1. Introduction

Vivid Graphics: The shadows shown in the picture on the right of Figure 1 and Figure 2 are sharper and more realistic, thanks to trapezoidal shadow maps (TSM), a new rendering technique. TSM calculates high quality shadows in real-time applications, allowing realistic shadows to be generated in moving graphics, thus contributing to the realism of computer generated images in games. Figure 3 shows some of the mathematics behind TSM.

Computer Science and Mathematics share a synergistic relationship in many ways – the foundation of computer science have its roots in mathematics, starting from the notion of computation (the Turing machine); discrete mathematics is an indispensable tool in understanding structures and systems in computer science. On the other hand, inventions and advances in computer science have generated new frontiers for research in mathematics. As a result, many fundamental areas in Computer Science such as computability and computational complexity are very much part of Mathematics and vice versa. The Double Degree Programmes in Computer Science and Mathematics/Applied Mathematics celebrate and leverage the synergistic relationship between the two disciplines.

The Double Degree Programmes in Computer Science and Mathematics/ Applied Mathematics emphasise quality over quantity, and are targeted at ‘A’ level holders with good results or special talent in mathematics or computing. Admission is highly selective, and students maintain consistently good results to remain in the programmes. Students who can withstand the rigour and stay the course will develop into graduates who are at ease with tackling multifaceted computational problems in both industry and research.

Following the NUS convention of naming degree programmes after the host faculties, the formal title of the programmes is Double Degree Programmes in Bachelor of Computing (Computer Science) and Bachelor of Science (Honours/non-Honours) Mathematics or Applied Mathematics.

2. Specialisations

Students in the Double Degree Programmes may choose to pursue one of the following two specialisations:

Algorithms and Computation: Graduates with this specialisation will be at the forefront of solving myriad complex computational problems, in both industry and research. They will apply their advanced learning in the theory of computation, a fundamental area that influences every field of computing, to tackle industry needs in complex scheduling, network optimisation, physical simulation, software reliability, etc. Their advanced knowledge in algorithmic design will also enable them to adapt to a wide variety of computing fields. The specialisation covers areas such as: computational complexity, cryptography, algorithmic graph theory and combinatorics, randomness in computing, parallel and distributed computation, machine learning, applications of logic, algorithmic algebra, coding theory, etc.

Multimedia Modelling: Recent advances in computing, networking and multimedia technologies have facilitated the construction of large and complex multimedia systems. To fully comprehend the complexity of such undertakings, proper modelling of multimedia information and systems must be carried out. The objective of this specialisation is to produce graduates with in-depth mathematical knowledge and advanced computing skills to contribute to the construction of multimedia models and modelling tools. Graduates with this specialisation will form the vanguard in the advancement of interactive digital media (IDM) technology. They will apply their mathematical logic and learning in networking and multimedia technologies to develop more realistic animation, better special effects, and generate a more immersive experience in virtual reality that engages the various human senses more fully. Graduates with this specialisation will find their niche in high-end technology companies in the IDM sector, as well as in the field of research.  The specialisation covers areas such as: Numerical PDE, 3D Differential Geometry, Computational Geometry, Game Development, etc.

Anatomical Humanoid Models: Character appeal can be enhanced by modelling real or exaggerated sub-skin tissue deformation. Complex representation, simulation and deformation mathematical models have been applied in animated features. These include analytical tissue models, Finite Element models, mass-spring models, integration calculus, implicit functions and matrix algebra. The above model uses simplified representation (ellipsoidal fusiforms extruded from quadratic action curves), dynamics (single mass-spring approximation for entire muscles and fast Verlet Integration), and deformation (parallelisable weighted smooth skinning with stable local coordinate generation for muscle slices) to create natural and convincing soft-tissue  movements in real time. Such technologies based on mathematics concepts breathe life into the computer generated images (CGI) of games and animated features

Requirement for completion of specialisation

Students must read at least 32 modular credits (for the double honours programme) or 28 modular credits (for single honours programme) from modules offered in one of the two specialisation lists, with the following requirements:

• Students must read at least 12 MCs of modules offered by each department.
• Students in the double honours programme must undertake an Integrated Honours Project.

Modules offered in each specialisation are listed here.


3. Admission Requirements

The double-honours degree programme follows a dual entry system:

(i) Direct admissions through university admissions exercise (http://www.nus.edu.sg/oam)

Applicants must satisfy one of the following two criteria:
1. Grade A in either 'A'-level Mathematics or 'A'-level Further Mathematics,  and a good grade at 'A'-level in either Computing or Physics or Chemistry or Biology or Physical Science.

2. Demonstrated special talents in Mathematics and/or Computing (e.g., Mathematics and/or Informatics Olympiad awards, etc.)

If the candidate meets criteria 1, no interview will be required.

(ii) Admissions at the completion of first–year studies in BComp (Hons) or BSc (Hons).

Candidates will be assessed on the merits of their first-year results. Interested students should contact the programme administrator on receipt of their results.

4. Programme Structure and Curriculum Requirements


(A) BComp (Hons) – BSc (Hons) Double Honours Programmes
The proposed double honours programmes require students to take a total of 202 MCs and 206 MCs for BComp (Hons) – BSc (Hons)(Math) and BComp (Hons) – BSc (Hons)(ApplMath) degrees, respectively.

These programmes consist of the following:

a. Bachelor of Computing – Honours in Computer Science (130 MCs)

BComp students normally take 160 MCs of modules to fulfil the University Level Requirements (ULR), Programme requirements, and Unrestricted Electives. Under this programme, 30 MCs would be waived under double degree rules. The 30 MCs will come from the Unrestricted and Breadth Electives.

b. Bachelor of Science – Honours in Mathematics (126 MCs)

BSc students in the four-year BSc degree programme normally take 160 MCs of modules to fulfil the University Level Requirements (ULR), Faculty and Major Requirements, and Unrestricted Electives. Under this programme, 34 MCs would be waived under double degree rules. The 34 MCs will come from the Unrestricted and Breadth Electives.

c. Bachelor of Science – Honours in Applied Mathematics (130 MCs)

BSc students in the four-year BSc degree programme normally take 160 MCs of modules to fulfil the University Level Requirements (ULR), Faculty and Major Requirements, and Unrestricted Electives. Under this programme, 30 MCs would be waived under double degree rules. The 30 MCs will come from the Unrestricted and Breadth Electives.

The details are set out here.


(B) BComp (Hons) - BSc Single Honours Programmes
The proposed single honours programmes require students to take a total of 182 MCs.

These programmes consist of the following:

a. Bachelor of Computing – Honours in Computer Science (130 MCs)

BComp students normally take modules of 160 MCs to fulfil University Level Requirements (ULR), Programme Requirements, and Unrestricted Electives Requirements. Under this programme, 30 MCs will be waived under double degree rules. The 30 MCs will come from Unrestricted and Breadth Electives.

b. Bachelor of Science – non-Honours in Mathematics (85 MCs)

BSc students in the three-year BSc degree programme normally take modules of 120 MCs to fulfil University Level Requirements (ULR), Faculty and Major Requirements, and Unrestricted Electives Requirements. Under this programme, 35 MCs will be waived under double degree rules. The 35 MCs will come from Unrestricted and Breadth Electives.

c. Bachelor of Science – non-Honours in Applied Mathematics (89 MCs)

BSc students in the three-year BSc degree programme normally take modules of 120 MCs  to fulfil the University Level Requirements (ULR), Faculty and Major Requirements, and Unrestricted Electives Requirements. Under this programme, 31 MCs will be waived under double degree rules. The 31 MCs will come from Unrestricted and Breadth Electives.

The details are set out here.


5. Integrated Honours Project

Students pursuing one of the listed specialisations in the double honours degree programme must undertake an integrated honours project in Mathematics and Computer Science. The project will provide the students with the opportunity to explore and integrate their knowledge in the specialised field. A Student pursuing a double honours degree programme without specialisation can choose to undertake:

i. one integrated honours year project or
ii. one Computing honours year project and one Mathematics honours year project or
iii. one Mathematics honours year project and 12MCs of level-4000 ‘CS’ prefixed modules.

to fulfil the graduation requirements of the double degree programme. In the case that integrated honours year project is not chosen, a student can choose to undertake 12MCs of common modules from Common Modules Table 2 for double-counting purpose.

The integrated honours project will be jointly supervised by faculty members from the Department of Computer Science and the Department of Mathematics, and must contain elements of both computer science and mathematics.


6. Grading and Degree Classification

Double Honours Programmes

The degree classification for Computing Degree (Honours) will be based on CAP calculated from 130 MCs: 86 MCs Computer Science Modules, 32 MCs Common Modules, 8 MCs General Education Modules (GEMs) and 4 MCs Singapore Studies Module.

The degree classification for Science Degree (Honours) majoring in Mathematics will be based on CAP calculated from 126 MCs: 18 MCs Faculty Requirement Modules, 64 MCs Mathematics Modules, 32 MCs Common Modules, 8 MCs General Education Modules (GEMs) and 4 MCs Singapore Studies Module.

The degree classification for Science Degree (Honours) majoring in Applied Mathematics will be based on CAP calculated from 130 MCs: 18 MCs Faculty Requirement Modules, 68 MCs Mathematics Modules, 32 MCs Common Modules, 8 MCs General Education Modules (GEMs) and 4 MCs Singapore Studies Module.

The list of common modules is given here.


BComp (Hons) – BSc in Mathematics: Single Honours Programme

The degree classification for Computing Degree (Honours) will be based on CAP calculated from 130 MCs: 102 MCs Computer Science Modules, 16 MCs Common Modules, 8 MCs General Education Modules (GEMs) and 4 MCs Singapore Studies Module.

The degree classification for Science Degree (non-Honours) majoring in Mathematics will be based on CAP calculated from 85 MCs: 13 MCs Faculty Requirement Modules, 44 MCs Mathematics Modules, 16 MCs Common Modules, 8 MCs General Education Modules (GEMs) and 4 MCs Singapore Studies Module.

The list of common modules is given here.


BComp (Hons) – BSc in Applied Mathematics: Single Honours Programme

The degree classification for Computing Degree (Honours) will be based on CAP calculated from 130 MCs: 98 MCs Computer Science Modules, 20 MCs Common Modules, 8 MCs General Education Modules (GEMs) and 4 MCs Singapore Studies Module.

The degree classification for Science Degree (non-Honours) majoring in Applied Mathematics will be based on CAP calculated from 89 MCs: 13 MCs Faculty Requirement Modules, 44 MCs Mathematics Modules, 20 MCs Common Modules, 8 MCs General Education Modules (GEMs) and 4 MCs Singapore Studies Module.

The list of common modules is given here.


7. Fee

The tuition fees payable for the duration of this programme will follow existing guidelines set by the University.


8. Progression Criteria

Students in the Double Degree Programme in Computer Science and Mathematics/Applied Mathematics must maintain a CAP of 4.00 or above. Students who fail to meet the criteria for two consecutive semesters will not be allowed to remain in the Double Degree Programme, but may continue with either BSc or Computer Science studies at NUS.

9. Enquiries

If your home faculty is School of Computing, please direct all queries to bcomp@comp.nus.edu.sg with the subject clearly marked: "Double Degree in Computer Science and Applied Mathematics/Mathematics Programme". Otherwise, please send to: AskMathUG@nus.edu.sg if you are in Science Faculty.