The below-mentioned applies to students admitted to the Master’s Degree programme in Mathematics in the Summer 2006 or later. Except for Ph.D.-students. Special rules for obtaining a MA apply for this group.

Students holding a Bachelor’s degree in Mathematics from the University of Aarhus (regardless of  special area of study), from the University of Copenhagen or from the University of Southern Denmark are qualified for the Master’s degree programme in Mathematics. The same applies for qualifications in Mathematics assessed by the university to be equivalent to the above-mentioned degree programmes as regards to level, content and extent. However, students holding less than a Bachelor’s degree might be qualified. See the academic regulations for these other possibilities.

Bachelor students from the University of Aarhus usually apply through the central online self-service. If deadline is exceeded you may use a special form or contact the main responsible for the University Studies Office. Students from other institutions may download an application form and submit it to the University Studies Office, Fredrik Nielsens Vej 5, 8000 Aarhus C.

If you fall behind schedule with less than 20 ECTS on your Bachelor’s degree programme you may submit an application for exemption to the board of studies at the Faculty of Science and ask for a temporary enrolment in the Master’s degree programme. For further information about the rules of admission and temporary enrolment, see admission  at the homepage of  the Faculty of Science. Application forms can be found under forms. You can also go and ask for it at the Studies Office at the Faculty of Science.

The legally binding academic regulations for the Master’s Degree Programme can be found under Academic Regulations.

The Master’s degree programme is equivalent to 120 ECTS credits including a MA thesis of 30 ECTS and courses in the field of mathematics to an extent of at least 60 ECTS. (For some specific combinations of subjects the ECTS credits must be equivalent to 150, e.g. if you combine mathematics with an upper secondary school subject within humanities).

Your study programme must contain advanced courses within 2 of the 3 main study areas: Algebra, Geometry/Topology and Analysis to an extent of at least 20 ECTS credits for each main study area. (Besides algebraic subjects the area algebra contains s such as Cryptology and Mathematical Logic. In this connection the area Analysis also contains Numerical Analysis and Probability Theory).

• Furthermore, the courses in your Master’s degree programme and your Bachelor’s degree programme must jointly contain:At least 2 of the 3 courses Advanced Algebra, Advanced Analysis and Introduction to Topology.
  
• The compulsory courses in mathematics in the special area of study ‘Mathematics’ in the Bachelor’s Degree programme, equivalent to 100 ECTS (or equivalent courses). The courses in question are: Calculus 1 and 2, Introduction to Mathematical Analysis, Mathematical Analysis 1 and 2, Linear Algebra, Algebra, Geometry, Differential equations, Complex function theory, Measure Theory, Real analysis, Philosophy of Mathematics.
• The compulsory courses in Statistics and Probability Theory.
• An introductory course of Programming.
• Subject areas outside the field of mathematics to an extent of at least 2 electives = 60 ECTS
• At least 180 ECTS credits within mathematics.

When applying for the Master’s degree programme (also in case of a temporary admission) you must draw up a study programme for your Master degree together with the departmental teaching committee. You have to use a special form for the application (only in Danish). The composition of your study programme may be modified regularly in cooperation with the departmental teaching committee. For every change of the programme a new form must be filled in. The director of studies requires a form every 6 month.

Before you complete your Master’s degree programme, i.e. before you submit your MA thesis you must obtain an approval of your final Master’s degree programme. The form Godkendelse af kandidatoverbygning (only in Danish) must be used for this purpose.

The Master’s thesis is the final exam, meaning that all courses etc. must be passed before you go for the Master’s thesis exam.

The range of advanced courses in Mathematics varies from year to year. Though, the courses “Advanced Algebra”, “Advanced Analysis” and “Introduction to Topology”  are offered every year. Proposals from the students are welcome.

An advanced studies programme is based on one or more courses required in the Bachelor’s degree programme for the special study area Mathematics. The advanced studies programme may build on one or other more advanced studies programmes. The prerequisites are indicated in the course descriptions.

Every year in April/October the department terminates the planning of the advanced courses for the coming Semester. Course descriptions are published in the Course Catalogue and on the notice board beside the classroom “Koll D. Furthermore, orientation and individual meetings are held around 1 May/November.

Courses offered by other departments (e.g. at the Department of Computer Science or the Steno Institute) and which have a mathematical content may replace advanced courses of mathematics if approved  beforehand.

For course registration, go to the online self-service registration. The period of registration for courses in the Autumn is 1-15 May and for courses in the Spring the registration period is 1-15 November. A course may be cancelled if only a few students register.

In particular cases special courses are arranged. At these courses the students examine a specific topic under the instruction of a member of the academic staff.

In principle the courses are held in English, but only if attended by foreign students. Otherwise it will usually be held in Danish. Books and other teaching resources are normally in English.

If you enroll in a course the University Studies Office will automatically register you for the exam of the course in question. But to be on the safe side it is a good idea to check that it has happened.

In addition to the usual version advanced studies in Mathematics are usually also offered as a so-called honours version. The honours versions are aimed at Ph.D students and potential Ph.D. students. Only Master’s degree students and Ph.D. students are allowed to take courses at honours level.

You sign up for the honours version by signing up for the usual version and afterwards inform the lecturer that you wish to take the honours level. You have to obtain the lecturer’s acceptance. You may regret and go back to the usual version within a deadline determined by the lecturer.

The thesis is a clearly defined and delimited assignment on a complete mathematical topic. It is equivalent to 30 ECTS. The thesis must be submitted in the form of a written paper.

Completing the MA thesis may be done in another way than by submitting a thesis. You may complete your studies with a thesis “assignment”. In fact, this possibility has never been practiced at the Department of Mathematical Sciences. Only the possibility of submitting a MA thesis is described below. For both possibilities see the academic regulations.

A main supervisor is appointed by the department, normally according to the student’s proposal. The main supervisor must be a member of the academic staff tenured at the Faculty of Science. In particular cases the student may have a project supervisor in addition to the main supervisor. The MA thesis is performed independently by the student but in consultation with the supervisor(s).

Before writing the thesis the student and the main supervisor must enter into an agreement. The agreement must be drawn up in a special form which must be submitted to the teaching committee of the department for approval. If necessary, see the guidance on how to fill in the form.

The agreement must contain a deadline for submission of the MA thesis. The deadline must not be more than one year ahead. Until 2 months before deadline the agreement can be altered in case of special circumstances (e.g. if the student gets ill). The director of studies has to approve such a change, it must not be done by the department. A withdrawal cannot take place. You are allowed to submit the MA thesis earlier than the stated deadline.

About 1 month before deadline the Studies Secretariat sends an e-mail to the student asking for the exact  title of the thesis among other things as the title of the thesis is going to be registered in Danish and in English in the Diploma. In case you hand in your thesis before deadline, please contact the Studies Secretariat.

Specialet skrives som hovedregel på dansk eller engelsk. Det skal i alle tilfælde forsynes med et resumé på engelsk. Specialets titel skal foreligge på både dansk og engelsk.

The thesis is usually written in Danish or in English. In any case it must contain an abstract in English. The title of the thesis must be written both in Danish and in English.

3 copies of the MA thesis must be submitted to the Information Office at the Department (unless another agreement has been made), but in case of 2 supervisors (main and project supervisor) 4 copies must be submitted.

An oral examination is held in connection with the MA thesis when the supervisor and the external examiner have scrutinized the submitted thesis. The Information Office at the Department will be informed of the time for the examination. The examination takes one hour and consists of a lecture of about 30 minutes on a prescribed topic connected to the thesis and a 30 minutes discussion of the lecture and the thesis. Based on an assessment of the written thesis, the lecture and the discussion an overall mark is given according to the Danish 7-point marking scale. Apart from the academic content of the thesis the student's spelling and formulating capacity must also be part of the assessment.

Du kan kombinere matematik med et sidefag, hvorved du får faglig kompetence (populært kaldet undervisningskompetence) til at undervise i begge fag i gymnasiet. Sidefaget kan kun vælges fra den gymnasiale fagrække. Se tilvalg for listen over mulige sidefag. Sidefagsstudiet (hovedfaget matematik + sidefag) er et studium for sig, som man skal skifte over til under bachelorstudiet. For yderligere oplysninger om sidefag og undervisningskompetence kan du studere

1. Matematik kombineret med et andet (gymnasie)fag under beskrivelsen af bacheloruddannelsen i matematik.
2. Aarhus Universitets hjemmeside om tilvalg.
3. Punkt 2 af Studieordningen
4. Faglig rammebeskrivelse for sidefaget i matematik

I parentes bemærket er kravet til faglig kompetence i matematik ca. en bachelorgrad med studieretning matematik + 5 ECTS i matematikkens historie + 5 ECTS i matematikdidaktik. For studerende med hovedfag uden for naturvidenskab kræves yderligere et 5 ECTS kursus i matematiske modeller.

Hvis du i dit sidefagsstudium kombinerer matematik med et centralt gymnasiefag uden for naturvidenskab, udvides studiet med 30 ECTS.

Ph.d.-studerende på del A er normalt optaget på både kandidatstudiet og ph.d.-studiet. Derfor skal enhver ph.d.-studerende have sit kandidatprogram godkendt af Kandidatstudienævnet. Der er dog nedenstående særlige regler for ph.d.-studerende:

• Optages man på ph.d.-studiet, bortfalder kravet om et tilvalg på kandidatuddannelsen.
• Del A-eksaminen erstatter specialet, men tæller 60 ECTS, hvor specialet kun er på 30 ECTS. Der er derfor kun plads til kurser i et omfang på 60 ECTS på kandidatstudiet. Øvrige kurser under del A (mindst 30 ECTS) placeres på ph.d.-studiet.

Instituttet udbyder ph.d.-kurser. Et sådant er en struktureret vejledning i et bestemt emne for ph.d.-studerende. Ligesom kurser under det normale kursusudbud kan et ph.d.-kursus kun registreres som en kandidataktivitet, hvis det er tilgængeligt i Universitetets system (Delfi).

Fakultetets ph.d.-skole kan udbyde specielle kurser, der så også vil blive kaldt ph.d.-kurser.

1. Matematisk Institut har et undervisningsudvalg. Du er velkommen til nårsomhelst at spørge dets medlemmer til råds om dine kandidatstudier. Du kan f.eks. kontakte Udvalget for overbygningskurserne, hvis formand er Simon Kristensen (kontor A4.33), eller undervisningsudvalgets formand Jens Carsten Jantzen (kontor A3.18).
2. Orienteringsmøder: Hvert halve år, dvs ca. 1. maj og 1. november, holder Undervisningsudvalget et orienteringsmøde for alle kandidatstuderende og hvem der ellers måtte være interesseret om det kommende semesters overbygningskurser mv.
3. Individuelle samtaler: I forbindelse med hvert orienteringsmøde arrangeres der individuelle samtaler med formanden for Udvalget for overbygningskurserne. Der bliver lagt en tilmeldingsliste frem i Matematisk Instituts informationskontor, som du kan skrive dig på. Sådanne samtaler er obligatoriske, idet der til sidst i Studieordningen står "Opfølgning på det godkendte kandidatprogram sker gennem halvårlige statussamtaler mellem den studerende og Institut for Matematiske Fag".