Programme Structure 4AU
Introduction
A strong mastery of mathematics will enable educators to teach better and to promote higher order thinking among students in the learning of mathematics. Mathematics specialists in education institutes will also benefit from this programme because a good understanding of mathematics is crucial for handling various tasks related to mathematics education, such as the design of contemporary and rigorous curriculum, assessment of mathematics learning, and development of teaching resources.
The programme emphasises the acquisition of wide and in-depth content knowledge in mathematics as well as its linkage to mathematics teaching. Candidates will have the opportunity to study subjects in different areas of mathematics, conducted by active working mathematicians, many of them holding a qualification in teaching of mathematics.
Courses are classified under prescribed strands: Analysis-Geometry, Algebra-Number Theory, Discrete Mathematics, Applied Mathematics and Statistics. Within each strand lies one to two Foundation Level courses that cover most of the basic concepts needed for advancement along that strand. Organising the courses along these strands not only helps students see clearly which foundational courses are required as pre-requisite for advanced courses but also delineate clearly possible study plans that are grouped naturally along given strands.
Foundational Level courses equip the students, especially those who had no prior training in tertiary mathematics, with core mathematical knowledge and skills needed for advancement in various Advanced Level courses. Foundation Level courses are designed to build a strong foundation for students in the first year of the programme, and each of them make a tight connection between tertiary level mathematics and the mathematics taught at schools. Advanced courses then go deeper into various fields of mathematics organised under the five strands, and are intended to equip learners with state-of-the-art development in various sub-disciplines of advanced mathematics.
The programme is open to graduates in Mathematics as well as graduates in non-Mathematics disciplines, who have a strong mathematics background to pursue a study of mathematics at the Masters level.
Programme Details
Admission Requirements
For admission as a candidate for the degree of Master of Science, the applicant should possess a
(a) Bachelor of Science with Honours degree, or equivalent, in a relevant discipline,
or
(b) Bachelor of Science degree, or equivalent, in a relevant discipline with at least one year of professional working experience.
Duration of Candidature
The programme is offered on either on a full-time or a part-time basis, and is only based on coursework (as indicated by the title).
The minimum (respectively, maximum) period of full-time candidature is 1 year (respectively, 2 years).
The minimum (respectively, maximum) period of part-time candidature is 2 years (respectively, 4 years).
Degree requirement
Participants are required to complete 8 courses comprising:
- 1 core course (MSM900 Mathematical Research Method) worth 2AU
- 7 elective courses (each worth 4AU) with at most three at Foundation Level
| Core (MSM900 Mathematical Research Methods) | Electives | ||||||||
|
|
Figure 1. Degree requirement = Complete 1 Core Course and 7 Elective Courses
Courses
The programme offers a range of courses that will broaden and deepen the candidate’s mathematical content knowledge. It will also provide opportunities for candidates to traverse the boundaries of mathematical research.
The Core Course
Elective Courses in this programme are organized along five strands:
- Analysis-Geometry
- Algebra-Number Theory
- Discrete Mathematics
- Applied Mathematics
- Statistics
| Core Courses | |
| MSM900 | Mathematical Research Methods |
| Elective Courses | |||||
| Level | Analysis-Geometry strand | Algebra-Number Theory strand | Discrete Mathematics strand | Applied Mathematics strand | Statistics strand |
| Foundation | MSM910 Calculus and Analysis for Educators | MSM911 Ring Theory for Educators | MSM912 Discrete Mathematics for Educators | MSM913 Computing and Programming Techniques for Educators | MSM914 Statistical Theory for Educators |
| Advanced | MSM921 Real Analysis | MSM931 Number Theory | MSM941 Selected Topics in Graph Theory | MSM951 Numerical Mathematics and Applications | MSM961 Multiple Linear Regression |
MSM922 Theory and Applications of Differential Equations | MSM932 Commutative Ring Theory | MSM942 Algorithms and Applications in Graph Theory | MSM952 Large Scale Systems in Operations Research | MSM962 Multivariate Methods | |
MSM923 Topology | MSM933 Topics in Applied Algebra | MSM953 Contemporary topics in Applied Mathematics | |||
MSM924 Euclidean and non-Euclidean Geometry | MSM934 Group Theory | MSM954 Models of Computation | |||
MSM925 Contemporary topics in Analysis, Geometry and Topology | MSM935 Contemporary topics in Algebra and Number Theory | ||||
| MSM970 Mathematical Inquiry | |||||
Figure 2. Programme structure organized along strands with two levels: Foundation/Advanced
Advanced Level courses may require the candidate to have completed a Foundation Level course as pre-requisite (see Figure 3).
| Advanced Level Courses | Pre-requisite Foundation Level Courses or equivalent | Non-mandatory preferences |
| Calculus-Geometry Strand | ||
MSM921 Real Analysis | MSM910 | |
MSM922 Theory and Applications of Differential Equations | MSM910 | |
MSM923 Topology | MSM910 | Set Theory |
| Algebra-Number Theory Strand | ||
MSM931 Number Theory | MSM911 | |
MSM932 Commutative Ring Theory | MSM911 | |
MSM933 Topics in Applied Algebra | Linear Algebra or Matrix Algebra at undergraduate level | |
MSM934 Group Theory | MSM911 | |
| Discrete Mathematics Strand | ||
MSM941 Selected Topics in Graph Theory | MSM912 | |
MSM942 Algorithms and Applications in Graph Theory | MSM912 | |
| Applied Mathematics Strand | ||
MSM951 Numerical Mathematics and Applications | ||
MSM954 Models of Computation | MSM913 | |
| Statistics Strand | ||
MSM961 Multiple Linear Regression | MSM914 Linear Regression and Linear Algebra | Matrix Algebra |
MSM962 Multivariate Methods | MSM914 Linear Regression and Linear Algebra | Matrix Algebra |
| Research Elective | ||
| MSM970 | MSM900 | |
Figure 3. Table of Pre-requisites and Non-mandatory Preferences for Advanced Courses
A student who had a priori completed certain relevant undergraduate courses (see Figure 4 below) may apply through Office of Academic Administration and Services (before registration) for “waiver of pre-requisite”, i.e., waiver of the Foundational level course required as pre-requisite for an Advanced level course(s). Students who successfully obtain a “waiver of pre-requisite” must still fulfil the programme requirement of completing the core course (MRM) plus seven elective courses.
Relevant undergraduate courses considered for “waiver of pre-requisite”
| Advanced level course(s) | Foundation level course required as pre-requisite to Advanced level course(s) | Eligibility for “waiver of pre-requisite” based on a prior completion of the following relevant undergraduate courses or their equivalent |
| MSM921, MSM922, MSM923 | MSM910 | AAM20B Calculus II and AAM33D Real Analysis |
| MSM931, MSM932, MSM934 | MSM911 | AAM33E Modern Algebra |
| MSM941, MSM942 | MSM912 | AAM33J Combinatorial Analysis and AAM43J Graph Theory |
| MSM954 | MSM913 | Introductory programming course in either C, Java, Basic, etc., at undergraduate level |
| MSM961, MSM962 | MSM914 | AAM33H Statistics III and AAM43B Statistical Theory |
Figure 4. Considerations for Waiver of Pre-requisites
While certain advanced courses specifically require a student to have completed and passed the foundation course within the given strand, there are others that require additional pre-requisite(s) or preferred background knowledge which are spelt out clearly in the attached course descriptions, where applicable. When reading advanced courses, students at graduate level are expected to exercise academic independence in the acquisition of additional prior knowledge if they have not possessed such.
Click here for Course Descriptions
Courses Offered
2024-2025 August 2024
| Course code | Title | Lecturers |
| MSM921 | Real Analysis | Ho Weng Kin |
| MSM924 | Euclidean and Non-Euclidean Geometry | Zhao Dongsheng |
| MSM931 | Number Theory | Toh Pee Choon |
2023-2024 January 2024
| Course code | Title | Lecturers |
| MSM911 | Ring Theory for Educators | Teo Kok Ming |
| MSM912 | Discrete Mathematics for Educators | Dong Fengming |
| MSM914 | Statistical Theory for Educators | Zhu Tianming |
| MSM970* | Mathematical Inquiry* | Zhao Dongsheng (Coordinator) |