Master’s studies

Syllabus for Master Programme in Mathematics

Masterprogram i matematik

  • 120 credits
  • Programme code: TMA2M
  • Specialization Code: MATE
  • Established: 2009-05-06
  • Established by: The Educational Board of Science
  • Revised: 2017-11-09
  • Revised by: The Faculty Board of Science and Technology
  • Reg. no: TEKNAT 2017/120
  • Syllabus applies from: Autumn 2018
  • Responsible faculty: Faculty of Science and Technology

Entry Requirements

Financial Mathematics


Academic requirements
A Bachelor's degree, equivalent to a Swedish Kandidatexamen, from an internationally recognised university.
Also required is 90 credits in mathematics with 20 credits in probability theory, programming and/or numerical analysis.

Language requirements
All applicants need to verify English language proficiency. This is normally attested by an internationally recognised test such as TOEFL or IELTS with the following minimum scores:

  • IELTS: an overall mark of 6.5 and no section below 5.5
  • TOEFL: Paper-based: Score of 4.5 (scale 1–6) in written test and a total score of 575. Internet-based: Score of 20 (scale 0–30) in written test and a total score of 90
  • Cambridge: CAE, CPE
Exemptions for students from certain countries.

Mathematics


Academic requirements
A Bachelor's degree, equivalent to a Swedish Kandidatexamen, from an internationally recognised university.
Also required is 90 credits in mathematics.

Language requirements
All applicants need to verify English language proficiency. This is normally attested by an internationally recognised test such as TOEFL or IELTS with the following minimum scores:

  • IELTS: an overall mark of 6.5 and no section below 5.5
  • TOEFL: Paper-based: Score of 4.5 (scale 1–6) in written test and a total score of 575. Internet-based: Score of 20 (scale 0–30) in written test and a total score of 90
  • Cambridge: CAE, CPE
Exemptions for students from certain countries.

Applied Mathematics and Statistics


Academic requirements
A Bachelor's degree, equivalent to a Swedish Kandidatexamen, from an internationally recognised university.
Also required is 90 credits in mathematics with 20 credits in probability theory, programming and/or numerical analysis.

Language requirements
All applicants need to verify English language proficiency. This is normally attested by an internationally recognised test such as TOEFL or IELTS with the following minimum scores:

  • IELTS: an overall mark of 6.5 and no section below 5.5
  • TOEFL: Paper-based: Score of 4.5 (scale 1–6) in written test and a total score of 575. Internet-based: Score of 20 (scale 0–30) in written test and a total score of 90
  • Cambridge: CAE, CPE
Exemptions for students from certain countries.

Decisions and Guidelines

According to a decision taken by the Vice Chancellor 2006-09-16, Uppsala University will offer two-year Master programmes in biology, computer science, physics, earth science, sustainable development, chemistry, mathematics, computational science and applied biotechnology, all from 2007-07-01.

Aim

The Programme has the following three specialisations:

  •  Mathematics
  • Financial Mathematics
  • Applied Mathematics and Statistics
 The specialisation "Mathematics" contains mostly studies in pure mathematics (i.e. algebra, analysis, geometry and probability theory). It is designed to give the student a broad and deep mathematical education.
The student obtains a deeper insight into modern mathematical theory and into how its general and powerful methods and techniques can be used within mathematics and its areas of application.
 
The specialisation "Financial Mathematics" should make students well prepared for activities in the financial sector, where use of advanced mathematical, statistical and numerical methods and theories play an important role. The program should also give students the qualification to be accepted for Ph.D. study in mathematics and, in case of an appropriate choice of additional courses, to Ph.D. study in national economy or mathematical statistics.
 
The specialisation “Applied Mathematics and Statistics” gives the student access to a broad spectrum of mathematical and statistical methods with particular weight given to applications in other sciences. It also makes the student eligible for PhD studies in mathematics, applied mathematics or statistics.
 

Learning Outcomes

According to the Higher Education Act, the following applies for second-cycle studies:
Second-cycle studies shall be based fundamentally on the knowledge acquired by students during first-cycle courses and study programmes, or its equivalent.
Second-cycle studies shall involve the acquisition of specialist knowledge, aptitudes and accomplishments in relation to first-cycle courses and study programmes, and in addition to the requirements for first-cycle courses and study programmes shall:

  • further develop the ability of students to integrate and make autonomous use of their knowledge,
  • develop the students' ability to deal with complex phenomena, issues and situations, and
  • develop the students' potential for professional activities that demand considerable autonomy, or for research and development work. Ordinance (2006:173).
Objectives for a Degree of Master (120 credits) according to the Higher Education Ordinance, System of Qualifications.

Knowledge and understanding
For a Degree of Master (120 credits) students must
  • demonstrate knowledge and understanding in their main field of study, including both broad knowledge in the field and substantially deeper knowledge of certain parts of the field, together with deeper insight into current research and development work; and
  • demonstrate deeper methodological knowledge in their main field of study.
For the Master Programme in Mathematics this means, for instance, how the central concepts in advanced mathematical theory are logically connected, how they can be used to model mathematical, technical, scientific and financial phenomena, and how such models can be studied, theoretically as well as by numerical computations. The weight assigned to different types of knowledge and understanding varies with the general direction that the student chooses for her studies.

Skills and abilities
For a Degree of Master (120 credits) students must
  • demonstrate an ability to critically and systematically integrate knowledge and to analyse, assess and deal with complex phenomena, issues and situations, even when limited information is available;
  • demonstrate an ability to critically, independently and creatively identify and formulate issues and to plan and, using appropriate methods, carry out advanced tasks within specified time limits, so as to contribute to the development of knowledge and to evaluate this work;
  • demonstrate an ability to clearly present and discuss their conclusions and the knowledge and arguments behind them, in dialogue with different groups, orally and in writing, in national and international contexts; and
  • demonstrate the skill required to participate in research and development work or to work independently in other advanced contexts.
For the Master programme in mathematics, this means, for instance, to construct proofs for mathematical statements, to analyze the structure of the mathematical proofs of others, to independently create and analyze models based on mathematical and statistical theory, methods and techniques, and to perform computer based calculations. The weight assigned to different types of skills and abilities varies with the general direction that the student chooses for her studies.

Judgement and approach
For a Degree of Master (120 credits) students must
  • demonstrate an ability to make assessments in their main field of study, taking into account relevant scientific, social and ethical aspects, and demonstrate an awareness of ethical aspects of research and development work;
  • demonstrate insight into the potential and limitations of science, its role in society and people’s responsibility for how it is used; and
  • demonstrate an ability to identify their need of further knowledge and to take responsibility for developing their knowledge.
For the Master programme in mathematics this means, for instance, that the student understands the role of mathematics in other sciences, in technical and financial applications, and in society in general. It also contains the ability to make ethical judgements about the applications of mathematics in relevant situations. Furthermore, that the student can develop her competence when needed, follow theoretical developments and evaluate new results by critical study and use of research literature.
 

Layout of the Programme

The courses and general plan of the programme can be seen from the outline below. The extent of the courses is given in higher education credits (hp). Courses, up to 30 hp, can also be chosen from other fields within the Faculty of Science and Technology.

Instruction

Education in the Masters programme builds upon upon the prior knowledge and experience of the students. Students are expected to participate actively in their education and take responsibility for personal learning outcomes as well as contributing to the learning of others. Academic staff in the programme have the primary responsibility for establishing foundations for active individual and collective learning. Continuos educational development builds on a respectful dialogue between students and staff, through which everyone is empowered to contribute to educational evolution and mutual learning.
 

Degree

Upon request, a student who has received a pass grade in a course is to receive a course certificate from the higher education institution. Upon request, a student who meets the requirements for a qualification is to receive a diploma from the higher education institution.

A Degree of Master is a so called general degree, which means that the student achieve the degree in its main subject according to the criteria below, regardless of the courses being part of the program or not, therefore there is a possibility also to include single subject courses in the degree.

Regulations according to Higher Education Ordinance
A Degree of Master (120 credits) is obtained after the student has completed course requirements of 120 higher education credits with a certain area of specialisation determined by each higher education institution itself, including at least 60 higher education credits with in-depth studies in the main field of study. In addition, the student must hold a Degree of Bachelor, a Degree of Bachelor of Arts in…, a professional degree worth at least 180 higher education credits or an equivalent foreign qualification.

For a Degree of Master (120 credits) students must have completed an independent project (degree project) worth at least 30 higher education credits in their main field of study, within the framework of the course requirements. The independent project may comprise less than 30 higher education credits, but not less than 15 higher education credits, if the student has already completed an independent project at the second level worth at least 15 higher education credits in their main field of study, or an equivalent project in a foreign educational programme.

A Degree of Master (60 credits) is obtained after the student has completed course requirements of 60 higher education credits with a certain area of specialisation determined by each higher education institution itself, including at least 30 higher education credits with in-depth studies in the main field of study. In addition, the student must hold a Degree of Bachelor, a Degree of Bachelor of Arts in…, a professional degree worth at least 180 higher education credits or an equivalent foreign qualification.

For a Degree of Master (60 credits) students must have completed an independent project (degree project) worth at least 15 higher education credits in their main field of study, within the framework of the course requirements.

Local regulations
A Degree of Master (60 credits) may, except for courses on advanced level, contain one or several courses on basic level comprising not more than 15 higher education credits. A degree of Master (120 credits) may, except for courses on advanced level, contain one or several courses on basic level comprising not more than 30 higher education credits. The course or the courses are meant to provide such additional competence as is needed for in-depth studies in the main field of study and cannot be included in the student’s basic degree.

For a Degree of Master (120 credits) students must have completed an independent project (degree project) worth at least 30 higher education credits.

Other Directives

Students who, outside the programme, have acquired equivalent qualifications corresponding to at least 15 credits on advanced level in addition to the degree at Bachelor’s level, may apply to be accepted to a later part of the programme. The application deadline is for the autumn term May 1 and for the spring term December 1.