The Bachelor’s Degree Programme in Mathematics

The Bachelor’s degree programme in Mathematics consists of a number of courses and projects which must have a total of 180 ECTS. The programme offers two special areas of study which  are:

1. Mathematics

2. Mathematical Modelling

The special area of study Mathematics gives you a lot of possibilities to combine Mathematics with other subjects. Especially, Mathematics can be combined with Physics from the very start. Further possibilities are described below. You can also read about the possibilities in the file concerning the choice of special area of study and elective subjects intended for students at the end of their first year of study.

 The following text is aimed at students who begin their studies in 2009 or later. Students enrolled earlier are referred to this homepage.

For most mathematical undergraduate students the table of their first year has the following form (the standard form):

If you wish you can combine Mathematics with Physics from the very start. In this case your first year will look as follows:

If you wish to follow this model you must go to the Studies Secretariat at the Faculty of Science after your admission and ask them to register Physics as your subsidiary subject in order that the content of the 1st-year examination can be set.

You can also combine Mathematics with Computer Science as early as in the 1st year. In this case your 1st year will look as follows:

If you wish to follow this model you will have to decide during the 1st quarter as it varies from the standard model from the 2nd quarter onwards. You must sign up for the course Programming 2 no later than at the end of the 5th week of the quarter.

At the end of your 1st year of study you must have participated in the examinations that make up the 1st year examination. After your 2nd year of study you must have passed the exams. The 1st year examination consists of the following courses:

• Calculus 1 (5 ECTS)
• Calculus 2 (5 ECTS)
• Perspectives in Mathematics (5 ECTS)
• Introduction to Mathematical Analysis (5 ECTS)
• Mathematical Analysis 1 (5 ECTS)
• Mathematical Analysis 2 (5 ECTS)
• Linear Algebra (10 ECTS)
• Introduction to Programming (5 ECTS)

However, Introduction to Programming (5 ECTS) will be replaced by

- Introductory Mechanics (5 ECTS)

if you have registered Physics as your subsidiary subject from the beginning of your studies.

The choice between the special areas of study ‘Mathematics’ and ‘Mathematical Modelling’ can be postponed until after the 1st year of study. This does not apply if you already have chosen Mathematics in combination with Physics or Computer Science during the 1st year. In these cases you have, in fact, chosen ‘Mathematics’ as special area of study.

Furthermore, it is possible to change within 2 special areas of study after the 2nd year of study. A change from ‘Mathematical Modelling’ to ‘Mathematics’ can be done without any prolongation of the study programme if you do not choose another subsidiary subject than ‘Mathematics’. A change from ‘Mathematics’ to ‘Mathematical Modelling’ may be done without prolongation of your studies if you choose Statistics as elective subject in the special area of study ‘Mathematics’ and you choose appropriate courses (see below under Elective in Statistics).

Box diagram for the special area of study Mathematics:

The courses in the table are the courses that must be part of the Bachelor’s degree programme for the special area of study ‘Mathematics’. The tables for the 1st year show that the temporal placement of a few of the courses can be modified. Also the choice of subsidiary subject or elective subject may make it necessary to change the sequence of the courses.

In the 2nd quarter in the 2nd year there is an optional course of Mathematics of 5 ECTS where you have the possibility to choose one of the courses Vector Analysis or a course of History of Mathematics (the last-mentioned course is part of the requirements for qualifications for teaching Mathematics at upper secondary school).

The fields in blue must be filled in with optional courses and at least one elective subject.

Box diagram for the special area of study Mathematical Modelling:

Stochastic Processes (10 ECTS), Differential Equations (5 ECTS), History of Mathematics (5 ECTS) or an advanced course in Statistics (5 or 10 ECTS) are examples of courses which can be placed in the optional blocks.

As we wish to expand on this subject it has been placed on a seperate page

• Bachelor’s Project and Bachelor’s Degree Programme

Studying ‘mathematics’ you also have to take courses outside Mathematics. In this connection you must choose either an elective subject or a subsidiary subject. 

If you wish to qualify for teaching a subject at the upper secondary school e.g. ‘Physics’ you must enrol as a subsidiary subject student in this upper secondary school subject. Particular regulations apply for educations with subsidiary subjects. See section teaching qualifications below.

If you do not register for a subsidiary subject, you must choose one or two elective subjects. An elective subject consists of a number of courses equivalent to 30 ECTS from a specific subject, the elective subject. You can choose any subject within the Faculty of science except Mathematics. You may choose Statistics or Mathematics-Economics.

The Special Area of Study ‘Mathematical Modelling’

If you choose the special area of study ‘Mathematical Modelling’ you have in fact chosen Statistics as elective subject and thereby met all requirements for elective subjects. In return your 3rd year of study includes optional courses equivalent to 20 ECTS. Examples of courses which can be placed in these optional blocks can be found above, under the table of the special area of study. It is a good idea to choose the optional courses (and the topic of the Bachelor’s project) together with a lecturer.

The Special Area of Study ‘Mathematics’

If you choose the special area of study ‘Mathematics’ you must choose at least 1 elective and you must choose no more than 2 electives in the Bachelor’s degree programme. Examples are shown below.

Your compulsory courses in your Bachelor’s degree programme are equivalent to about 120 ECTS. The remaining 60 ECTS can be composed of two possibilities:

• 2 electives
• 1 elective plus graduate courses of 30 ECTS in Mathematics, e.g. the courses Advanced Algebra, Introduction to Topology and Advanced Analysis. (It is not coincidently that these three courses are mentioned - they are introductory to the Master’s degree programme in three extensive areas of Mathematics: Algebra, Geometry and Analysis, respectively).

The advanced courses you choose by the second possibility belong to your Bachelor’s degree programme and not to your Master’s degree programme.

If you choose only 1 elective, naturally you will have more Mathematics in your Bachelor’s degree programme than if you choose 2 electives. But if you choose 2 electives in the same upper secondary school subject you keep the possibility of choosing this subject as a subsidiary subject and thus you obtain qualifications of teaching this subject.

If you choose only 1 elective during your Bachelor’s degree programme you will have to choose another elective during your Master’s degree programme. But you may also divide your second elective between the two programmes, e.g. 10 ECTS in your Bachelor’s degree programme and 20 ECTS in your Master’s degree programme.

In order to obtain teaching qualifications (formally termed academic qualifications??) to teach an upper secondary school subject as for example Mathematics or Physics you must fulfil certain academic minimum requirements within the subject in question. For scientific subjects these minimum requirements are almost equivalent to the content of the Bachelor’s degree programme in the subject. The exact requirements can be seen at the homepage of the Faculty of Science under Academic Regulations (only in Danish).

A student with the special area of study Mathematics lacks, for instance, a course in History of Mathematics (5 ECTS) and a course in Didactics of Mathematics (5 ECTS) in order to have the qualifications of teaching Mathematics. A student with the special area of study Mathematical Modelling lacks furthermore the course Differential Equations (5 ECTS) in order to have the qualifications of teaching Mathematics.

The principal for a school decides who he would like to employ. If you have the qualifications of teaching a specific subject he cannot reject you by referring to a lack of qualifications in that subject.

If you study the special area of study Mathematics you obtain teaching qualifications in another subject as e.g. Physics or Danish if you choose the relevant subject as subsidiary subject and fulfil the equalling subsidiary subject studies (also called subsidiary subject). If you have a subsidiary subject you obtain teaching qualifications in 2 subjects, namely in Mathematics and in the subsidiary subject.

The subsidiary subject study programme is a special study for which you must sign up in case you want a subsidiary subject. The content must meet some specific requirements as it aims at teaching at the upper secondary school. When you are admitted to the subsidiary subject studies, the subsidiary subject becomes part of your complete Bachelor’s and Master’s degree programmes in Mathematics. In this case the requirement of electives no longer applies.

A form for enrolment can be found at Admission to elective subjects at the University of Aarhus.

For Regulations, see Studieordning for tilvalgsfag i naturvidenskabelige fag (only in Danish).

In the formal communication about subsidiary subject the expression the central subject occurs. For those who have been admitted to Mathematics, the central subject = Mathematics.

The section ‘Examples of Electives in the Special Area Mathematics’ also comprises the requirements for different subsidiary subjects

• Elective in Statistics
• Mathematics with Physics as Subsidiary Subject starting at the 1st year
• Elective in Physics starting at the 2nd year
• Elective in Computer Science starting at the 1st Year
• Elective in Computer Science starting at the 2nd Year
• Elective in Chemistry
• Elective in Mathematics-Economics
• Elective in Biology
• Mathematics combined with another upper secondary school subject