Mathematics

Established by the First Vice President on 2005-05-17, registration number C 2005/604. 

Latest revised on 2021-06-01, registration number MV 2021-0033. 

This syllabus applies to doctoral students admitted as of 2021-08-01.

Regarding older syllabus, please contact the first vice/vice head of department.

Transitional regulations: 

A doctoral student admitted to an older syllabus may earn a degree in accordance with this, provided that the current Appointment regulation for doctoral programmes and current Local Qualifications Framework – third cycle qualifications are followed. 

Doctoral students admitted to an older syllabus of the graduate school mathematics can, however, change to the current syllabus by an application to the Deputy/Vice Head of Department. The change must be documented in the individual study plan. 

The graduate school is regulated by the Appointment regulation for doctoral programmes and the Local Qualifications Framework for Chalmers University of Technology - third cycle qualifications and is described in the syllabus for the graduate school. In the event of any conflict between the documents, the Appointment regulation for doctoral programmes and the Local Qualifications Framework for Chalmers University of Technology - third cycle qualifications are governing. For the most recent version of all regulatory documents referenced in this syllabus, see Chalmers’s internal website. 

Mathematics is a science where, based on axioms, logical reasoning is used to draw conclusions about questions of very different kinds. The questions studied are often inspired by other subjects such as physics. In addition, there are questions that come from the subject itself. Mathematics can also be of a more applied nature and is used in many areas in our society. The purpose of the doctoral program in mathematics is to provide the student with general knowledge in mathematics, information on current issues and practical uses, in-depth insights in one or more parts of the subject, and skills in research methodology. The education as a licentiate aims to enable the student to independently participate in research work in mathematics. The goal of the doctoral program is to provide the ability to critically and independently plan, lead, complete and present research and development work in mathematics.

The national objectives for third cycle degrees (licentiate and doctoral degree) and local requirements are stated in the Local Qualifications Framework for Chalmers University of Technology – third cycle qualifications.

To be qualified for admission in the Mathematics graduate school the student must have earned a degree at the second-cycle level. The orientation of the student’s degree shall also have a sufficiently close connection to the subject of the doctoral programme. Equivalent requirements apply to individuals who have taken their first degree in a country other than Sweden. The examiner, in consultation with the principal supervisor, shall assess whether the applicant has the requisite capacity to successfully complete the doctoral programme. Other requirements for general entry are regulated in Appointment regulation for doctoral programmes. 

Regulations regarding admission are stated in Appointment regulation for doctoral programmes. 

The study programme towards a doctoral degree encompasses 240 higher education credits. The study programme towards a licentiate degree encompasses at least 120 higher education credits. One year of full-time studies equals 60 credits. 

For the licentiate degree programme the credits are distributed between courses and thesis work as follows: courses 45 credits and thesis 75 credits. 

For the doctoral degree programme the credits are distributed between course work and thesis work as follows: courses 90 credits and thesis 150 credits.

Courses within the graduate school include general courses that cover all doctoral programmes at Chalmers as well as courses specific for the graduate school. 

General courses in Chalmers’s doctoral programmes 

The general course requirements for doctoral programmes at Chalmers are regulated in Local Qualifications Framework for Chalmers University of Technology – third cycle qualifications. 

30 of the required higher education credits must consist of four courses (at least 7.5 higher education credits each), one from each of the areas listed below. The courses are chosen in consultation with the examiner and the thesis advisor and aim to provide a good mathematical basis and prepare the student in choosing the subject area for the dissertation. All four courses must be completed before the licentiate degree.

It is up to the examiner in consultation with the supervisor to decide what courses count in the four areas listed above. Examples of courses in Mathematical analysis are Integration theory and Functional analysis. Examples of courses in Algebra are Galois theory and Commutative algebra. Examples of courses in Topology and Geometry are Topology and Advanced differential calculus. In the area of Applied Mathematics, a course is chosen that suits the doctoral student's interests and specialization; for example, a course in partial differential equations, optimization, mathematical physics, mathematical statistics, computational mathematics, etc. 

In addition to the 30 higher education credits mentioned above, the examiner and supervisor, in consultation with the doctoral student, determine an individual course package, which corresponds to 60 higher education credits (incl. the Chalmers general courses) for the doctoral degree. At least 15 of the 60 higher education credits should be completed for the licentiate degree. Participation in seminar activities can give up to 7.5 higher education credits. 

At least 60 higher education credits must be Ph.D. courses or joint MSc/PhD level courses. 

A licentiate thesis shall be written in English. In exceptional cases it can be written in Swedish; in such cases it shall contain a summary in English. 

The purpose of the licentiate thesis is to account for the relevant scientific results that have been attained during the thesis work and describe these in a way that is accessible outside of the scientific inner circle of researchers. A licentiate thesis can either be written as a compilation thesis or as a monograph. If the licentiate thesis is a compilation thesis it should begin with an introduction, a summarizing text, followed by the included scientific articles. The purpose of the summarizing text is to put the studies in context, and to present relevant results that for various reasons are not described within the articles. 

The licentiate 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.

Other regulations concerning the licentiate thesis are stated in Appointment regulation for doctoral programmes. 

A doctoral thesis shall be written in English. In exceptional cases it can be written in Swedish; in such cases it shall contain a summary in English.

The purpose of the doctoral thesis is to account for the relevant scientific results that have been attained during the thesis work and describe these in a way that is accessible outside of the scientific inner circle of researchers. A doctoral thesis can either be written as a compilation thesis or as a monograph. If the doctoral thesis is a compilation thesis it should begin with an introduction, a summarizing text, followed by the included scientific articles. The purpose of the summarizing text is to put the studies in context, and to present relevant results that for various reasons are not described within the articles. 

The doctoral 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. 

Other regulations concerning the doctoral thesis are stated in Appointment regulation for doctoral programmes. 

The Appointment regulation for doctoral programmes states that for each doctoral student at least two supervisors shall be appointed. One of them shall be appointed principal supervisor. The doctoral student has the right to supervision during the studies unless the Head of Department decides otherwise. 

After completion of a doctoral programme a doctoral degree is awarded. A licentiate degree can be an intermediate stage in a doctoral degree. If a licentiate degree is not a part of the individual study plan, a midway seminar shall be held to denote that licentiate level has been reached. 

For a licentiate degree to be awarded, the doctoral student must have received a grade of pass for the licentiate thesis and its presentation and must also have received a grade of pass for the other elements that are included in the programme. 

For a doctoral degree to be awarded, the doctoral student must have had a doctoral thesis and its defence approved and must also have passed the other elements that are included in the programme. 

Other regulations regarding examination are stated in:

The title of qualification is Teknologie doktorsexamen i Matematik or Filosofie doktorsexamen i Matematik. The English translation of the title of the qualification is Degree of Doctor of Philosophy in Mathematics.

For a licentiate degree the title of the qualification is Teknologie licentiatexamen i Matematik or Filosofie licentiatexamen i Matematik. The English translation of the title of qualification is Degree of Licentiate of Technology in Mathematics or Degree of Licentiate of Philosophy in Mathematics.

The degree is given a title corresponding to the name of the faculty within which the undergraduate degree was earned. The title is determined by the Head of Department in connection with admission. 

Any decision regarding exemption from use of the defined title is made by the Head of Department. In some individual cases, it is possible to use a title that does not correspond to the name of the faculty within which the undergraduate degree was earned.