predicate calculus; consequence and deduction; truth and satisfac- tion: Godel com~leteness theorem: Lowenheim-Skolem theorem; Boolean algebra;
axidmatic theories. Prerequisite: MATH 11 1 MATH 230 lntroduction t o Numerical Methods
Computer arithmetric; matrix computation; interpolation and approximation; numerical intearation: solution of nonlinear eauations. Exclusion: MATH 231 Prerequisite: MATH
~ ~ ~ " O ~ M A T H 1 1 3 o r ~ ~ ~ ~ 152 '
Reference: K. E. Atkinson, An lntroduction to Numerical Analysis
MATH 231 Numerical Analysis [3-1-0:4]
Basic numerical analysis, including stability of computation, linearsystems, eigenvalues and eigenvectors, nonlinear equations, interpolation and approximation, numerical integration and solution of ordinary differential equations, optimisation. Fortran may also be taught. Exclusion: MATH 230 Prerequisite: MATH 11 1 or MATH 152 Reference: Kahaner, Moler and Nash, Numerical Methods and Software
MATH 241 Probability [3-1-0:4]
Sample spaces; conditional probability; random variables; independence; discrete and continuous distributions; expectation; correlation; moment generating function; law of large numbers and limit theorems. Corequisite: MATH 10011 01
Reference: G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes
MATH 243 Statistical Inference [3-1-0:4]
Distributions of functions of random variables; sampling theory; order statistics; limiting distributions; point estimation; confidence intervals; hypothesis testing; non-parametric methods. Prerequisite: MATH 241
Reference: John Rice, Mathematical Statistics and Data Analysis
MATH 244 Applied Statistics [3-1441
A systematic introduction to statistical inference, including the necessary probabilistic background, point and interval estimation, hypothesis testing. Prerequisite:MATH 001 or AL Pure Mathematics
Reference: Hines and Montgomery, lntroduction to Probability and Statistics in Engineering and Management Science
316
Undergraduate Course Descriptions
MATH 251 Introduction to Complex Variables [2-1-0:2]
Analvtic functions; Cauchy-Riemann relations; Cauchv's theorem; Taylor and Laurent series; residuesand applications; argument and maximum modulus principles; conformal ma~oinas:
. .
- . Schwarz-Christoffel transoformations: intearal re~resentation of harmonic functions; two-dimensional flows. Exclusions: MATH-304, MATH 351 Prerequisite:MATH 100 or MATH 150 or MATH 151
Reference: E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis
MATH 252 Introduction t o Partial Differential Equations [2-1-0:2]
Derivations of heat, potential and wave equations; initial and boundary value problems;
se~aration of variables; Fourier series; Dirichlet and Neumann problems: Laplace's e&ation; harmonic functions. ~xclusion: MATH 352 ~ r e r e ~ u i s i t e : ' ~ ~ ~ ~ 150 or MATH 151
Reference: W. Strauss, Partial Differential Equations: An lntroduction
MATH 281 Introduction to Operations Research [3-1-0:4]
Linear programming; simplex method; duality theory; network analysis; dynamic pro- gramming; game theory; integer programming; stochastic processes; queueing theory;
inventory theory; forecasting; decision analysis. Prerequisite: MATH 241 or MATH 244
~eference: Hiller and ~ieberman, lntroduction to operations Research
MATH 300 Special Topics [I -4 credit@)]
Focuses on a coherent collection of topics selected from a particular branch of mathematics. A student may repeat the course for credit if the topics studied are different each time.
MATH 301 Real Analysis [3-1-0:4]
Topology of Euclidean space, functions of several variables, implicit and inverse function theorem, Lebesgue measure and integral on the real line. Prerequisite: MATH 20 1
References: Royden, Real Analysis and
Rudin, Principles of Mathematical Analysis
MATH 302 Mathematical Analysis [3-1-0:4]
Advanced topics in mathematical analysis, which may include approximation theory, Fourier series, Fourier transform and special functions. Additional topics chosen by the instructor.
MATH 303 Theory of Ordinary Differential Equations [3-1-0:4]
[Previous Course Code: MATH 1031 Existence and uniqueness theorems of ordinary differential equations; theory of linear systems; stability theory; study of singularities;
boundary value problems. ~rere~uisites: MATH 101 and MATH 11
i -
Reference: Hirsch and Smale, Differential Equations, DynamicalSystems and Linear Algebra
MATH 304 Complex Analysis [3-1-0:4]
[Previous Course Code: MATH 2041 Complex differentiability; Cauchy-Riemann equations; contour integrals, Cauchy theory and consequences; power series repre- sentation; isolated singularities and Laurent series; residue theorem; conformal map- pings. Exclusions: MATH 251, MATH 351 Prerequisites: MATH 101 and MATH 201 References: Bak and Newman, Complex Analysis,
Lang, Complex Analysis, and Ahlfors, Complex Anlaysis
Undergraduate Course Desrriptions
MATH 305 Introduction t o Functional Analysis [3-1441 Normed space; inner product space; topological vector spaces; closed graph theorem;
Hahn-Banach theorem; principle of uniform boundedness; LF space; elementary Banach space theory; contraction principle and its applications to differential and integral equations and numerical analysis. Prerequisites: MATH 301 and MATH 302 Reference: G.F. Simmons, lntroduction to Topology and Modern Analysis
MATH 306 Partial Differential Equations 13-1 -0:4]
Classification of oartial differential eauations: first order eauations: second order linear equations; ~reeil's functions; maximlm prindip~es; characieristicsf Riemann's method;
well-posed problems. Prerequisites: MATH 101 and MATH 11 1 Reference: Copson, Partial Differential Equations
MATH 307 Dynamical Systems 13-1 -0:4]
Modern development of dynamical systems; Hamiltonian systems; dissipative systems;
bifurcations: stranae attractors: chaoticsvstems: fractals; Hausdorff dimension; Lyapunov - . exponents. ' prerequisites: MATH 151 -and MATH 301
MATH 308 Mathematical Theory of Fluid Dynamics 13-1 -0:4]
Lagrangian and Eulerian methods of description; Euler equations, Navier-Stokes equations; potential flow; boundary layer theory; compressible flow, shock and expan- sion waves; the Riemann problem. Exclusions: MECH 322, ClVL 151, ClVL 252 Prerequisites: MATH 304 or MATH 351 ; and MATH 306 or MATH 352
MATH 31 1 Algebra I [3-1-0:4]
Polynomials; Jordan canonical form, minimal polynomials, rational canonical form;
equivalence relation; group, coset, group action; introduction to rings and fields.
Prerequisite: MATH 1 1 1
Reference: S.H. Friedberg, A.J. lnsel and L.E. Spence, Linear Algebra, and J.B. Fraleigh, A First Course in Abstract Algebra
MATH 312 Algebra II [3-1-0:4]
Sylow theorem, finitely generated abelian group, composition series; integral domain, ideals, principal ideal domain, unique factorization; modules; field extension, ruler and compass, finite fields, Galois group. Prerequisite: MATH 31 1
References: J.B. Fraleigh, A First Course in Abstract Algebra, and I.N. Herstein, Topics in Algebra
MATH 315 Number Theory and Applications [3-1-0:4]
Prime numbers; unique factorisation; modular arithmetic; quadratic number fields; finite fields; p-adic numbers; coding theory; computational complexity. Prerequisite: MATH 31 1
References: Ireland and Rosen, A Classical lntroduction to Modern Number Theory, and
Niven, Euckerman, Montgomery, An lntroduction to the Theory of Num- bers
MATH 321 Differential Geometry [3-1-0:4]
Curve theory; curvature and torsion, Frenet-Serret frame; surface theory: Weingarten map, first and second fundamental forms, curvatures, Gaussian map, ruled surface, minimal surface; instrinsic geometry: Theorema Egregium, Coddazi-Mainardi equa- tions, parallel transport, geodesics, exponential map, Gauss-Bonnet theorem. Prereq- uisite: MATH 101
Reference: M.P. do Carmo, Differential Geometry of Curves and Surfaces
Underpraduate Course DescriDtions
MATH 323 Topology [3-1-0:4]
Euler number; invariants and classification; topology of Euclidean spaces; topological space; continuous map; metric space; connectedness and compactness; Tietze exten- sion theorem; covering space; fundamental group. Prerequisites: MATH 101 and MATH 11 1
References: M.A. Armstrong, Basic Topology and J.R. Mundres, Topology - A First Course
MATH 325 Algebraic Topology [3-1-0:4]
Homotopy theow; covering spaces and vibrations; simplicial and CW complexes;
manifolds; homoiogy theori&;'universal coefficients-and ~ u n n e t h formulas; Hurewicz theorem; applications to fixed point theory and other topics. Prerequisite: MATH 323 MATH 331 Numerical Solutions of Partial Differential Equations [3-1-0:4]
lntroduction to finite difference and finite element methods for the solution of elliptic, parabolic and hyperbolic partial differential equations; including the use of computer software for the solution of differential equations. Prerequisites: MATH 151 and MATH 231
Reference: Sewell, The Numerical Solution of Ordinary and Partial Differential Equations
MATH 333 Introduction to Scientific Computation I [3-1-0:4]
Case studies drawn from different areas of science to illustrate the use of computers as a problem-solving tool. Each integrates physical principles and mathematicai models, as well as numerical techniaues and cornouter imolementations. into a coherent perspective. Prerequisites: MATH 151 and MATH 231
MATH 334 Introduction to Scientific Computation II [3-1-0:4]
Continuation of MATH 333, with case studies involving the numerical solution of partial differential equations. Prerequisite: MATH 333
MATH 335 Applications of Mathematical Software [3-1-0:4]
Scientific computation analytically and numerically using standard mathematical and symbolic softv;are packages. ~ o ~ ' c s include: matrix computation, definite and indefinite intearation. oerturbation ex~ansions. solutions of ordinarv and ~artial differential
MATH 337 High Performance Scientific Computation [3-1-0:4]
Fundamentals of computer organisation; overview of high performance computer architectures; parallel programming tools: PVM, Paragon-NX; issues in high perform- ance numerical computations; computer graphics and scientific visualisation. Prereq- uisite: COMP 103 or COMP 104
MATH 341 Stochastic Modelling [3-1-0:4]
Discrete time Markov chains and the Poisson Drocesses. Additional t o ~ i c s include birth and death process, elementary renewal process and continuous-time Markov chains.
Prerequisite: MATH 241
Reference: H. M. Taylor and S. Karlin, An introduction to Stochastic Modelling
MATH 342 Regression Analysis [3-1-0:4]
Estimation and hypothesis testing in linear regression; residual analysis; multicollinearity;
indicator variables; variable selection; nonlinear regression. Exclusion: ISMT 552 Prerequisite: MATH 243
Reference: N. R. Draper and H. Smith, Applied Regression Analysis
Undergraduate Course DescriDtions Undergraduate Course Descriptions
MATH 343 Data Analysis [3-1-0:4]
Computer-oriented statistical analysis including generalised linear models, classifica- tion, principal component analysis, survival analysis, binary data. Real data sets presented for analysis using statistical packages such as GLIM, SAS, Minitab.
MATH 346 Sampling [3-1-0:4]
Basic and standard sampling design and estimation methods. Particular attention given to variance estimation in sampling procedures. Topics include: simple random sam- pling, unequal probability sampling, stratified sampling, ratio and subpopulation and multistage designs. Prerequisite: MATH 243 or MATH 244
Reference: W. G. Cochran, SamplingTechniques
MATH 347 Multivariate Analysis [3-1-0:4]
Inferences of means and covariance matrices; canonical correlation; discriminant analysis; multivariate ANOVA; principal components analysis; factor analysis. Exclu- sion: ISMT 553 Prerequisites: MATH 1 11 and MATH 243
Reference: T. W. Anderson, An Introduction to Multivariate Statistical Analysis MATH 351 Functions of a Complex Variable and Applications [3-1-0:4]
Differentiation and integration in the complex plane; Cauchy's integral formula; Taylor series; Laurent series; analytic continuation; contour integration; conformal mapping;
special functions; integral transforms; asymptotic methods. Exclusions: MATH 251, MATH 304 Prerequisite: MATH 151
References: Fisher, Complex Variables, and
Churchill and Brown, Complex Variables and Applications
MATH 352 Applied Partial Differential Equations [3-1-0:4]
Methods to solve the Laplace equation, the wave equation and the diffusion equation;
separation of variables; integral transforms; Green's function; characteristics; vari- ational method. Exclusion: MATH 252
Reference: Sneddon, Elements of Partial Differential Equations
MATH 395 Scientific Computation Project I [O-0-9:3]
A scientiiic computation project under the supervision of a faculty member from any department. Projects may be in fluid mechanics, structural dynamics, chemistry, statistics, etc. May be graded PP.
MATH 396 Scientific Computation Project II Continuation of MATH 395. Prerequisite: MATH 395
MATH 398 Independent Study Project [2-3 credits]
Under the guidance of a faculty member. Scope may include (i) identifying a non- Reference problem and proposing methods of solution, and (ii) acquiring a specific research skill. May be repeated for credit, but the total credit may not exceed six.
MATH 399 Undergraduate Thesis [0-0-9:3]
Work in any area of mathematics under the guidance of a faculty member.