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. PG Prospectus
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.
A selective list of Ph.D. Recipients in the last five years
Name 
Graduate Year 
Advisor 
First job after HKUST 
JIANG, TP 
2021 
Xiang Yang 
Researcher at Huawei Tech Co Ltd 
CHEN, YP 
2021 
Xu Kun 
Researcher at Huawei HK Research Centre 
DENG, YZ 
2021 
Wu Lixin 
Researcher at Ping An Bank, China 
HU, W 
2021 
Wang Xiaoping 
Postdoc Research Fellow at Princeton University 
LIU, P 
2021 
Zhang Hai 
Postdoc at ETH Zurich 
RONG, Y 
2021 
Wang Yang 
Associate in Principal Investment at Goldman Sachs (Asia) 
WANG, JM 
2021 
Bao Zhigang 
Postdoc at Statistics Department, Harvard U 
YOU, JT 
2021 
Cai Jianfeng 
Postdoc fellow at Huawei Technologies Co Ltd 
ZHU, WZ 
2021 
Yao Yuan 
Quantitative researcher at Jane Street Asia Limited 
CAO, GY 
2020 
Xu Kun 
Postdoc at Southern University of Science & Technology 
CHU, KL 
2020 
Leung Shing Yu 
Assistant Lecturer at HKBU 
DAI, XZ 
2020 
Zhu Yongchang 
Postdoc at Shanghai Centre for Mathematical Sciences 
GUO, FF 
2020 
Ling Shiqing 
Postdoc at Beijing Institute of Technology 
HAN, RJ 
2020 
Chen Kani 
Research Assistant Professor at CUHK 
LI, ZZ 
2020 
Cai Jianfeng 
Postdoc at California Institute of Technology 
MIAO, LZ 
2020 
Wang Yang 
Postdoc at HKUST & Shenzhen Research Institute of Big Data 
QIN, XX 
2020 
Xiang Yang 
Postdoc at HKUST 
SUN, ZY 
2020 
Chen Beifang 
Researcher at Huawei Tech Investment Co Ltd 
TAN, CX 
2020 
Chen Kani 
Senior Engineer at Astri Hong Kong 
YE, RG 
2020 
Chen Kani 
Postdoc at HKUST 
CAO ZQ 
2019 
Wong Man Yu 
Research Engineer at Huawei Technologies Co Ltd 
CHAN CH 
2019 
Xiong Maosheng 
Postdoc at HKUST 
JI X 
2019 
Xu Kun 
Postdoc at HKUST 
LI T 
2019 
Jing Bingyi 
Postdoc at Yale University 
MAK HWL 
2019 
Fung Jimmy CH 
Lecturer at CUHK 
TANG HY 
2019 
Wu Lixin 
Quantitative Analyst at CREDIT SUISSE (HK) LIMITED 
ZHANG L 
2019 
Mu Mo 
Postdoc at Penn State University, USA 
CUI SD 
2018 
Wu Lixin 
Quantitative Researcher in JP Morgan Chase & Co. 
DAI LL 
2018 
Chen Kani 
Assistant Professor at Southwestern Univ of Finance & Economics 
JIANG Y 
2018 
Peng Xianhua 
Quantitative Researcher at Goldman Sachs 
LIU H 
2018 
Leung Shing Yu 
Postdoc at Georgia Institute of Technology 
SHE R 
2018 
Ling Shiqing 
Assistant Professor at Southwestern Univ of Finance & Economics 
WEI XY 
2018 
Wang Xiaoping/ Qian Tiezheng 
Postdoc at University of Illinois UrbanaChampaign 
YU XS 
2018 
Jing Bingyi 
Postdoc at University of Michigan 
ZHANG DW 
2018 
Wu Lixin 
Associate at Goldman Sachs 
CHENG KH 
2017 
Chiang Yik Man 
Postdoc at HKUST 
LUO L 
2017 
Wang Xiaoping 
Assistant Professor at Shenzhen Institute of Advanced Technology 
LUO T 
2017 
Xiang Yang 
Golomb Visiting Assistant Professor at Purdue University 
NIU XH 
2017 
Xiang Yang 
Assistant Professor at Jimei University 
WANG D 
2017 
Wang Xiaoping 
Assistant Professor/Lecturer at University of Utah 
ZHAO HB 
2017 
Zhu Yongchang 
Research Fellow at Sun Yat Sen University (zhuhai) 
ZHANG LC 
2017 
Xiang Yang 
Research Fellow at National University of Singapore 
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)
20222023 Fall Semester
MATH 5111  Advanced Algebra I
Description 
Advanced theory of groups, linear algebra, rings, modules, and fields, including Galois theory.

(3 units) 

Course Instructor:
Prof MENG, Guowu 
MATH 5145  Introduction to Lie Groups
Description 
This course is an introduction to the structure and representation theory of compact and noncompact reductive Lie groups. Topics include general properties of Lie groups and Lie algebras, PeterWeyl Theorems, representations of compact Lie groups, theorems of the highest weight, HarishChandra isomorphism, Weyl character formula, the structure theory of noncompact semisimple and reductive Lie groups, classification of simple real Lie algebras, induced representation and Frobenius reciprocity, classical branching theorems.

(3 units) 

Course Instructor:
Prof ZHU, Yongchang 
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 HO, Quoc 
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 LI, Weiping 
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 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 GUO, Xinzhou

MATH 5472  Computer Age Statistical Inference with Applications
Description 
This course is designed for RPg students 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 6250K  Geometry and Mechanics
Description 
Advanced topics of current interest in geometry.

(3 units) 

Course Instructor:
MENG, Guowu

MATH 6450J  Optimization for Machine Learning
Description 
Advanced topics of current interest in probability and statistics.

(3 units) 

Course Instructor:
ZHANG, Tong

MATH 6510C  Derivatives Pricing Models
Description 
Advanced topics of current interest in financial mathematics.

(3 units) 

Course Instructor:
KWOK, Yue Kuen

MATH 6771  Professional Development Training in Mathematics
Description 
This onecredit course aims at providing research postgraduate students basic training in teaching skills, research management, career development in and outside academia, and related professional skills in Mathematics. This course lasts for one semester, and is composed of a number of miniworkshops or tasks. Graded PP, P or F.

(1 units) 

Course Instructor:
TBA

20212022 Spring semester
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, Yik Man

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 MARBERG, Eric Paul

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 MENG, GuoWu

MATH 5261  Algebraic Geometry II
Description 
Derived functors, cohomology of coherent sheaves on schemes, extension groups of sheaves, higher direct image of sheaves, Serre duality, flat morphisms, smooth morphisms, and semicontinuity, basics of curves and surfaces.

(3 units) 

Course Instructor:
Prof LI, WeiPing

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 5353  Multiscale Modeling and Computation for Nonequilibrium Flows
Description 
Introduction of the NavierStrokes equations and the flow modeling in the hydrodynamic scale. The derivation of the Boltzmann equation in the kinetic scale. The basic mathematical analysis of the ChapmanEnskog expansion and the numerical methods for the Boltzmann equation. The multiscale modeling from the kinetic to the hydrodynamic scales and the discretized governing equations. The study of nonequilibrium transport phenomena in gas dynamics, radiative and heat transfer, and plasma physics.

(2 units) 

Course Instructor:
Prof XU, Kun

MATH 5412  Advanced Probability Theory II
Description 
Stable laws; infinitely divisible distributions; weak convergence on general metric spaces; Donsker’s invariance principle; basic martingale theory; optional stopping theorem; martingale convergence theorems; martingale CLT; Concentration inequalities; logarithmic Sobolev inequality; large deviation.

(3 units) 

Course Instructor:
Prof BAO, ZhiGang

MATH 5460  Time Series Analysis
Description 
Basic idea of time series analysis in both the time and frequency domains. Topics include: autocorrelation, partial ACF, Box and Jerkins ARIMA modeling, spectrum and periodogram, order selection, diagnostic and forecasting. Real life examples will be used throughout the course.

(3 units) 

Course Instructor:
Prof LING, ShiQing

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 YAO, Yuan

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

(3 units) 

Course Instructor:
Prof IP, Ivan Chi Ho

MATH 6250J  Introduction to Enumerative Geometry
Description 
Advanced topics of current interest in geometry.

(3 units) 

Course Instructor:
Prof CHANG, HuaiLiang

MATH 6380U  Introduction to Molecular Simulation
Description 
Advanced topics of current interest in applied mathematics.

(3 units) 

Course Instructor:
XIANG, Yang

The University, the School of Science and the Department of Mathematics offer opportunities and awards to enhance our PG students' research experience.
RedBird PhD Scholarships
It is a scholarship for excellent PhD students, in recognition of their outstanding academic performance and research capacity.
List of Awardees
2020/21 
SHI Zhongyi 
YU Xinyi 
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
2019/20 
CAO Guiyu 
CAI Mingxuan 
2018/19 
JI Xing 
MAK Hugo Wai Leung 
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
2019/20 
JIANG Tianpeng 
LIN Xiaoli 
QIN Xiaoxue 
2018/19 
LI Zhenzhen 
LUK Hoi Ping 
HUANG Yiyi 
Zonta International Amelia Earhart Fellowship
This is for female PhD students in good academic record conducting research applied to aerospace engineering or space sciences.
List of Awardees
PG Intranet
