To achieve these objectives, students must first learn the foundations of applied mathematics by doing course work. However, the program is research oriented and students will spend most of their time with research work. In order to foster an environment conducive to international level research, the School of Mathematics has entered into collaboration with applied mathematics departments at various universities abroad.

**Areas of Research:** Since most applied problems involve differential
equations or require solutions on the computer, the program emphasizes
various aspects of ordinary and partial differential equations, applied
analysis and numerical analysis. The following research groups reflect
the interests and activities of the School members, and students may
choose their thesis problems from among these:

**Applied Analysis**: control theory, wavelet theory.**Computational Mathematics**: finite element method, computational fluid dynamics, computer aided graphic design, numerical optimization, parallel algorithm design.**Differential Equations**: analytical methods for constructing exact solutions of partial differential equations, dynamical systems.

**The Master of Science (M.Sc.) Degree:** A Master of Science course
consists of three or four terms of beginning mathematics graduate
courses, followed by a thesis. The course requires a minimum enrollment
of two years and must be completed within four years. During the third or
fourth term, the student must successfully complete a comprehensive
examination, covering the fundamentals of analysis, functional analysis
and numerical linear algebra. After passing the comprehensive
examination students will take up their thesis work, which usually takes
about one year to complete.

The goal of a program leading to the Master's degree is to demonstrate individual accomplishment of high professional and academic standard, as well as to show competence in a topic of current mathematical research.

**The Doctor of Philosophy (Ph.D.) Degree:** The Ph.D. course requires a
minimum period of enrollment of three years and must be completed
within five years for students starting with a M.Sc. degree, or eight years
for students starting with a Bachelor's Degree. The first four terms (two
years for students starting with a B.Sc. degree) are spent mainly with
course work and are followed by a preliminary examination which must
be taken between the fourth to sixth terms. Successful completion of the
preliminary examination will make the student a candidate for the Ph.D.
degree and mark the beginning of the research phase.

A Ph.D. degree is awarded for independent and original research which can be classed as a contribution to knowledge. At least parts of this research must be worthy of publication in a journal of an international standard. To demonstrate such an achievement a candidate is expected to submit a thesis in acceptable format and contents to the thesis committee.

**The Nature of Studies at the Graduate Level:** Graduate study
emphasizes the exploration of new ideas, as well as putting what you
have learnt into context. Such exploration usually requires a much higher
degree of initiative and self-reliance as is expected at the undergraduate
level, a consideration which applies in particular to the thesis work.
While a M.Sc. degree is often pursued to give graduates better
professional qualifications, the main purpose of study at the Ph.D. level is
to prepare for careers in research and development.

Some students may feel that they are interested in research as a goal in itself, and that they wish to pursue graduate studies for this reason. Although this may be an excellent motivation, you should still question whether you fully understand what research is about and what it requires. Talk to the members of the School of Mathematics about your plans and expectations; they are in a good position to answer such questions from personal experience.

A researcher needs to possess sound knowledge of basic mathematical concepts and techniques, skills which are acquired at the beginning of the program through course work. More importantly, as research projects are usually focused on very particular problems, the researcher also needs to have deep insight into the specific subject area. This knowledge is obtained by independent study over an extended period of time, requiring a high degree of motivation and persistence by the student. To be a good researcher you must be genuinely interested in learning new things, and to better understand what you already know. Research is aimed at the discovery of new or clarification of existing but fuzzy ideas. This should be contrasted with product development, which focuses on new products, processes and techniques that have some kind of economic value. Masters or Ph.D. programs can lay a foundation for both types of careers, although a Ph.D. will definitely be required to apply for an academic position at a good university.

**Guidelines for M.Sc. and Ph.D. Students:** Once a student has been
admitted for graduate studies, a general advisor will be appointed by the
School. The student should choose a research area and a thesis advisor as
early as possible, but not later than after the first year of studies.

Students must enroll full time on a continuous basis and register for 7-14 credit hours per term. One graduate course in the School of Mathematics usually carries 4 credit hours. During their research phase, students must register for at least 6 credit hours of thesis work per term.

Students should prepare themselves early for the comprehensive and preliminary examinations, respectively. These examinations not only cover material presented in the lectures, but also undergraduate background and other topics considered fundamental mathematical knowledge. The preliminary examination to be taken by Ph.D. students also evaluates the students ability of independent thought and research potential. A failed examination may be repeated once.

A written thesis proposal, containing a description of the research topic as well as a preliminary work schedule, must be submitted early during the research phase. The proposal must be approved by the thesis committee, which includes among others the thesis advisor and an external examiner who must be from outside the School in the case of a M.Sc. thesis, and from outside the university in case of a Ph.D. thesis. Each student's research progress is evaluated continuously and students showing unsatisfactory progress may be required to withdraw from the program. Graduate students must also present their results in public seminars which are not intended to be an examination of students, but are conducted to allow students gain experience in preparing and presenting their work. It is expected that such seminars will be attended by most staff of the School, including the student's thesis advisor, as well as by all other graduate students in the school.

Students in the Ph.D. program must pass a foreign language examination within their first three years of studies. For students whose first language is not English this usually means an English proficiency test, evaluating the student's ability to read and write scientific literature and communicate with other scientists. This examination is offered every term and can be repeated any number of times.

An oral examination given by the thesis committee and covering the issues raised by the thesis will complete the degree course. This examination is open to the public.