Master of Philosophy in Mathematics
Doctor of Philosophy in Mathematics
MPhil(MATH)
PhD(MATH)
Both full and parttime
MPhil
Fulltime: 2 years
Parttime: 4 years
PhD
Fulltime: 3 years (with a relevant research master’s degree), 4 years (with a bachelor’s degree only)
Parttime: 6 years
PG Programs Coordinator:
Prof Yang XIANG, Professor of Mathematics
The Master of Philosophy (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. A candidate for an MPhil degree is expected to demonstrate knowledge in the discipline and to synthesize and create new knowledge, making a contribution to the field. It can be a terminal degree or a preliminary degree leading to the PhD.
The Doctor of Philosophy (PhD) Program aims to prepare students to become research scholars in an academic or industrial environment and enable students to do independent and original research. It provides a broad background in mathematics and mathematical sciences. Students can choose to focus their research in one of the three areas: Pure Mathematics, Applied Mathematics, and Probability and Statistics. A candidate for a PhD degree is expected to demonstrate mastery of knowledge in the chosen discipline and to synthesize and create new knowledge, making an original and substantial contribution to the discipline.
The programs are offered by the Department of Mathematics with the following research foci and stateoftheart facilities, strengthening students’ knowledge in mathematics and training them to carry out original research independently and innovatively.
Research Foci
Algebra and Number Theory
The theory of Lie groups, Lie algebras and their representations play an important role in many of the recent development in mathematics and in the interaction of mathematics with physics. Our research includes representation theory of reductive groups, KacMoody algebras, quantum groups, and conformal field theory. Number theory has a long and distinguished history, and the concepts and problems relating to the theory have been instrumental in the foundation of a large part of mathematics. Number theory has flourished in recent years, as made evident by the proof of Fermat's Last Theorem. Our research specializes in automorphic forms.
Analysis and Differential Equations
The analysis of real and complex functions plays a fundamental role in mathematics. This is a classical yet still vibrant subject that has a wide range of applications. Differential equations are used to describe many scientific, engineering and economic problems. The theoretical and numerical study of such equations is crucial in understanding and solving problems. Our research areas include complex analysis, exponential asymptotics, functional analysis, nonlinear equations and dynamical systems, and integrable systems.
Applied Sciences
The applications of mathematics to interdisciplinary science areas include: material science, multiscale modeling, multiphase flows, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, astrophysics and space science.
Financial Mathematics
This is one of the fastest growing research fields in applied mathematics. International banking and financial firms around the globe are hiring science PhDs who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. The trend has been accelerating in recent years on numerous fronts, driven both by substantial theoretical advances as well as by a practical need in the industry to develop effective methods to price and hedge increasingly complex financial instruments. Current research areas include pricing models for exotic options, the development of pricing algorithms for complex financial derivatives, credit derivatives, risk management, stochastic analysis of interest rates and related models.
Geometry and Topology
Geometry and topology provide an essential language describing all kinds of structures in Nature. The subject has been vastly enriched by close interaction with other mathematical fields and with fields of science such as physics, astronomy and mechanics. The result has led to great advances in the subject, as highlighted by the proof of the Poincaré conjecture. Active research areas in the Department include algebraic geometry, differential geometry, lowdimensional topology, equivariant topology, combinatorial topology, and geometrical structures in mathematical physics.
Numerical Analysis
The focus is on the development of advance algorithms and efficient computational schemes. Current research areas include: parallel algorithms, heterogeneous network computing, graph theory, image processing, computational fluid dynamics, singular problems, adaptive grid method, rarefied flow simulations.
Probability and Statistics
Statistics, the science of collecting, analyzing, interpreting, and presenting data, is an essential tool in a wide variety of academic disciplines as well as for business, government, medicine and industry. Our research is conducted in four categories. Time Series and Dependent Data: inference from nonstationarity, nonlinearity, longmemory behavior, and continuous time models. Resampling Methodology: block bootstrap, bootstrap for censored data, and Edgeworth and saddle point approximations. Stochastic Processes and Stochastic Analysis: filtering, diffusion and Markov processes, and stochastic approximation and control. Survival Analysis: survival function and errors in variables for general linear models. Probability current research includes limit theory.
Facilities
The Department enjoys a range of uptodate facilities and equipment for teaching and research purposes. It has two computer laboratories and a Math Support Center equipped with 100 desktop computers for undergraduate and postgraduate students. The Department also provides an electronic homework system and a storage cloud system to enhance teaching and learning.
To assist computations that require a large amount of processing power in the research area of scientific computation, a High Performance Computing (HPC) laboratory equipped with more than 200 highspeed workstations and servers has been set up. With advanced parallel computing technologies, these powerful computers are capable of delivering 17.2 TFLOPS processing power to solve computationally intensive problems in our innovative research projects. Such equipment helps our faculty and postgraduate students to stay at the forefront of their fields. Research projects in areas such as astrophysics, computational fluid dynamics, financial mathematics, mathematical modeling and simulation in materials science, molecular simulation, numerical ocean modeling, numerical weather prediction and numerical methods for micromagnetics simulations all benefit from our powerful computing facilities.

Minimum Credit Requirement
MPhil: 24 credits
PhD: 36 credits

Credit Transfer
PhD students who have obtained an MSc or MPhil degree from other institutions may be granted credit transfer of up to 18 credits, subject to departmental approval.

Required Courses
MPhil:
24 credits in mathematics or related fields, normally including at least 18 credits of mathematics courses at postgraduate level.
PhD:
36 credits in mathematics or related fields, including at least 24 credits of mathematics courses at postgraduate level.
PhD students can choose to focus their research in one of the three areas:

Pure Mathematics;

Applied Mathematics; and

Probability and Statistics.
Students with a first degree in an area other than mathematics may be required to take additional courses.

Professional Development Course Requirement
Students are required to complete PDEV 6770. The 1 credit earned from PDEV 6770 cannot be counted toward the credit requirements.
PhD students who are HKUST MPhil graduates and have completed PDEV 6770 or other professional development courses offered by the University before may be exempted from this requirement, subject to prior approval of the School.
Fulltime students are also required to complete MATH 6771. The 1 credit earned from MATH 6771 cannot be counted toward the credit requirements.
PhD students who are HKUST MPhil graduates and have completed MATH 6771 before may be exempted from this requirement, subject to prior approval of the School.

English Language Requirement
Fulltime RPg students are required to take an English Language Proficiency Assessment (ELPA) Speaking Test administered by the Center for Language Education before the start of their first term of study. Students whose ELPA Speaking Test score is below Level 4, or who failed to take the test in their first term of study, are required to take LANG 5000 until they pass the course by attaining at least Level 4 in the ELPA Speaking Test before graduation. The 1 credit earned from LANG 5000 cannot be counted toward the credit requirements.
Students must complete and pass LANG 5010, which should be taken in the first year of study. The 1 credit earned from LANG 5010 cannot be counted toward the credit requirements.
PhD students who are HKUST MPhil graduates may be considered for exemption from this requirement, subject to prior approval from the Department Head and PG Coordinator.

Postgraduate Seminar
Fulltime students are required to complete MATH 6900 in their first four regular terms of study. The maximum number of credits to be earned from this course is 4.

PhD Qualifying Examination
PhD students are required to pass a qualifying examination.
Pure Mathematics
To become PhD candidates, students must first pass a written qualifying examination (normally at the end of the first year of study) on two of the three subject areas: analysis, algebra, and geometry. At a later date (normally no later than the end of the second year of study) an oral examination on a major area excluding the two areas covered in the written examination.
Applied Mathematics
To become PhD candidates, students must first pass a written preliminary examination (normally before the end of the first year of study) on two subjects: advanced calculus and linear algebra. Students must also submit a thesis proposal, and pass an oral examination on the thesis proposal and two minor subjects. The oral examination should normally take place before the end of the second year of study.
Probability and Statistics
To become PhD candidates, students must pass an oral qualifying examination on one major subject and two minor subjects (normally no later than the end of the second year of study). For Probability students, the major subject is Probability while the two minor subjects would be Statistics and an area in Mathematics or an appropriate area outside Mathematics. For Statistics students, the major subject is Statistics while the two minor subjects would be Probability and an area in Mathematics or an appropriate area outside Mathematics.

Thesis Research
MPhil:

Registration in MATH 6990; and

Presentation and oral defense of the MPhil thesis.
PhD:

Registration in MATH 7990; and

Presentation and oral defense of the PhD thesis.
Last update: 31 July 2018
Scientific Computation Concentration
In addition to the existing program requirements, students who opt for the Scientific Computation concentration are required to:

MPhil:
Complete a minimum of 7 credits from the following course lists.
PhD:
Complete a minimum of 10 credits from the following course lists.
The credits earned under the concentration will be counted toward the total credit requirements of the programs.
Core Courses
MPhil: at least 3 credits
PhD: at least 6 credits
All students must take MATH 6915 and MATH 6916. Credits earned from MATH 6915 can be repeated for up to 2 credits.
Elective Courses

Conduct research in the area of scientific computation.
Last update: 25 March 2021
To qualify for admission, applicants must meet all of the following requirements. Admission is selective and meeting these minimum requirements does not guarantee admission.

Applicants seeking admission to a master's degree program should have obtained a bachelor’s degree from a recognized institution, or an approved equivalent qualification;

Applicants seeking admission to a doctoral degree program should have obtained a bachelor’s degree with a proven record of outstanding performance from a recognized institution; or presented evidence of satisfactory work at the postgraduate level on a fulltime basis for at least one year, or on a parttime basis for at least two years.
Applicants have to fulfill English Language requirements with one of the following proficiency attainments:

TOEFLiBT: 80

TOEFLpBT: 550

TOEFLRevised paperdelivered test (effective from 2018/19 admission): 60
(total scores for Reading, Listening and Writing sections) 
IELTS (Academic Module): Overall score: 6.0 and All subscore: 5.5
Applicants don't need to present TOEFL or IELTS score if

their first language is English, or

they obtained the bachelor's degree (or equivalent) from an institution where the medium of instruction was English.