General Study Syllabys for Applied Mathematics and Statistics
Applied Mathematics and Statistics
Swedish title: Tillämpad matematik och statistik
Responsible department: Department of Mathematics
Subject-specific parts (*) in Swedish adopted by the Faculty Board (the Doctoral Education Board) on 2015-09-08.
Faculty-common parts approved by the Faculty Board of Science and Technology on 2022-04-26. Revision on 2023-02-07.
The faculty-common parts go into force on 1 July 2022. The Faculty-common parts also apply to those who started their doctoral education prior to 1 July 2022, except if this would have a negative impact on the conditions for doctoral students.
Subject description *
Applied mathematics and statistics includes applied mathematics, mathematical modelling, statistical methods and applications of statistical methods. Research in applied mathematics and statistics has strong connection to medicine, technical sciences, natural sciences and similar areas. The core of applied mathematics and statistics is by now well established but the subject has grown considerably during the last decade and new subareas appear constantly. A doctoral student should have good understanding of research in various areas of mathematics, applied mathematics and statistics and also the way these areas can be applied in different ways.
Aim and objectives of the education
Overall aim and objectives of the education
Doctoral education shall develop the knowledge and skills needed to be able to conduct research independently (Higher Education Act, 1992:1434). The Higher Education Ordinance’s System of Qualifications (Appendix 2, 1993:100) sets out the requirements to be met for a doctoral and licentiate degree, respectively (see individual study plan template).
Subject-specific objectives *
Building on basic research, the doctoral studies are expected to provide further insight into the most important areas of the subject as well as in-depth knowledge within at least one subdivision. By conducting a degree project guided by a supervisor, the doctoral student shall also be able to present her/his goals and results orally and in writing to different target groups in English and, in the case of Swedish-speaking doctoral students, in Swedish.
General entry requirements
General entry requirements for doctoral education are regulated in the Higher Education Ordinance as follows:
An applicant shall be considered as meeting the general entry requirements if they have
- completed a degree at the advanced level (Master’s level), or
- completed course requirements of at least 240 credits, of which at least 60 credits are at the advanced level (Master’s level), or
- acquired substantially equivalent knowledge in some other way in Sweden or abroad.
The University may permit an exemption from the general entry requirements for an individual applicant, if there are special grounds (Chapter 7, § 39 of the Higher Education Ordinance).
In order for a person who has completed course requirements of at least 240 credits (under the second item above) to be considered eligible at Uppsala University, the 60 credits at advanced level must include a degree project of at least 15 credits (AFUU § 2, UFV 2022/729).
Special entry requirements *
A person who has passed at least 90 higher education credits worth of courses in mathematics or in subjects relevant for mathematics, or who has corresponding education from abroad, has special eligibility. Normally, a thesis of at least 15 higher education credits is also required.
Examples of educational programs which give special eligibility are
- Bachelor's program in mathematics (provided that the basic eligibility criteria are fulfilled)
- Bachelor's program in computer sciences (provided that the basic eligibility criteria are fulfilled)
- Bachelor’s program in statistics (provided that the basic eligibility criteria are fulfilled)
- Master's program in mathematics
- Master's program in computer sciences
- Master’s program in statistics
- Civil engineering program with specialisation in technical physics
For other programs additional mathematics courses may be needed for special eligibility. For questions in individual cases contact the professor responsible for doctoral education
Advertisement, selection and admission
Information and advertisement
Admission shall be made on a competitive basis following open advertisement of a doctoral place, with the exception of that which is specified in Chapter 7, § 37 of the Higher Education Ordinance. The advertisement shall be made available locally and on the University’s website (www.uu.se) at least three weeks before the application deadline and should be given appropriate national and international dissemination.
Selection among the applicants shall be carried out with consideration given to their ability to successfully conduct their studies. The assessment criteria for selection are:
- knowledge and skills relevant to the thesis work and the subject/specialisation
- assessed ability to work independently, for example
- ability to formulate and address scientific problems
- written and oral communication skills
- ability to carry out independent critical analysis
- other experience relevant to doctoral studies, e.g. professional experience.
The assessment criteria may be demonstrated, for example, by supporting documents, an interview or a skills test.
In addition, an assessment is made of the applicant’s general competence and personal qualities, as well as their ability to collaborate. If a number of applicants are judged as being equal, preference shall be given to applicants from the underrepresented legal gender among the doctoral students in the subject/specialisation.
The mere fact that an applicant is deemed to be able to be awarded credits for prior studies or professional experience for the purpose of doctoral studies shall not give an applicant preference over other applicants during selection (Chapter 7, § 41 of the Higher Education Ordinance).
A doctoral student is admitted to a doctoral programme in a doctoral subject/specialisation. Admission of a doctoral student with full-time employment in their doctoral studentship at Uppsala University is decided by the head of the relevant department, except in cases specified in the Faculty’s guidelines for doctoral education (TEKNAT 2021/301). Admissions with other forms of funding are decided by the Faculty Board’s Working Committee after preparation in the Doctoral Education Board.
Structure and content of doctoral education
Doctoral education consists of courses and research work, and can take various forms, as specified in the individual study plan.
The research project must be well-defined and the level of ambition must be set taking into account both the degree objectives of the programme and the net study time (maximum 48 months for a doctoral degree or maximum 24 months for a licentiate degree).
Requirements for doctoral degree *
The requirements for the doctoral degree consist of passed examinations in the courses included in the approved individual study plan of each doctoral student, as well as a passed public defense of the degree project. The studies awarded a doctoral degree comprise 240 higher education credits (four years of full-time studies), of which the doctoral thesis comprises a minimum of 120 higher education credits and the course part a minimum of 80 higher education credits.
Requirements for licentiate degree *
A doctoral student who has acquired at least 120 higher education credits (two years of full-time studies) is eligible for a licentiate degree. The requirements consist of passing the examinations included in the program stage and receiving a passing grade on an academic paper of at least 60 higher education credits. The part of the course amounts to a minimum of 40 higher education credits.
The head of department is responsible for ensuring that sufficient time is allotted for the department’s doctoral students to receive the necessary supervision. A doctoral student has the right to request a change of supervisor (Chapter 6, § 28 of the Higher Education Ordinance).
Individual study plan
The principal supervisor, in consultation with the professor responsible for doctoral studies (FUAP), is responsible for drawing up an initial individual study plan prior to admission. The head of department approves the study plan in connection with admission. The individual study plan shall contain a timetable for the doctoral studies, specification of how supervision is organised, and a description of the undertakings of the doctoral student and the department during the period of studies. The individual study plan also specifies the courses included in the doctoral student’s education.
The individual study plan must be revised at least annually in collaboration between the doctoral student and their supervisor. The revision involves following up on the doctoral student’s progress in relation to the degree objectives and previous plan, as well as planning for further studies. The FUAP approves the revised study plan.
Follow up *
A course in research ethics, with a minimum of 2 credits and content equivalent to the courses provided by the Faculty, shall be included for the licentiate and doctoral degrees. An introductory course to doctoral studies and a course in scientific writing are also recommended.
Doctoral students who teach should undergo teacher training for higher education. This is specified in the individual study plan, and can either be a credit-bearing course element or take place within the framework of the doctoral student’s departmental service.
Teacher training for higher education, lasting 5 weeks, is equivalent to 7.5 credits at the Faculty, and may be included in the doctoral programme.
Basic Swedish language training for doctoral students who do not have Swedish as their first language may be a credit-bearing course element or take place within the framework of the doctoral student’s departmental service.
Subject-specific courses *
The doctoral studies may include different kinds of courses, such as lectures, literature studies, practical training, field studies, etc. The courses are intended to provide a wider insight into the subject as a complement to the competence acquired during research. The courses included in the individual study plan may be selected among courses in mathematics and computer sciences as well as relevant courses in applied areas. For example, if a doctoral student does research in the area of mathematical biology, the student can take courses in biology/ecology.
Courses in the individual study plan are to be decided by the student and the main supervisor.
A selection of the following courses, or similar, should be included into education: partial differential equations, scientific computing III, complexity theory, measure theory and stochastic integration, theoretical statistics, mathematical statistics, analysis of time series, Markov processes, Computer intensive statistics and data-mining, selected topics in mathematical statistics, applied mathematics, Bayesian methods, validated numerical methods, mathematical biology, stochastic processes, modelling of complex systems, stational stochastic processes, stochastic processes with applications, probability theory.
The doctoral student should follow various research activities at the institute, in particular, taking part at research seminars and attending guest lectures.
For doctoral courses, the teacher responsible for the course normally serves as the examiner. The head of department appoints an examiner for a doctoral course. The task of the examiner is only to determine grades on examinations. The principal supervisor, in consultation with the FUAP and other supervisors, decides which courses and to what extent (number of credits) the doctoral student is allowed to be credited for in their doctoral studies, and this is documented in the individual study plan.
It is up to the principal supervisor, in consultation with the FUAP and other supervisors, to decide which examinations (courses or other elements carried out during the study period of the doctoral education) the doctoral student will be allowed to count towards their doctoral studies and to what extent (number of credits). This shall be documented in the individual study plan. The task of the examiner is only to determine grades on examinations.
An assessment must be made as to whether credits can be awarded for prior studies or professional or vocational experience (that have been completed prior to admission to doctoral education) (Chapter 6, § 8 of the Higher Education Ordinance). At the Faculty, the FUAP is responsible for the assessment.
Thesis, doctoral defence and licentiate seminar
The research work shall result in a scientific thesis that must be defended at a public doctoral defence. The research task may be carried out individually or in collaboration with others within or outside the department. However, the doctoral student must be trained to conduct independent research.
The doctoral thesis can be designed either as a monograph, i.e. a unified, coherent scientific work, or as a compilation thesis, i.e. a compilation of scientific papers with a summary of these. The thesis work must be equivalent to at least 120 credits (Chapter 6, §§ 4–5 of the Higher Education Ordinance, and Appendix 2, System of Qualifications). Theses within the Faculty shall include a popular science summary that is in Swedish and at least two pages long.
The doctoral thesis must either meet the requirements for publication in an international scientific journal with independent quality review, or be a summary of scientific papers with equivalent quality requirements. If the doctoral student has co-authored a paper with another person, this may be taken into account only to the extent that the individual effort can be distinguished. This should be done through a description of the doctoral student’s contribution in the papers on which a compilation thesis is based. If parts of the work have previously been published by the doctoral student in a licentiate thesis, this shall be made clear.
The licentiate thesis is smaller in scope, but is subject to the same quality requirements for constituent papers as apply for the doctoral thesis.
In consultation with the FUAP and other supervisors, the principal supervisor shall assess when the thesis work has progressed to the point that a date for doctoral defence or licentiate seminar can be set.
The forms of defence and the grading of doctoral theses are regulated in the Higher Education Ordinance, the Faculty’s Guidelines for doctoral education (TEKNAT 2021/301) and Admission and grading regulations for doctoral studies at Uppsala University (UFV 2022/729).
The doctoral thesis shall be defended orally in a public doctoral defence. An examining committee appointed by the Faculty decides on the grade for the doctoral thesis.
The Faculty’s guidelines for doctoral education (TEKNAT 2021/301) summarise the rules for the licentiate seminar.
The grade for a licentiate thesis shall be determined by the FUAP, or another professor delegated this duty, in consultation with the principal supervisor and the external reviewer. The principal or assistant supervisor for the doctoral student may not serve as examiner.
The following degree titles have been established for Applied Mathematics and Statistics:
Filosofie licentiat- och doktorsexamen
The English translation is Degree of Doctor/Licentiate of Philosophy.
Both the subject and the specialisation are listed on the degree certificate. The degree title (Teknologie/Filosofie licentiat- och doktorsexamen [Degree of Doctor/Licentiate of Philosophy]) shall be determined by the content of the doctoral education, and not by the doctoral student’s degree from a qualifying programme. If a doctoral student wishes to change their degree title to one that differs from that established for the doctoral subject dispensation is required from the Faculty Board (Working Committee). The request for a change of degree title must be made no later than the time of opponent and examining committee appointment or submission of the thesis for printing, whichever occurs first.
Doctoral and licentiate degree certificates are issued upon application in Ladok.
Regulatory framework and responsibilities for doctoral education
Doctoral education is regulated in the Higher Education Act (1992:1434) and the Higher Education Ordinance (1993:100). These are supplemented by the following local regulations: Guidelines for doctoral studies at Uppsala University (UFV 2022/728), Admission and grading regulations for doctoral studies and study programmes at Uppsala University (UFV 2022/729) and Guidelines for doctoral (third cycle) education at the Faculty of Science and Technology (TEKNAT 2021/301).
Responsibility for doctoral education ultimately rests with the University Board and the Vice-Chancellor (Chapter 2, §§ 2–3 of the Higher Education Ordinance). Through delegation, the Disciplinary Domain Board or Faculty Board has overarching responsibility and supervisory responsibility, but the day-to-day responsibility is exercised by the department in which the doctoral student is registered. Key functions in doctoral education are the head of department, professor responsible for doctoral studies (FUAP), director of doctoral studies, and the supervisor. See the Faculty’s Rules of Procedure (TEKNAT 2019/177) for a description of roles and responsibilities.
Research in applied mathematics and statistics is conducted in extensive international cooperation and requires extensive global information flow. It is therefore necessary that the student has the ability to read scientific works in other languages. The student should know how to write scientific texts in English and Swedish.
The thesis work is individual but cooperation with other doctoral students is very valuable. This is encouraged e.g. through doctoral student seminars. During the education doctoral students should take part and present their research results at international research conferences.
The doctoral students should also take notice of the activities in applied mathematics at Stockholm University, the Royal Institute of Technology in Stockholm and the Institute Mittag-Leffler. In order to widen the perspective and to increase the ability to use mathematical methods in the future career, contacts with other subjects at the university are valuable. This applies pure mathematics, as well as to subjects outside the department, e.g. biology, computer sciences, economy, geo sciences, chemistry, medicine, technical sciences, theoretical physics, and theoretical philosophy.