Director of Graduate Studies: Peter Hegarty

## Syllabus

(approved by the Pro-Vice-President on 17 May 2005. Ref. nr. C2005/604)

(revised 20 August 2007)

(revised 9 June 2014)

### 1. Goal of the program

The purpose of the graduate program is to give the student basic
knowledge of the various branches of mathematics, orientation about
current problems and applications, deeper insight into one or several
specialities, and skills in research methodology.

The aim of the licentiate degree is to enable the student to independently participate in research and development work.

The aim of the doctoral degree is to enable the student to
critically and independently plan, lead, carry through and present
research and development work.

### 2. Eligibility and prerequisites

The normal requirement for being accepted to the graduate school is
a Master’s degree in engineering mathematics, engineering physics or
mathematics.

Persons who have acquired comparable abilities in a different way are also eligible.

### 3. Structure of the program

The doctoral education comprises 240 credits and the licentiate
education 120 credits; one year’s full time studies should give 60
credits.

The graduate education consists of

- A basic study course
- An individual study course
- Participation in seminars and guest lectures
- Scientific work leading to a licentiate thesis for the licentiate degree and a doctoral thesis for the doctoral degree

### 4. Specializations

Besides mathematics without specialization, the education may be
specialized towards applied mathematics. The choice of specialization
should be reflected both in the study course and in the research work.
The specialization towards applied mathematics is aimed at developing
and analyzing numerical methods, optimization methods, or some other
mathematical methods of relevance to science and technology.

### 5. Courses

#### 5.1 Basic study course

The basic study course comprises 45 credits.

The first 30 credits consist of four courses, one from each of the
four groups indicated below. Specific courses are chosen by the student,
supervisor and examiner in consultation. They are aimed at giving the
student a solid foundation in mathematics and preparing the choice of
topic for the thesis. These courses should be taken at the Department of
Mathematics, though exceptions may be allowed subject to the agreement
of the supervisor and examiner, and the consent of the vice-prefect. All
four courses must be passed before the licentiate degree.

- Mathematical analysis
- Algebra
- Topology and geometry
- Applied mathematics

Within mathematical analysis, one can choose between the following alternatives:

- Integration theory, 7.5 credits
- Functional analysis, 7.5 credits
- Theory of distributions, 7.5 credits
- Complex analysis, 7.5 credits

Within algebra, one can choose between the following alternatives:

- Galois theory, 7.5 credits
- Commutative algebra, 7.5 credits
- Linear and multilinear algebra, 7.5 credits

Within topology and geometry, one can choose between the following alternatives:

- Higher differential calculus, 7.5 credits
- Topology, 7.5 credits
- Riemann geometry, 7.5 credits

Within applied mathematics, one 7.5-credit course is chosen in
accordance with the interests and specialization of the student.
Examples are courses in partial differential equations, optimization,
mathematical physics, mathematical statistics, computational mathematics
etc.

The remaining 15 credits consists of courses from the Chalmers-wide program in Generic and Transferrable Skills (GTS). Of these, 9 credits must be obtained before the licentiate degree. Of these 9 credits, 7.5 consist of the following obligatory courses: Introductory Day for PhD Students (GFOK015, 0 credits), Teaching, Learning and Evaluation (GFOK020, 3 credits), Re- search Ethics and Sustainable Development (GFOK025, 3 credits) and Career Planning – Your Personal Leadership (GFOK010, 1.5 credits). The student must give an oral Popular Science Presentation (GFOK070, 0 credits) in advance of the thesis defence. A written such presentation must also be included on the back of the thesis.

The student, supervisor and examiner determine in consulta- tion an
individual study course, which comprises 75 credits in total, of which
at least 21 are taken in advance of the licentiate degree.

Consultancy work related to the student’s research interests can give up to 7.5 credits.

### 6. Theses

#### 6.1 Licentiate thesis

For the licentiate degree, the student should write a thesis
corresponding to 60 credits. It is presented at a seminar, and graded on
a pass/fail basis.

#### 6.2 Doctoral thesis

For the doctoral degree, the student should write and publicly
defend a doctoral thesis corresponding to 120 credits. The thesis should
be of such quality that it fulfils normal requirements for publication,
in its entirety or in abridged form, in a scientific journal of good
quality. It is graded on a pass/fail basis. The grading is based both on
the thesis and on the defence.

### 7. Requirements for the degrees

#### 7.1 Licentiate degree

For the licentiate degree, the student must complete

- Courses from the four groups listed above, comprising 30 credits
- 9 credits of GTS courses, as listed above
- At least 21 credits from the individual study course
- The thesis of 60 credits

in total 120 credits.

#### 7.2 Doctoral degree

For the doctoral degree, the student must complete

- The basic study course of 45 credits
- The individual study course of 75 credits
- The thesis of 120 credits

in total 240 credits.

### 8. Degree names

The names of the degrees concluding the graduate education are normally

- Licentiate of Engineering in Mathematics
- Licentiate of Engineering in Mathematics with Specialization in Applied Mathematics
- Doctor of Philosophy in Mathematics
- Doctor of Philosophy in Mathematics with Specialization in Applied Mathematics

### 9. Supervision

A student accepted into the graduate school has the right to a
supervisor. For full-time students, supervision is guaranteed for four
years for the doctoral degree and for two years for the licentiate
degree; for part-time students the same amount is distributed over a
longer period of time. As soon as possible after admission to the
graduate program, the prefect assigns a supervisor and at least one
co-supervisor. The prefect also assigns an examiner, who approves the
study course and confirms higher education credits and grades on
courses. The supervisor and examiner must be two different people. The
examiner, supervisor and student work together to plan the student’s
progress through the program.

### 10. Examination

Examinati

on is organized for each course. It may be written or oral. Exams are judged on a pass/fail basis by a course examiner.

The grade for the doctoral dissertation is determined by a grading
committee, which is chosen separately for each thesis defence. The grade
for the licentiate essay is decided by the examiner.

### 11. Further instructions

The student should regularly give an account of his or her progress and plans.