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Course FAQs

- What constitutes Mathematical Sciences?
- What is my career prospect like with a degree in Mathematical Sciences?
- 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 would Mathematical Sciences in the university differ from the Mathematics we learnt in the junior college or polytechnic?
- What are the special features and strengths of the undergraduate programme in Mathematical Sciences at NTU?
- Must I spend four years to complete the degree, or can I accelerate?
- If I major in Mathematical Sciences, am I also required to read some other science Courses (like Courses from PAP or CBC) during my course of study?
- I am interested in Actuarial Science. Does the programme in Mathematical Sciences or the combined major in Mathematics and Economics prepare students to become actuaries?

- Is there an entry requirement to take a Minor from your division?
- Can the School help me if there are clashes in the time-table?
- What if I do not get selected for the Minor? Can I just take one Course?
- Will I be dropped from the Minor programme if I fail any of the MAS xxx Courses?
- In the curriculum for my major, we have already studied some mathematics. Can the credits from those Courses be counted towards the Minor in Mathematics also?
- Some of the MAS Courses seem to overlap quite a bit with some of the mathematics Courses in the curriculum of my major. (E.g., many engineering courses have some Courses in Calculus and Linear Algebra, while Computer Science has some Discrete Mathematics, and some other courses may have Probability and Statistics.) Am I still allowed to read the MAS Courses that overlap with these mathematics Courses that I have learnt in my major?
- My major curriculum has some mathematics (like Calculus, Linear Algebra, etc) that overlaps with certain MAS Courses which form the pre-requisites for other MAS Course. Can I use the mathematics Courses in my major to fulfill these pre-requisites?

Mathematical Sciences is a term used to describe a broad range of Courses related to mathematics, statistics and their applications. In particular, it includes what are commonly known as Pure Mathematics, Applied and Computational Mathematics, and Statistics. Certain subfields of computer science, engineering, life sciences, physical sciences and social sciences, in which mathematical tools play an important role, are also often regarded to be part of or related to mathematical sciences.

For the Major in Mathematical Sciences offered in NTU, students get to choose to focus on one of the three tracks in Pure Mathematics, Applied Mathematics and Statistics, with emphasis on both the theory and the applications – hence the name of the major.

An Honours degree in Mathematical Sciences equips a graduate with the skills and foundation for a wide range of careers in both the private and public sectors. Organisations in Singapore where graduates in Mathematical Sciences have found satisfying careers include: banks, insurance companies, IT companies, SIA, PSA, the education service, DSO National Laboratories, Mindef, Ministries of Home Affairs, Health, Trade and Industry, as well as various R&D organisations.

The jobs secured by graduates in Mathematical Sciences include: actuary, computer analyst, computer programmer, cryptologist, data analyst, financial analyst, financial planner, investment analyst, market research analyst, numerical analyst, operations research analyst, quality control analyst, research scientist, resource management analyst, software analyst, statistician, systems analyst, teacher, transportation analyst, etc. Other than these choices, many graduates in Mathematical Sciences have also found employment in non-technical positions such as administrators, where their training in analytical and problem-solving skills also come in handy.

Some other helpful websites that provide some answers to this burning question may be found at:

- Mathematical Sciences Career Information at www.ams.org/careers/
- Mathematical Association of America's profiles of individuals at www.maa.org/careers/index.html;
- A video of Careers in Mathematics containing interviews with graduates in mathematical sciences posted at www.msri.org/ext/CareersInMathematics.html.

To major in Mathematical Sciences at NTU, you should have at least a good pass at 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.

The curriculum for Mathematical Sciences does not assume knowledge of A Level Further Mathematics. Nonetheless, those who have done Further Mathematics at A Level might have a slightly better background to start with. However, what probably matters more is your readiness and ability to pick up new knowledge and to adapt to new approaches to the subject.

For one thing, you can expect to learn a wide range of new topics in the programme in Mathematical Sciences in the university. Furthermore, as the programme aims to equip the graduates with strong logical thinking, rigour in reasoning, analytical and problem-solving skills, much emphasis is placed on understanding of concepts and proofs, development of theory and mathematical arguments, as well as the links with applications.

First, as is common to any undergraduate programme in Mathematical Sciences, the programme at NTU aims to equip the graduates with strong logical thinking, rigour in reasoning, analytical and problem-solving skills.

Besides the above, our programme has built in the following special features, to provide value-added education to our graduates:

**IT skills**– believing that IT skills are important for the workplace of today and tomorrow, our curriculum incorporates the use of IT wherever it is appropriate. Apart from a compulsory Course in scientific programming, many Courses also include a laboratory or programming component.**Communication skills**– believing that communication skills are crucial for a successful career, our programme emphasizes this valuable asset and seeks to equip our graduates in this useful skill through both formal instruction and immersion. Besides the compulsory writing and communication Courses under the requirements of the SPMS and GER, the programme in Mathematical Sciences also has a compulsory Course in "Mathematical Exposition" where students will be taught the basic skills in oral and written presentations of technical material. Moreover, some Courses will also provide ample opportunities for the students to present their thoughts and ideas both orally and in writing.

**Special challenge for outstanding students**– recognising that we should not adopt the one-size-fits-all approach to educating our students, we have put in place a series of "Advanced Investigations" Courses in Levels 1 and 2 for those outstanding students who want to be given tough and challenging problems to work on. These additional Courses will allow them to be stretched and challenged, thus bringing out their best potential. At the higher levels, special Courses such as undergraduate research, special topics, project, supervised independent study, etc., will provide further opportunities for them to push themselves to greater heights.**Interdisciplinary studies**– recognising the important role played by mathematics and statistics in numerous applications in science, engineering and social sciences, and reflecting better the nature of Mathematical Sciences, the curriculum for the Major in Mathematical Sciences attempts to incorporate Courses from other relevant disciplines into the programme, so that graduates from the programme will, on the one hand, be firmly grounded in the theory and, on the other, be familiar with how the theory is used in practice.**Optional Industrial Internship**– acknowledging the value of exposure to how the skills and knowledge acquired during the studies are put to use at the workplace, we have an optional Industrial Internship programme that allows our undergraduates to spend some time working in a relevant industry and chalk up some credits at the same time. This experience will give them a foretaste of the work environment and could enhance their appreciation of how their knowledge can be put to use in practice.

Given the broadness of Mathematical Sciences, it is important to build in some focus in the Major in Mathematical Sciences, so that graduates from the programme have both breadth and depth in their knowledge. We have therefore organized the programme into three distinct tracks – Pure Mathematics, Applied Mathematics and Statistics.

Students are strongly advised to choose the track according to their interest, aptitude and intended career option.

**Pure Mathematics**is a term commonly used to describe theoretical mathematics, where the focus tends to be more on theory and foundations, as well as proving techniques. It is ideal for those who enjoy mathematics for the beauty and rigour of the subject. It is also an excellent preparation for those who aspire to go for graduate studies in mathematical sciences. This track is equally ideal for those planning on joining the teaching profession.**Applied Mathematics**, as the name suggests, is concerned with the kind of mathematics useful for application in everyday life, as well as the applications themselves. The focus of this track is to equip graduates with the mathematical knowledge that is relevant to real-life applications and basic knowledge and appreciation of some of these applications. Emphasis is thus given to problem-solving and IT skills that are useful in tackling real-life problems. Students will also be encouraged to learn about disciplines outside mathematics where mathematical tools have played an important role, e.g., engineering, computer science, biological sciences, physical science, etc.**Statistics**is about the collection, analysis and interpretation of numerical data, so this track will focus on these themes and will emphasise the practical aspect. As statistics is often used in applications in biological sciences, economics, finance, computer science, etc., students in this track are also urged to venture into some of these Courses to gain a better insight of how statistics is used in these applications.

All students in the Major in Mathematical Sciences, regardless of the track chosen, will read common core Courses in fundamental topics such as: calculus, linear algebra, basic discrete mathematics and number theory, probability, as well as scientific programming and mathematical exposition, before they branch into further specialized topics.

Topics that students in the track in Pure Mathematics can read include: algebra, analysis, discrete mathematics, geometry, logic, number theory, topology, etc.

For students in the track in Applied Mathematics, they may choose Courses from: analysis, computer science, discrete mathematics, numerical analysis, operations research, scientific computing, theoretical physics, etc.

As for students in the track in Statistics, they can read Courses from: applied statistics, mathematical statistics, operations research, probability, as well as Courses from business, economics, computer science, etc.

Sure. Within the 72 AU required for the Major in Mathematical Sciences, there is some room (a few AU) within each track for the students to read any MAS 3xx or 4xx Course with no restrictions (except that the pre-requisites must be satisfied).

Furthermore, students majoring in Mathematical Sciences have 42 AU of Unrestricted Electives in their graduation requirement. These 42 AU can be used in any way you like, including any MAS Course that you might like to read (so long as you have the pre-requisites). Hence, for example, if you have chosen the track in Applied Mathematics, but would like to read a few more Courses in either Pure Mathematics or Statistics, you can always make use of some of these 42 AU to do so!

It all depends. Some jobs may prefer graduates with certain specific backgrounds, while others may not have such a requirement. For example, some jobs which involve handling of numerical data may prefer someone who has some knowledge of statistics; an operations research analyst should of course know some operations research. However, many jobs may only require a degree in Mathematical Sciences in general and expect the applicants to pick up new knowledge and skills on-the-job. Generally, students who hope to land a job in a specific industry should probably try to read some Courses in a related subfield.

While the programme is generally structured into four years, students who can handle more than 18 AU per semester can always choose to accelerate their studies and graduate sooner. So long as a student meets the pre-requisites for a particular Course, he/she will be permitted to read it. However, it is also advised that students should not overload themselves in each semester so that they have ample time to gain an in-depth understanding of the Courses they read.

Students who enter the programme very well prepared may also be granted some Advanced Placement credits if they qualify.

There are no such requirements for students majoring in Mathematical Sciences (except PMC 111, which is part of the requirement for the major). However, we strongly encourage students to broaden their knowledge and build up an interdisciplinary interest, so it is not a bad idea to read some Courses from PAP and CBC, or even build a minor around them.

No. There is only one single major – in Mathematical Sciences. Pure Mathematics, Applied Mathematics and Statistics are just tracks within this one major. If you are interested in Courses in more than one track, you can always choose one track to focus on for your major, while at the same time read Courses from other tracks using the 42 AU of Unrestricted Electives available to you.

Yes, sure. However, you must still choose a track (in this case, either Pure Mathematics or Applied Mathematics) for your major and fulfill the requirements for this track (which already allows you some room to read Courses outside your track). You can also use part of the 42 AU of Unrestricted Electives to read additional MAS Courses. The reason we insist on your choosing a track is to ensure that you have sufficient focus in your selection of Courses, so that you will have both depth and breadth of knowledge when you graduate.

You are probably referring to the two concentrations here. Each concentration puts together a group of Courses in a related theme to give the students some additional depth and focus in their studies, if they would like to do so.

Mathematics of information and communication refers to topics in mathematical sciences commonly used in modern-day applications in information technology and communication. For example, cryptography is crucial in protecting confidentiality in electronic transactions and electronic commerce; coding theory plays an important role in detecting and correcting errors in telecommunications and data storage. Therefore, Courses in this concentration help to build a focused cluster of knowledge around this theme.

Computational mathematics – a much broader area – basically concerns the kind of mathematics that is used commonly in engineering and physical sciences, for example, where a mixture of analysis, numerical analysis and computing techniques come into play. Given the broadness of this concentration, students choosing this concentration can therefore opt to concentrate on the theory and methods of numerical analysis and scientific computing, or operations research, or topics related to information processing

Actuarial Science is an interesting and challenging field. Interesting because it involves a variety of skills – mathematics, statistics, econs, finance, etc., and challenging because the series of exams needed to be passed for one to qualify as a full-fledged actuary is very demanding and often requires many years of working experience as well. No degree program in any university is such that its graduates automatically qualify as an actuary. However, a good undergraduate program in either actuarial science or mathematical sciences can be an excellent preparation and can enable the student to either obtain exemptions from some of the stages of the professional exams, or they can at least prepare them very well so that they can pass those first few stages of the professional exams easily.

In particular, some comparisons with some of the best actuarial science programs in the UK suggest that the Mathematical Sciences major and the combined major in Mathematics and Economics in NTU are excellent preparations for students who want to do actuarial science eventually.

E.g., by comparing the Actuarial Science program in University of Kent in the UK (one of the most popular programs in the UK) and the Courses offered by the Mathematical Sciences major (or the combined major in Mathematics and Economics) at MAS Curriculum , it is easy to observe that about ¾ of the Kent curriculum is mathematics or statistics, and is covered by our track in Statistics – algebra, calculus, computing, discrete math, probability, mathematical methods, analysis, linear algebra, mathematical statistics, time series, stochastic processes, survival analysis, actuarial statistics, etc. Many of the remaining topics are covered by the Economics curriculum in the combined major in Mathematics and Economics.

Let’s take yet another example – LSE in the UK – another popular Actuarial Science program there. The curriculum is at BSc Actuarial Science. Once again, about ¾ of their Courses are covered by our Track in Statistics, while most of the remaining ones are covered by the Economics part of the curriculum in the combined major in Mathematics and Economics.

The existence of the combined major in Mathematics and Economics means that the timetables of the two divisions are coordinated in such a way to ensure no clashes in the key Courses. Hence, students in the combined major of Mathematics and Economics, as well as those who major in Mathematical Sciences (Track in Statistics) and do a concurrent minor in Economics or Business, will cover just about all the topics covered in the LSE or Kent Actuarial Science program.

In brief, our Major in Mathematical Sciences and the combined major in Mathematics and Economics also prepare students well for actuarial science.

No, except that you will need to satisfy the pre-requisites for each Course you choose to read. E.g., if you choose to read MAS 111, you should make sure you have a pass in A Level Mathematics or something equivalent.

It is the responsibility of the students to ensure that there are no clashes in their class and examination time-tables.

All students in NTU (except SPMS students majoring in Mathematical Sciences and NIE students in the B.Sc.(Ed) course with Mathematics as their Academic Subject) may select the Minor in Mathematics.

Students should, however, be aware that most MAS Courses do have a quota for enrolment, simply due to constraints in the resources available. Given the flexible curriculum for the Minor in Mathematics, you do have a wide range of Courses to choose from in order to fulfill the requirements of the minor. Hence, if you are not able to read a certain MAS Course in a particular semester (due to the quota), you have the freedom to either read a different Course to fulfill the requirements of the minor, or read this particular Course in a different year.

Students who do not intend to have a Minor in Mathematics but who are nonetheless interested in reading some MAS Courses may certainly also do so, again subject to the quota for each Course.

No. If you fail an MAS 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 of the Minor in Mathematics 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.

No. Credits from the same Course should not be counted towards both the major and the minor. You will still need to pass at least 15 AU from MAS Courses to obtain the Minor in Mathematics.

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 purpose of a minor is to help you build some expertise in a subject beyond your major. Reading MAS Courses that overlap significantly with Courses in your major defeats this purpose totally. You are missing a great opportunity to add value to your education!

This will be considered on a case-by-case basis, as it can depend on several factors, such as the extent of the overlap, the approach used (e.g., theoretical vs application), etc. If you feel that you should have the pre-requisite (through some other Courses you have passed), please submit the request and supporting documents to the Division of Mathematical Sciences, and the request will be considered carefully.