Overview

Programs

How to Apply

Financial Support

Courses

Awards

Events

PG Intranet


The Department of Mathematics has a large and distinguished faculty
with expertise in a wide range of areas of Mathematics,
including Algebra and Number Theory, Analysis and Differential Equations,
Geometry and Topology, Applied and Computational Mathematics, Probability and Statistics, and Financial Mathematics.
We are committed to fostering success of our students. As part of that commitment, we have been able to consistently provide
financial support
to nearly all of our doctoral students through Postgraduate Scholarship, Hong Kong PhD Fellowship, Asian Future Leaders Scholarship, etc.
HKUST is located in the beautiful Clear Water Bay area. The campus has a magnificent ocean view and is widely known as one of the most
beautiful campuses in the world. The city of Hong Kong ranks among the most dynamic cities in the world.
We offer one PhD program, one MPhil program, and four MSc programs.
Doctor of Philosophy (PhD) in Mathematics
The PhD program provides a broad background in mathematics and mathematical sciences. Students choose their
major research areas from three options: Pure Mathematics; Applied Mathematics; and Probability and Statistics.
For details of the program requirements, please click here.
Master of Philosophy (MPhil) in Mathematics
The MPhil program seeks to strengthen students' general background in mathematics and mathematical sciences,
and to expose students to the environment and scope of mathematical research. Submission and successful defense
of a thesis based on original research is required to obtain the degree. For details of the program requirements,
please click here.
Enquiry for the PhD program and MPhil program: mathpg@ust.hk
We also provide four MSc programs
Our postgraduate programs solicit applications worldwide.
Perspective students must apply online HERE.
The application materials include:
 A bachelor's degree from a recognized institution, or an approved equivalent qualification;
 Transcript
 Statement of purpose
 Recommendation letters

Applicants whose first language is not English, and whose bachelor's degree or equivalent qualification was awarded by an institution
where the medium of instruction was not English, are required to fulfill one of the following minimum English Language requirements:
 Test of English as a Foreign Language (TOEFL)  a paperbased test score of no less than 550; or an internetbased test score of no less than 80;
 International English Language Testing System (IELTS)  an overall score of 6.5 with no subscore lower than 5.5.
Summer Research Program
This Summer Research Program targets for outstanding end of year 3 undergraduate students who are interested in pursuing MPhil or PhD programs in the School of Science (including the math department) at HKUST. The program allows participants to experience the research life and to work with faculty mentors in our School to carry out research project in an interactive environment. Financial support will be provided.
Visiting UG students
This is a scheme for students to work with our faculty as visiting students.
All of our current PhD and MPhil students have been on full financial support in the form of postgraduate scholarship and fellowships since their arrival. Our support package is able to cover a living stipend that our students generally find to be sufficient.
Postgraduate Scholarship (PGS)
We offer a fouryear Postgraduate Scholarship, contingent on good progress in the program and competent
performance of teaching duties.
Hong Kong PhD Fellowship (HKPFS)
Hong Kong PhD Fellowship is an internationally recognized award to draw the best PhD students around the globe to Hong Kong. HKUST has the largest HKPFS awardee community in Hong Kong, with 400+ HKPFS recipients. More than 10% of our PhD students is from the Scheme, coming from 40 countries and regions.
Asian Future Leaders Scholarship (AFLSP)
20192020 Fall Semester
MATH 5011  Advanced Real Analysis I
Description 
Basic topology, continuous function spaces, abstract measure and integration theory, Lp spaces, convexity and inequalities, Hilbert spaces, Banach spaces, Complex measure. 
(3 units) 

Course Instructor: Prof LI, Dong 
MATH 5111  Advanced Algebra
Description 
Advanced theory of groups, linear algebra, rings, modules, and fields, including Galois theory. 
(3 units) 

Course Instructor: Prof HUANG, Jingsong 
MATH 5230  Differential Topology
Description 
Manifolds, embedding and immersion, Sard's theorem, transversality, degree, vector fields, Euler number, EulerPoincare theorem, Morse functions. 
(3 units) 

Course Instructor: Prof MENG, Guowu 
MATH 5251  Algebraic Geometry I
Description 
Projective spaces, algebraic curves, divisors, line bundles, algebraic varieties, coherent sheaves, schemes. Some commumative algebra and homological algebra such as notherian ring, regular ring, valuation ring, kahler differentials. 
(3 units) 

Course Instructor: Prof ZHU, Yongchang 
MATH 5285  Applied Analysis
Description 
Contraction mapping theorem, Fourier series, Fourier transforms, Basics of Hilbert Space theory, Operator theory in Hilbert Spaces, Basics of Banach space theory, Convex analysis. 
(3 units) 

Course Instructor: Prof ZHANG, Hai 
MATH 5311  Advanced Numerical Methods I
Description 
Numerical solution of differential equations, finite difference method, finite element methods, spectral methods and boundary integral methods. Basic theory of convergence, stability and error estimates. 
(3 units) 

Course Instructor: Prof WANG, Xiaoping 
MATH 5350  Computational Fluid Dynamics for Inviscid Flows
Description 
Derivation of the NavierStrokes equations; the Euler equations; Lagriangian vs. Eulerian methods of description; nonlinear hyperbolic conservation laws; characteristics and Riemann invariants; classification of discontinuity; weak solutions and entropy condition; Riemann problem; CFL condition; Godunov method; artificial dissipation; TVD methods; and random choice method. 
(3 units) 

Course Instructor: Prof XU, Kun 
MATH 5351  Mathematical Methods in Science and Engineering I
Description 
Modeling and analytical solution methods of nonlinear partial differential equations (PDEs). Topics include: derivation of conservation laws and constitutive equations, wellposedness, traveling wave solutions, method of characteristics, shocks and rarefaction solutions, weak solutions to hyperbolic equations, hyperbolic Systems, linear stability analysis, weakly nonlinear approximation, similarity methods, calculus of variations. 
(3 units) 

Course Instructor: Prof XIANG, Yang 
MATH 5380  Combinatorics
Description 
Numerical solution of differential equations, finite difference method, finite element methods, spectral methods and boundary integral methods. Basic theory of convergence, stability and error estimates. 
(3 units) 

Course Instructor: Prof CHEN, Beifang 
MATH 5411  Advanced Probability Theory I
Description 
Probability spaces and random variables, distribution functions, expectations and moments, independence, convergence concepts, law of large numbers and random series. 
(3 units) 

Course Instructor: Prof BAO, Zhigang 
MATH 5431  Advanced Mathematical Statistics I
Description 
Theory of statistical inference in estimation. Topics include: sufficiency, ancillary statistics, completeness, UMVU estimators, information inequality, efficiency, asymptotic maximum likelihood theory. Other topics may include Bayes estimation and conditional inference. 
(3 units) 

Course Instructor: Prof JING, Bingyi 
MATH 5471  Statistical Learning Models for Text and Graph Data
Description 
This course will introduce a number of important statistical methods and modeling principles for analyzing largescale data sets, with a focus on complex data structures such as text and graph data. Topics covered include sequential models, structure prediction models, deep learning attention models, reinforcement learning models, etc., as well as open research problems in this area.

(3 units) 

Course Instructor:
Prof SONG, Yangqiu

MATH 5520  Interest Rate Models
Description 
Theory of interest rates, yield curves, short rates, forward rates. Short rate models: Vasicek model and CoxIngersollRoss models. Term structure models: HullWhite fitting procedure. HeathJarrowMorton pricing framework. LIBOR and swap market models, BraceGatarekMusiela approach. Affine models.

(3 units) 

Course Instructor:
Prof WU, Lixin

MATH 6150H  Introduction to Cluster Algebra
Description 
Advanced topics of current interest in algebra.

(3 units) 

Course Instructor:
Prof IP, Ivan Chi Ho

MATH 6380O  Deep Learning: Toward Deeper Understanding
Description 
Advanced topics of current interest in applied mathematics.

(3 units) 

Course Instructor:
Prof YAO, Yuan

MATH 6380R  Theoretical Neuroscience
Description 
Advanced topics of current interest in applied mathematics.

(3 units) 

Course Instructor:
Prof HU, Yu

MATH 6380S  Fundamentals in Integrated Engineering
Description 
Advanced topics of current interest in applied mathematics.

(3 units) 

Course Instructor:
Prof HU, Jishan

MATH 6450F  Advanced Algorithms and Theory of Machine Learning
Description 
Advanced topics of current interest in probability and statistics.

(3 units) 

Course Instructor:
Prof ZHANG, Tong

20192020 Spring semester (Tentative)
MATH 5030  Complex Function Theory
Description 
Review of basic properties of analytic functions. PhragmenLindelof principle, normal family, Riemann mapping theorem. Weierstrass factorization theorem, Schwarz reflection principle, analytic continuation, harmonic function, entire function, Hadamard factorization theorem, Picard theorem.

(3 units) 

Course Instructor:
Prof CHIANG, YikMan

MATH 5112  Advanced Algebra II
Description 
Advanced topics in algebra: group representations, associative algebras, commutative algebra, homological algebra, algebraic number theory. 
(3 units) 

Course Instructor:
Prof HUANG, JingSong

MATH 5143  Introduction to Lie Algebras
Description 
Lie algebras. Nilpotent, solvable and semisimple Lie algebras. Universal enveloping algebras and PBWtheorem. Cartan subalgebras. Roots system, Weyl group, and Dynkin diagram. Classification of semisimple Lie algebras. Representations of semisimple algebras. Weyl character formula. HarishChandra isomorphism theorem. 
(3 units) 

Course Instructor:
Prof MENG, GuoWu

MATH 5240  Algebraic Topology
Description 
Fundamental group, covering space, Van Kampen theorem, (relative) homology, exact sequences of homology, MayerVietoris sequence, excision theorem, Betti numbers and Euler characteristic.

(3 units) 

Course Instructor:
Prof CHANG, HuaiLiang

MATH 5281  Partial Differential Equations
Description 
This is an introductory postgraduate course on Partial Differential Equations (PDEs). We will start with the classical prototype linear PDEs, and introduce a variety of tools and methods. Then we will extend our beginning theories to general situation using the notion of Sobolev spaces, Holder space and weak solutions. We will prove the existence, uniqueness, regularity and other properties of weak solutions.

(3 units) 

Course Instructor:
Prof JIN, Tianling

MATH 5312  Advanced Numerical Methods II
Description 
Direct and iterative methods. Programming techniques and softwares libraries. Sparse solvers, Fast algorithms, multigrid and domain decomposition techniques. 
(3 units) 

Course Instructor:
Prof CAI, JianFeng

MATH 5352  Mathematical Methods in Science and Engineering II
Description 
Asymptotic methods and perturbation theory for obtaining approximate analytical solutions to differential equations. Topics include: local analysis of solutions to differential equations, asymptotic expansion of integrals, global analysis and perturbation methods, WKB theory, multiplescale analysis, homogenization method. 
(2 units) 

Course Instructor:
Prof XIANG, Yang

MATH 5412  Advanced Probability Theory II
Description 
Characteristic functions, limit theorems, law of the iterated logarithm, stopping times, conditional expectation and conditional independence, introduction to Martingales. 
(3 units) 

Course Instructor:
Prof BAO, Zhigang

MATH 5432  Advanced Mathematical Statistics II
Description 
Theory of statistical inference in hypothesis testing. Topics include: uniformly most powerful tests, unbiasedness, invariance, minimax principle, largesample parametric significance tests. Concept of decision theory also covered. 
(3 units) 

Course Instructor:
Prof XIA, Dong

MATH 5470  Statistical Machine Learning
Description 
This course covers methodology, major software tools and applications in statistical learning. By introducing principal ideas in statistical learning, the course will help students understand conceptual underpinnings of methods in data mining. The topics include regression, logistic regression, feature selection, model selection, basis expansions and regularization, model assessment and selection; additive models; graphical models, decision trees, boosting; support vector machines; clustering. 
(3 units) 

Course Instructor:
Prof JING, BingYi

MATH 5472  ComputerAge Statistical Inference
Description 
This course is designed for PhD students (year 1) in applied mathematics, statistics, and engineering who are interested in learning from data. It covers advanced topics in statistical learning and inference, with emphasis on the integration of statistical models and algorithms for statistical inference. This course aims to first make connections among classical topics, and then move forward to modern topics, including statistical view of deep learning. Various applications will be discussed, such as computer vision, human genetics, and text mining. 
(3 units) 

Course Instructor:
Prof Yang, Can

MATH 6150  Topics in Algebra
Description 
Advanced topics of current interest in algebra.

(3 units) 

Course Instructor:
Prof MARBERG, Eric

MATH 6170  Topics in Number Theory
Description 
Advanced topics of current interest in number theory.

(3 units) 

Course Instructor:
Prof ZHU, YongChang

The University, the School of Science and the Department of Mathematics offer opportunities and awards to enhance our PG students' research experience.
School of Science Postgraduate Research Excellence Award
This is for research postgraduate students in year 2 or above in recognition of their outstanding research performance.
List of Awardees
2018/19 
JI Xing 
MAK Hugo Wai Leung 
2017/18 
LIU Hao 
ZHANG Luchan 
George K Lee Award
This is for fulltime postgraduate students who perform high standard of academic excellence in the area of science and intellectual qualities.
List of Awardees
2018/19 
Cao Zhiqiang 
2017/18 
Ji Xing 
DinYu Hsieh Teaching Award
This is for research postgraduate students in recognition of their outstanding teaching performance.
List of Awardees
Overseas Research Award
This is to support our PhD students to study aboard for 26 months with subsidy.
List of Awardees
2018/19 
LI Zhenzhen 
LUK Hoi Ping 
HUANG Yiyi 
2017/18 
WEI Xiaoyu 
ZHANG Lian 
PG Intranet
