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1.
数学教育
Master of Science Program in Mathematics for Educators
https://www.math.hkust.edu.hk/maed/maed-courses.html
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课程设置：
MAED Courses
5 core courses offered every year
Mathematical analysis and its applications I (MAED 5021)
This course is introduction to analysis and its applications. Topics will be selected from: Countable and uncountable
sets, metrics, norms, open sets, closed sets, continuity, homeomorphisms, connectedness, complete metric spaces,
totally bounded sets, fixed points, compact metric spaces, uniform continuity, category, the Baire Category
Theorem, sequences of functions, pointwise and uniform convergence, the space of bounded functions.
Algebra and its applications I (MAED 5121)
This course is an introduction to abstract algebra and it applications. Topics include: Groups, rings,
homomorphisms, quotients, group actions, polynomial rings, chinese remainder theorem, applications to encryption
and codes, field extensions geometric constructions.
Classical and modern geometry (MAED 5211)
This course is about important ideas in the development of geometry. Topics include logic and axiomatic system,
projective geometry, Hilbert’s axioms, hyperbolic models, geometric transformations, hyperbolic trigonometry.
Probablity and Statistics (MAED 5421)
This course serves those who want to use statistics in their careers or teach statistics/probability (or topics related to
statistics and probability). Topics include: Descriptive statistics, examples of commonly-used probability
distributions and their applications, main techniques for estimation and testing of model parameters, and regression
modeling. Statistical and probabilistic techniques will be illustrated by using the open source statistics package "R"
to analyze data in education.
Problem solving strategies (MAED 5731)
This course covers strategies and techniques for solving math problems that appear in high school or university
level math competitions, such as the International Mathematical Olympiad or the William Lowell Putnam Math
Competition. Students will have opportunities to present solutions of these problems. It is hoped they can compare
the strength and weakness of these methods.
At least 3 elective courses offered every year on a rotational basis from:
Mathematical analysis and its applications II (MAED 5031)
This course is a continuation of MAED 5021. It covers the space of continuous functions, the Stone-Weierstrass
Theorem, functions of bounded variation, the Riemann-Stieltjes Integrals, Fourier Series, Lebesgue measure,
measurable functions, Lebesgue integrals, Convergence in measure, L_p spaces, differentiation.
Applications of geometry and analysis (MAED 5032)
This course will show how mathematical analysis can be used to investigate a variety of physical phenomena.
Kepler’s laws of planetary motion will be derived from Newton’s law gravitation. Further topics will be the use of
differential geometry, in particular Gaussian curvature, in describing space curves and surfaces. Additional topics
will be other historically important uses of differential equations, Fourier series and harmonic analysis.
Classical and abstract algebra (MAED 5111)
This is a course on real numbers and polynomials. Topics include: Real and complex number systems, Dedekind
cuts, fundamental theorem of algebra, cubic and quartic equations, conics, symmetric polynomials, special
polynomials.
Algebra and its applications II (MAED 5131)
This course is an follow-up course to MAED 5121 and covers the theory of groups and its applications.
Applications selected from among: The impossibility of expressing the roots of a general polynomial in terms of
radicals, the 17 classes of wallpaper groups, applications to combinatorics and the enumeration of sets, introduction
to Lie groups and their uses in describing continuous motions.
Combinatorics (MAED 5321)
This course to provide students with general knowledge of useful principles in combinatorics. Topics will be
selected from: Graph theory, systems of distinct representatives, flows in networks, Latin squares, Hadamard
matrices, Reed-Muller codes, combinatorial designs and projective geometries.
Topics in Mathematics (MAED 5821)
This course in which students are shown how mathematical theories are applied to various disciplines. It consists of
four modules chosen from mathematical physics, mathematical biology, game theory, image processing and traffic
flow.
Scientific computation (MAED 5851)
This course is an introduction to case studies drawn from different areas of science to illustrate the use of computers
as a problem-solving tool. Each integrates physical principles and mathematical models, as well as numerical
techniques and computer implementations, into a coherent perspective. Topics include: Damped-driven pendulum,
phase space, Fourier series, spectral analysis, visualization, fractals, and computational fluid dynamics (CFD).
Independent Study (MAED 6981)
This course is for independent study under the guidance of an MAED instructor.
1.2
申请要求：
数学或相关科学或工程领域的
1.3
学费：
HK$115,000
