Historically, mathematics has been broadly grouped into the fields of "pure" and "applied" mathematics. Recently, however, mathematical development has gone in such a way that this distinction becomes less rigid. Well-known examples include the use of group theory in physics, number theory in the development of codes, foundations and combinatorics in computer science. The latter especially has had some effect on the development of curricula in mathematics. Departments tend to put less emphasis on the traditional calculus sequence, but rather emphasize combinatorial and structural topics, as well as integrate the use of computers into the curriculum wherever appropriate. The current curriculum aims to reflect this change in outlook.

mathematics at UBD

BSc (Mathematics)

The successful completion of the courses of study for this four year honours degree programme with a Major in Mathematics and a choice of a Minor in some other (not necessarily science) subjec as set out in the Regulations shall lead to the award of a BSc(Maths) degree. The aim is to produce marketable graduates who, with a sound foundation in mathematics, will possess an expertise attractive to a wide range of potential employers in Brunei and elsewhere. During the long vacation after Semester 6, the candidate shall be required to undertake a practical attachment. This shall involve the candidate's attachment to an institution in the public or private sector in Brunei or elsewhere, to gain first-hand experience in the application of the theories and techniques learnt at UBD and to investigate problems in a real-world environment. A short research project will be carried out by the candidate in semesters 7 and 8.

BSc (Computer Science)

This is a four year honours degree programme with a Major in computer Science and a choice of a Minor in some other (not necessarily science) subject. The aim is to produce graduates with a sound foundation of Computer Science. Students taking Mathematics as their Minor may transfer to the University of Strathclyde, Glasgow, Scotland, after completing semester 4; their final degree in this twinning arrangement is awarded by the University of Strathclyde after two further years.

BSc (Mathematics Minor)

The Department of Mathematics offers courses in mathematics to candidates for a BSc degree in the Faculty of Science, who take Mathematics as a minor subject. Such candidates must normally have an Advanced Level pass at a G.C.E. or equivalent examination. A total of 16 units of mathematics courses must be taken from Semester 1 to Semester 6 in order to satisfy the minor part requirements for the BSc programme.

Twinning and credit transfer programmes in Computer Science

A candidate who has successfully completed the examinations for Semesters 1 & 2 of the BSc(Maths) programme may elect to enter the Computer Science stream of the programme. After successfully completing Year 2 in this stream, the candidate may transfer to Year 3 of the BSc twinning programme in Computer Science at the University of Strathclyde in Scotland or to another university with which UBD has established a credit transfer agreement in Computer Science. He/she must also complete and pass the prescribed courses for such transfer students, as set out in the Schedule of Courses, and satisfy other conditions as spelt out in the BSc(Maths) Regulations.

The successful completion of the courses of study for the twinning or credit transfer programme, initially at UBD and subsequently at the partner university, shall lead to the award of a BSc in Computer Science by that university.

Twinning program in Electronics and Electrical Engineering with the University of Glasgow in Scotland

The Department of Mathematics offers mathematics and computer science courses in the twinning programme in Electronics and Electrical Engineering at the University of Glasgow, during the first four semesters (i.e. two years), to prospective candidates at UBD.

A candidate who has successfully completed the examinations for Semesters 1 to 4 at UBD, as prescribed for the twinning program, and who has also satisfied other conditions as specified in the Regulations for this twinning programme, shall be transferred to the University of Glasgow for the last two years (i.e. six terms) of the programme.

The successful completion of the courses of study for this twinning programme, initially at UBD and subsequently at the University of Glasgow, shall lead to the award of a BEng (Electronics and Electrical Engineering) by the University of Glasgow.

BA (Faculty of Arts and Social Sciences; Minor in Mathematics)

The Department of Mathematics offers courses in mathematics and computer science to candidates for a BA degree in the Faculty of Arts and Social Science, who take Mathematics as a minor subject. Such candidates must normally have an Advanced Level pass in Mathematics at a G.C.E. or equivalent examination.

A total of 32 units of mathematics and computer science courses must be taken and passed from Semester 1 to Semester 6 in order to satisfy the minor part requirements for this BA programme. The break-down of the units to be taken and passed is as follows: 4 units in Semester 1, 4 units in Semester 2, 6 (=2+2+2) units in Semester 3, 6 (=2+2+2) units in Semester 4, either 4 or 8 units in Semester 5, and either 6 or 2 units in Semester 6. In Semesters 5 and 6, candidates may choose any 8 units from the courses :

MA 2110 (2) Introduction to Statistics, or
MA 2111 (4) Statistics I,
MA 2213 (4) Real Analysis,
MA 3203 (2) Introduction to Complex Analysis,
MA 3611 (2) Operations Research I,
MA 3612 (2) Operations Research II,

[Candidates must choose one (and only one) of the Statistics courses MA 2110 and MA 2111.]

BScEd (Sultan Hassanal Bolkiah Institute of Education[SHBIE], Major and Minor in Mathematics)

The Department of Mathematics provides courses for the mathematics and computer science components of the BScEd programme offered by SHBIE.

a. Aims and Objectives

The aim is to produce competent graduates who will be able to teach mathematics and computer studies successfully in secondary schools up to and including GCE A-level standard or equivalent. It is expected that after four years of study, the graduates should

• have detailed knowledge and mastery of the mathematics in the secondary schools curriculum,
• display a mastery of the principal skills required for work in mathematics,
• have a perspective of the secondary schools mathematics and computer studies curriculum acquired from familiarity with the advanced developments of mathematics and computer studies to which the secondary schools studies lead,
• have sufficient appreciation of the power and elegance of mathematics, and of the impact of computers on society, to successfully motivate the pupils under his charge.

b. Programme Structure

A candidate majoring in mathematics reads 44 units of mathematics courses over five semesters. A minor in mathematics reads 20 units of mathematics courses over 4 semesters

Semester	Units for Major	Units for Minor
1	4	4
2	4	4
3	10	6
6	10	6
7	16	-
Sum:	44	20

Obtaining all of these units is a necessary requirement for successfully completing the mathematics component of the BScEd programme. In addition, the compulsory courses CO 1601 Introduction to Computing and CO 1603 Computer Programming (each of weight two units) must be passed.

c. Programme Outline

The first year courses serve as an introduction to mathematical techniques and methods, using topics from calculus and analytic geometry. Arguments will be mainly intuitive, although proofs will be given for some theorems. Furthermore, strategies and patterns of problem solving will be developed. Each of the courses carries four credit units.

In addition, in each of the first two semesters there will be a compulsory two credit unit course on introduction to computers and programming. Candidates are taught to use microcomputers and to write simple programs using an appropriate language.

These first year courses are to be taken by every candidate choosing Mathematics as one of the two science subjects. For those candidates in the BScEd programme who do not read Mathematics and those in the BEd (General Science) programme who do not have A-level Mathematics, there are two compulsory preliminary mathematics courses in which basic algebra, calculus and statistics are taught.

In Semester 3, a range of courses is offered. The topics to be studied by major and minor students are Introduction to Discrete Mathematics, Algebra I, Ordinary Differential Equations with Applications and Real Analysis (major students only).

BScEd and BAEd candidates do not take any Mathematics courses during Semesters 4 and 5. In Semester 6, BScEd (Major) candidates continue with Algebra II, Statistics I, Multivariate Calculus and Numerical Analysis I, while BScEd (Minor) and BAEd (Minor) continue with Introduction to Statistics, Multivariate Calculus and Numerical Analysis I. For BscEd (Minor) and BAEd (Minor) candidates, Mathematics courses end at Semester 6.

In Semester 7, BScEd (Major) candidates continue with a wide range of more specialised Mathematics courses, totalling 16 units, which would include electives and the Mathematics Seminar course.

BA Ed (SHBIE, Minor in Mathematics)

The Department of Mathematics offers courses in Mathematics for the BAEd programme with Mathematics as a minor subject. Candidates take the same programme as BScEd Mathematics Minor students, except they omit CO1601 and CO1603.

BEd (General Science) [SHBIE]

The BEd (General Science) programme was introduced by SHBIE in the academic year 1998/99, to produce graduates capable of teaching integrated science and combined science. Candidates without A-level Mathematics are required to take MA 1601 and MA 1602 in their second year of study, during semester 3 and semester 4, respectively. Candidates with A-level Mathematics or equivalent take CO 1601 and CO 1603, in lieu of MA 1601 and MA 1602.

units & assessment

A 4-unit course normally consists of four 50-minute lectures per teaching week and tutorial/problem-solving sessions as necessary.

A 2-unit course normally consists of two 50-minute lectures per teaching week and tutorial/problem-solving sessions as necessary.

In Computer Science courses there are generally fewer lectures but a substantial number of practical/laboratory classes.

A candidate's performance in each course shall be assessed by coursework and a written examination at the end of the semester. The coursework component normally constitutes 20% of the total mark and the final examination 80% for Mathematics courses. For Computer Science courses the weightage is normally 30% for the coursework and 70% for the final examination. Particular courses may require modifications of these norms in some cases. A different mode of assessment applies to MA 4614 (Mathematics Seminar) for example, and MA 4217 (Mathematics Project) in the fourth year: these courses are continuously assessed, and there is no required end-of-semester examination.

methods of evaluation

Instructional Components

In a normal lecture course, the student receives instruction by

1. listening to explanations given by the lecturer,
2. participating in class discussions,
3. reading the relevant sections of the textbook or the lecture notes as well as selected chapters from reference books.
4. solving problems in class and in assignments
5. attending tutorial or problem-solving sessions,
6. receiving personal guidance by the lecturer,
7. taking quizzes and tests.

Areas of Evaluation

Students are assessed in the following areas for the purpose of evaluation in accordance with the objectives and the level of each course:

1. knowledge and information acquired: recall of theorems, definitions, and concepts;
2. techniques and skills: computation, manipulation of symbols, application of rules;
3. comprehension: ability to understand problems, to translate symbolic forms, to follow and extend proofs;
4. analysis: to analyze, and formulate, problems, and determine the concepts and methods which are applicable;
5. application of appropriate concepts to familiar, and unfamiliar mathematical and non-mathematical situations.

Objectives of Evaluation

Any form of evaluation such as, in particular, a test or quiz, for a course is expected to be both

formative: the objective is to monitor the candidate's progress and improve his performance, and to serve as feed-back for both learner and instructor, in case adjustments of learning and teaching have to be made;

summative: the objective is to give the learner the opportunity to demonstrate understanding, and the teacher the opportunity to assess teaching and learning effectiveness.

Forms of Evaluation

For the majority of courses, evaluation of students' performance is by tests, quizzes, written assignments, classroom participation, and end-of-semester examination. The main methods of assessment during the semester are tests, quizzes, or assignments from tutorial question sheets.

Normally a quiz is a useful instrument to assess the knowledge of basic definitions, theorems, and techniques. It can be short and is well-suited for selected response types of questions. Quizzes are usually conducted with closed books. A test, which is normally longer than a quiz, assesses the other components outlined above. Tests as well as end-of-semester examinations may be conducted with open books, if the course contents so permit. Regular assignments give the learner the necessary experience to apply techniques acquired to solve problems on his own.

For the end-of-semester assessment, apart from the usual written examination, other forms may be more suitable, such as an oral examination or a project within the course. This is particularly suitable for courses offered in Semester 7 and Semester 8.