**The Mathematical Sciences Programme**- What are the Mathematical Sciences?
- What is the intake size?
- What are the requirements for applying to the major in Mathematical Sciences?
- Would I be disadvantaged if I did not do Further Mathematics at A Level?
- How does Mathematical Sciences in the university differ from the Mathematics we learnt in junior college or polytechnic?
- What are the special strengths of the undergraduate programme in Mathematical Sciences at NTU
- What do the "tracks" in the major programme refer to?
- After choosing one track, can I still read courses from the other tracks?
- Can I complete the degree in less than 4 years?
- As a Mathematical Sciences major, will I need to read other science courses (e.g., physics or chemistry)?

**Career Prospects****Double Major Programmes****Minor in Mathematics**- Is there an entry requirement to take a Minor in Mathematics?
- Can the School help me if there are clashes in the time-table?
- If I am not in the Minor programme, can I just take one course?
- Will I be dropped from the Minor programme if I fail a MHXXXX course?
- The curriculum for my major includes some mathematics. Can the credits from those courses count towards the Minor in Mathematics?
- Some MAS courses topics overlap with courses in my major. Can I still read MAS courses on topics I have already learnt?
- Some MAS courses topics overlap with courses in my major. Can I use the courses from my major to fulfill course prerequisites for MAS courses?

**SPMS Co-Operative Education Programme****Final Year Projects and Internships**- Can I do both the Final Year Project and an Internship?
- Can I choose not to do the Final Year Project or an Internship?
- How do I choose between Final Year Project and Internship?
- I am doing a Double Major in Mathematical Sciences and Economics. Can my Final Year Project supervisor be from the Division of Economics?
- Will I be automatically granted Honours (Highest Distinction) if I do the Final Year Project?
- How do I prepare the Final Year Project proposal?
- How do I prepare for the FYP presentation?
- How do I write the Final Year Project thesis?
- What are the marking criteria for Final Year Project?

# The Mathematical Sciences Programme

## 1. What are the Mathematical Sciences?

The Mathematical Sciences refers a range of topics relating to mathematics and its applications. It includes areas commonly known as Pure Mathematics, Applied and Computational Mathematics, and Statistics. Certain subfields of computer science, engineering, life sciences, physical sciences and social sciences, where mathematical methods play an important role, are also included.

The Mathematical Sciences major programme is designed with flexibility in mind. Students get to choose a track of study — Pure Mathematics, Applied Mathematics, Statistics, or Business Analytics — that most appeals to them.

## 2. What is the intake size?

Each year's planned intake size is around 200, but the number may change depending on the quality of the applicants and other factors.

## 3. What are the requirements for applying to the major in Mathematical Sciences?

Click here for our admission requirements. Broadly speaking, you need a good pass in A-Level Mathematics or its equivalent. If you are a diploma holder from a polytechnic in Singapore, you should preferably have done well in several mathematics courses.

## 4. Would I be disadvantaged if I did not do Further Mathematics at A Level?

Our curriculum does not assume knowledge of A-Level Further Mathematics. Students who have studied A-Level Further Mathematics might have a slight advantage, but what matters most is each individual student's readiness to learn, ability to absorb new knowledge, and effort.

## 5. How does Mathematical Sciences in the university differ from the Mathematics we learnt in junior college or polytechnic?

You can expect to learn a wide range of new mathematical topics (both pure and applied) not covered in pre-university curricula. Moreover, Mathematical Sciences at the university level places special emphasis on thinking and reasoning in a logical and rigorous way, and arriving at deep understandings of concepts and proofs (which can include eventually developing one's own concepts and proofs).

## 6. What are the special features and strengths of the undergraduate programme in Mathematical Sciences at NTU?

Similar to many other undergraduate programmes in the Mathematical Sciences, our programme aims to equip the graduates with strong logical thinking, reasoning, and problem-solving skills. Compared to some other Mathematics or Mathematical Sciences programmes, ours stands out in the following ways:

**Computational skills**are incorporated throughout our curriculum. Such skills are increasingly important both in the workplace and in mathematical research. Apart from a compulsory course in scientific programming, many courses include a programming component.- We offer
**special challenges for outstanding students**, in the form of "Advanced Investigations" courses taken in tandem with our regular courses (calculus, linear algebra, etc.) These enrich the material by introducing additional challenging problems to solve. At higher levels, we offer a variety of Special Courses and the opportunity to pursue a research project under the personal supervision of a faculty member. - Our programme is deliberately
**interdisciplinary**in nature, in recognition of the important role played by mathematics and statistics in science, engineering and social sciences. Our curriculum is not limited to courses from the Division of Mathematical Sciences; prescribed electives in other disciplines can be used to fulfill the coursework requirements.

## 7. What do the "tracks" in the major programme refer to?

Once each student has acquired a strong set of mathematical fundamentals, it is important to specialize in one area for advanced study. We have organized the programme into four distinct tracks – Pure Mathematics, Applied Mathematics, Statistics, and Business Analytics.

**Pure Mathematics**focuses on theoretical and foundational issues, as well as proving techniques. It is ideal for students who enjoy mathematics for the beauty and rigour of the subject, as well as those planning to pursue a career in mathematics research or education.**Applied Mathematics**is concerned with the development and use of mathematical methods that have scientific, technological, or business applications. Emphasis is given to problem-solving and IT skills that are useful in tackling real-world problems. Students are encouraged to learn about disciplines outside mathematics, such as engineering, computer science, the biological sciences, the physical sciences, etc.**Statistics**is about the collection, analysis and interpretation of numerical data. It has important and specialized applications in biological sciences, economics and finance, computer science, etc. Students in this track are encouraged to venture into some of those application areas, to gain better insight into how statistical techniques are used in practice.**Business Analytics**is about the application of advanced mathematical methods for optimizing, predicting and decision-making in the business world. This includes topics such as Optimization, Operations Research, Data Mining, Time Series Analysis, etc. This track includes courses from the Nanyang Business School and the School of Computer Science and Engineering.

For Pure Mathematics, Applied Mathematics, and Statistics, the choice of track only needs to be made in the second year of study. For the Business Analytics track, some additional advance planning is necessary, due to the need to take courses from other schools. Click here for the curriculum details.

## 8. After choosing one track, can I still read courses from the other tracks?

Yes. Within the curriculum, there is some room (a few AU) in each track for students to read any MH3XXX/4XXX course as Prescribed Electives (so long as course prerequisites are met). You can also take courses from other tracks as Unrestricted Electives.

## 9. Can I complete the degree in less than 4 years?

While the programme is structured for four years of study, students who can handle more than 18 AU per semester can accelerate their studies and graduate sooner; click here for information about the Accelerated Bachelor Programme. If a student meets the prerequisites for a particular course, he/she is permitted to read it. However, we do not advise students to overload in every semester, so that they have ample time to gain an in-depth understanding of the material.

Students who enter the programme with exceptional amounts of prior preparation might be granted some course exemptions. For inquiries, please email SPMS_UG_Adm@ntu.edu.sg.

## 10. As a Mathematical Sciences major, will I need to read other science courses (e.g., physics or chemistry)?

For Mathematical Sciences majors in the Pure Mathematics, Applied Mathematics, and Statistics tracks, there are no requirements to read physics or chemistry courses (though we do encourage students to broaden the scope of their knowledge and interests). For students in the Business Analytics track, some courses in the Nanyang Business School are required.

For students in joint programmes, courses in the allied discipline are obviously required. For example, the Mathematical Sciences and Economics (Double Major) programme requires taking Economics classes.

# Career Prospects

## 1. What are my career prospects with a degree in Mathematical Sciences?

A Mathematical Sciences degree equips a graduate with skills for a wide range of careers. Jobs landed by our recent graduates include: actuary, computer programmer, cryptologist, data analyst, financial analyst, financial planner, investment analyst, operations research analyst, quality control analyst, research scientist, resource management analyst, statistician, systems analyst, teacher, transportation analyst, etc.

Companies and organisations that have employed our recent graduates include HSBC, Citibank, ANZ, the Singapore Department of Statistics, GIC, DSO, and Microsoft. Some of our graduates have gone on to further studies at renowned universities like UC Berkeley, Brown, Cornell, UC Davis, LSE, and Princeton.

## 2. I am interested in Actuarial Science. Does your programme prepare students to become actuaries?

Actuarial Science is an interdisciplinary field involving a combination of skills from mathematics, statistics, econonomics, and finance. To qualify as a full-fledged actuary requires passing professional examinations as well as having working experience. To our knowledge, no degree program in any university automatically qualifies its graduates as actuaries.

An undergraduate degree in the Mathematical Sciences is excellent preparation for becoming an actuary, and may even enable the student to obtain exemptions from some stages of the professional examinations. Students in the Mathematical Sciences and Economics (Double Major) programme are particularly advantaged, because of their extra exposure to economics and finance topics.

# Double Major Programmes

## 1. What topics are covered in the Math and Comp Science Double Major programme?

In the BSc in Mathematical and Computer Sciences (Double Major) programme, students take courses in foundational mathematics and follow it up with in-depth topics in Computer Science, focusing on the more mathematical aspects as such Theoretical Computer Science, Cryptography and Cybersecurity, Financial Modelling, and Data Science. Click here for more information.

## 2. In the Math and Comp Science Double Major, do I still choose a Maths specialisation track?

No. The curriculum for this Double Major programme uses its own list of advanced mathematics electives, which are not divided into tracks like in the Mathematical Sciences degree programme.

## 3. What is the difference between the Maths and Comp Science Double Major and the Data Science and AI (DSAI) programme?

The Mathematical and Computer Sciences programme is a Double Major programme, whereas the DSAI programme is a single major programme. The former has a heavier courseload (149 AU versus 135 AU) and covers a wider range of topics, whereas the latter focuses on a more specialised set of topics revolving around data science, statistics, and machine learning.

## 4. How does the Maths and Econs Double Major curriculum differ from the Mathematical Sciences curriculum?

In the BSc in Mathematical Sciences and Econonomics (Double Major) programme, students fulfill roughly 85 percent of both the Mathematics curriculum and the Economics curriculum. The curriculum is designed to emphasise the areas of mathematics most relevant to Economics. Click here for more information.

## 5. In the Maths and Econs Double Major, do I still choose a Maths specialisation track?

Yes, students in this programme pick one mathematical specialisation track, similar to the Mathematical Sciences degree programme.

## 6. What is the difference between the Physics and Mathematical Sciences Double Major and the Physics with Second Major in Mathematics (PHMA) programme?

The old PHMA programme was classified as a Second Major rather than a Double Major. It will no longer be offered from Academic Year 2020 onward (except for returning NSMen, who will be given a choice to remain in PHMA or switch to the new Double Major programme).

Whereas the PHMA programme had slightly more emphasis on physics coursework, the new Physics and Mathematical Sciences Double Major programme strikes a roughly even balance between physics and mathematics coursework (both subjects take up equal numbers of Academic Units in the curriculum).

## 7. In the Physics and Mathematical Sciences Double Major, do I still choose a Maths specialisation track?

No. The curriculum for this Double Major programme uses its own list of advanced mathematics electives, which are not divided into tracks like in the Mathematical Sciences degree programme.

# Minor in Mathematics

## 1. Is there an entry requirement to take a Minor in Mathematics?

No, except that you must satisfy the prerequisites for each course you choose to read.

## 2. Can the School help me if there are clashes in the time-table?

Unfortunately not. It is the responsibility of the students to ensure that there are no clashes in their class and examination time-tables.

## 3. If I am not in the Minor programme, can I just take one Course?

Students who do not intend to pursue a Minor in Mathematics, but who are interested in reading some mathematics courses, may certainly also do so. However, note that most MAS courses have a quota for enrolment, due to constraints in available teaching resources. Priority is given to students who need to complete the course to fulfill major or minor requirements.

## 4. Will I be dropped from the Minor programme if I fail a MHXXXX course?

No. If you fail a course, you can always read it again the next time it is offered, or even read a different Course to fulfill the requirements of the Minor in Mathematics. So long as you satisfy all the requirements by the time you graduate, you will graduate with the Minor in Mathematics. If, for some reason, you are unable to complete the requirements for the Minor in Mathematics by the time of your graduation, then you will simply graduate without the minor.

## 5. The curriculum for my major includes some mathematics. Can the credits from those courses count towards the Minor in Mathematics?

No. Credits from the same course cannot count towards both a major and a minor.

## 6. Some MAS courses topics overlap with courses in my major. Can I still read MAS courses on topics I have already learnt?

You are strongly advised and encouraged to read something different in this case – and there are enough MAS courses for you to choose from to avoid such overlaps. The intended purpose of a minor is to help you build expertise in a subject beyond your major. Reading MAS Courses that overlap significantly with courses in your major defeats this purpose. You are missing a great opportunity to add value to your education!

## 7. Some MAS courses topics overlap with courses in my major. Can I use the courses from my major to fulfill course prerequisites for MAS courses?

This will be considered on a case-by-case basis, depending on factors like the extent of the overlap, the approach used, etc. For inquiries, please email SPMSUndgrad@ntu.edu.sg.

# SPMS Co-Operative Education Programme

## 1. What is the Co-Operative Education Programme?

The SPMS Co-Operative Education Programme places students in well-established companies for work experiences throughout their four years of studies in NTU. Participating students undertake an intensive credit-earning internship (some of which may be conducted overseas) in a participating company. The final 30-week work term also doubles up as an industrial Final Year Project (FYP), co-supervised by the company and a professor.

The aim of the programme is to enhance participating students' education with practical work experiences. This enables them to progressively master the practical skills needed for their future careers.

## 2. What is the difference between the Co-Op Programme and normal internship?

The normal internship is shorter (22 weeks) and usually starts in Year 3 or 4. The Co-Op Programme consists of 50 weeks of internship, starting from the end of Year 1 and spread over 3 terms. It provides a much more structured and in-depth working and training experience.

However, for new students enrolling into SPMS from AY2021-22 onwards, a Professional Internship OR Professional Attachment with a Final Year Project is required, as part of NTU's ICC curriculum.

## 3. When and how do I apply for the Co-Op Programme?

Interested students must first apply for an SPMS degree programme. Once admitted, they will be directed to apply for the programme through the SPMS website, typically after the first semester of study. The candidates are then interviewed by NTU and representatives from the partner companies, in order to match the interests and capabilities of the students with the companies.

Please note that students in Double Major programmes, the CN Yang Scholars Programme, and the University Scholars Programme are not eligible for the Co-Operative Programme, because the additional academic/scholarship commitments make it impossible to fulfill the Co-Op internship requirements.

## 4. Do I get paid doing the internship with the company?

Yes. Interns are paid a monthly stipend; the exact amount depends on the company.

## 5. Do I have to stick to one company throughout the Programme?

Yes, participating students are expected to stay with the same company throughout the programme. The extended training within a single company is intended to give exposure to different functions within the organisation.

# Final Year Projects and Internships

## 1. Can I do both the Final Year Project and an Internship?

Students doing (or planning to do) a Final Year Project are not allowed to take MH4903 (Professional Internship), the 22-week long internship programme. However, it is still possible to undertake a 12-week attachment, MH4907 (Professional Attachment), as an Unrestricted Elective.

However, for new students enrolling into SPMS from AY2021-22 onwards, a Professional Internship OR Professional Attachment with a Final Year Project is required, as part of NTU's ICC curriculum.

2. Can I choose not to do the Final Year Project or an Internship?

For most of our programmes, the answer is yes. You simply have to make up the remaining AU through other courses in the chosen track; please consult the curriculum for details. Please note that students are only eligible to graduate with Honours (Highest Distinction) if they take the Final Year Project, and obtain a grade of A- or better. The Double Major programme in Mathematical Sciences and Economics does require a Final Year Project.

However, for new students enrolling into SPMS from AY2021-22 onwards, a Professional Internship OR Professional Attachment with a Final Year Project is required, as part of NTU's ICC curriculum.

3. How do I choose between Final Year Project and Internship?

It depends on each student's needs. The Final Year Project is strongly encouraged for students who intend to pursue further studies (at the Master and/or PhD level). Students who have a strong interest in building a career may benefit from doing an internship.

Please also note that students are only eligible to graduate with Honours (Highest Distinction) if they take the Final Year Project, and obtain a grade of A- or better.

4. I am doing a Double Major in Mathematical Sciences and Economics. Can my Final Year Project supervisor be from the Division of Economics?

For students pursuing a Double Major in Mathematical Sciences and Economics, the Final Year Project (MH4900) **must** have an MAS faculty member as the main supervisor. If the project covers both Mathematics and Economics disciplines, students can choose a co-supervisor from the Division of Economics.

## 5. Will I be automatically granted Honours (Highest Distinction) if I do the Final Year Project?

No, you will need to satisfy all the requirements for Honours (Highest Distinction). This includes receiving an FYP grade of A- or above.

## 6. How do I prepare the Final Year Project proposal?

The proposal should be no more than 2 pages, and it should succinctly describe the motivation/significance of the project, the fundamental problems and underlying difficulties, and your research plan and methods. For more detailed advice, please consult the faculty member who has agreed to be your supervisor.

## 7. How do I prepare for the FYP presentation?

A good FYP presentation should cover the following ground:

- General introduction to the project
- Motivations and relevance
- Difficulties and your specific goals
- Relevant highlights from your literature review
- Your choice of methods / techniques / equipment
- Your main results, outline of the proofs and/or the experiments you conducted
- Your insights and conclusions
- Some ideas for extending your work

For more detailed advice, please consult your supervisor.

## 8. How do I write the Final Year Project thesis?

Here are some basic requirements and tips:

- The thesis should be prepared in Word or LaTeX, formatted for printing on A4 paper with appropriate fonts (Word: Arial 11; LaTeX: Computer Modern 11pt). A good size for margins is 2.5 cm top and bottom, 2 cm on the right and at least 2.5 cm on the left (maybe more, depending on the binding process).
- The title page should contain the project title, your name, the purpose of the project (“it is submitted as part of the honours requirements”), the name of supervise/co-supervisor, the submission date (month and year), and the Division (“Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University”). The next page should contain an Abstract. The page after that may be used for Acknowledgements.
- There should be a table of contents, listing the chapters, sections and sub-sections (if any), each with its page number. Do not subdivide any further.
- After the table of contents, you may incldue separate lists of figures, tables, and/or code segments.
- Chapters constitute the main body of the thesis. In all, they should occupy about 30–50 pages (single-spaced). Writing more than 50 pages is discouraged.
- A list of references, and possibly an annotated bibliography, should follow the main body. References should use the commonly used styles (including author and year).
- You may include appendices containing relevant but secondary material (e.g., program listings) may be added. Appendices help to keep the main text more focused.

## 9. What are the marking criteria for Final Year Project?

The FYP grade consists of:

- FYP thesis (50%)
- FYP presentation (40%)
- FYP middle-term progress report (10%)