Master of Philosophy in Mathematics
Doctor of Philosophy in Mathematics
MPhil(MATH)
PhD(MATH)
Both full- and part-time
MPhil
Full-time: 2 years
Part-time: 4 years
PhD
Full-time: 3 years (with a relevant research master’s degree), 4 years (without a relevant research master’s degree)
Part-time: 6 years
PG Programs Coordinator:
Prof Tianling JIN, Assistant 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.
On successful completion of the MPhil program, graduates will be able to:
- Conduct research in mathematics;
- Demonstrate knowledge in the chosen discipline of mathematics;
- Be able to synthesize and create new knowledge and to making contributions to the discipline of mathematics; and
- Demonstrate communication skills in presenting reporting findings in mathematics.
On successful completion of the PhD program, graduates will be able to:
- Be able to conduct independent and original research in mathematics;
- Demonstrate mastery of knowledge in the chosen discipline of mathematics;
- Be able to synthesize and create new knowledge and to make original and substantial contributions to the discipline of mathematics;
- Demonstrate a broad knowledge in mathematics and mathematical sciences; and
- Demonstrate effective communication skills in presenting and publishing findings in mathematics.
The programs are offered by the Department of Mathematics with the following research foci and state-of-the-art facilities, strengthening students’ knowledge in mathematics and training them to carry out original research independently and innovatively.
Research Foci
Algebra and Number Theory
Representation theory of reductive groups, quantum groups, infinite dimensional Lie groups and Lie algebras and applications to mathematical physics and number theory.
Geometry and Topology
Algebraic geometry, differential geometry, low dimensional topology, equivariant topology, combinatorics and combinatorial topology, and geometrical structures in mathematical physics.
Analysis and Differential Equations
Complex analysis, exponential asymptotics, functional analysis, harmonic analysis, wavelets analysis, nonlinear equations and dynamical systems, integrable systems, fluid dynamics, and inverse problems.
Applied and Computational Mathematics
Modeling and simulation in fluid dynamics and materials science, computational fluid dynamics, multiscale modeling, kinetic theory, atomistic simulations, image processing, computational harmonic analysis, inverse problems and wave propagation, graph theory, optimization, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, numerical analysis, parallel algorithms, and numerical software.
Financial Mathematics
Asset allocation/management, derivative modeling, pricing and hedging and division or firm-wise risk management are traditional research areas. The recent trend of financial mathematics research is data driven, adopting methodologies of big data and machine learning.
Probability and Statistics
Time series and dependent data, resampling methodology, stochastic processes and stochastic analysis, and survival analysis, random matrix, statistical physics and high-dimensional statistics.
Data Science
Financial statistics, econometrics, statistical machine learning, statistical genetics and genomics, computational biology and bioinformatics, error in variables model, generalized linear models; biological and medical statistics, topological and geometric methods in data analysis.; mathematical data analysis, in terms of accuracy, running time, memory efficiency, scalability, or other computational measures.
Facilities
The Department enjoys a range of up-to-date facilities and equipment. Apart from a computer laboratory with 40 high-end desktop computers, there is also a High Performance Computing laboratory equipped with 200 powerful CPU- & GPU-based computer servers having 250 TFLOPS aggregate processing power and 1.5PB storage capacity. Moreover, Tianhe2 Supercomputer is also available in the Guangzhou HKUST Fok Ying Tung Research Institute.
-
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.
-
Graduate Teaching Assistant Training
All full-time RPg students are required to complete PDEV 6800. The course is composed of a 10-hour training offered by the Center for Education Innovation (CEI), and session(s) of instructional delivery to be assigned by the respective departments. Upon satisfactory completion of the training conducted by CEI, MPhil students are required to give at least one 30-minute session of instructional delivery in front of a group of students for one term. PhD students are required to give at least one such session each in two different terms. The instructional delivery will be formally assessed.
-
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 taking PDEV 6770, subject to prior approval of the School.
Students are 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 in Mathematics and have completed MATH 6771 before may be exempted from taking MATH 6771, subject to prior approval of the Department Head or Department PG Coordinator.
-
English Language Requirement
Full-time 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 are required to complete LANG 5005 and advised to complete it in the first year of study. The 1 credit earned from LANG 5005 cannot be counted toward the program credit requirements. PhD students who are HKUST MPhil graduates may be considered for exemption from this course, subject to the approval of their department.
-
Postgraduate Seminar
Full-time 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: 1 June 2023
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.
All students must take MATH 6915 and MATH 6916. Credits earned from MATH 6915 can be repeated for up to 2 credits.
All students must take at least one course of other departments (excluding MATH 6915 and MATH 6916) or one CSIC course.
Elective Courses
-
Conduct research in the area of scientific computation.
Last update: 18 July 2024
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 full-time basis for at least one year, or on a part-time basis for at least two years.
Applicants have to fulfill English Language requirements with one of the following proficiency attainments:
-
TOEFL-iBT: 80 *
-
TOEFL-pBT: 550
-
TOEFL-Revised paper-delivered test: 60 (total scores for Reading, Listening and Writing sections)
-
IELTS (Academic Module): Overall score: 6.5 and All sub-score: 5.5 *
* Refers to scores in one single attempt only. Test at home option is not accepted.
Applicants are not required 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.
