Course of study	Prerequisite	Processing time	ECTS
Two-Major Bachelor	60 ECTS credits in the subject of the thesis have been completed	3 months	10
Bachelor of Science	80 ECTS points in compulsory and elective mathematics (incl. internal BOK) have been completed	3 months	12
	additionally in PO 2021: presentation of the Bachelor thesis		1
Master of Education (also extension master)	60 ECTS points in the course of study have been completed	4 months	15
Master of Science	60 ECTS credits in the study program have been completed	6 months	30
	additionally: presentation of the master thesis		3

There are no requirements regarding the number of pages of the thesis or the duration and framework of the presentation of the Bachelor's or Master's thesis. This must be discussed with the supervisor of the thesis.

The processing period begins on the day on which the topic is officially assigned. This date is entered on the registration form.

Supervision at the Mathematical Institute:

The supervision of Bachelor's and Master's theses is primarily the responsibility of the professors (including junior professors and private lecturers) of the Institute of Mathematics. They are listed with their research and interest areas on the webpage Lecturers and Research Areas.

Non-professorial academic staff (i.e. who do not hold the title "Privatdozent/in" or "Dr. habil") may only officially supervise Bachelor's or Master's theses if they have been authorized to do so. In case of doubt, this must be inquired about.

It may well be that the work is de facto supervised by a research assistant. However, this is not legally relevant - the term "supervisor" always refers to the person officially designated and responsible for supervising the work.

External care:

Co-opted professors also have the right to supervise mathematical theses. These are usually mathematicians who hold a professorship at another faculty, but by virtue of their co-optation are eligible to examine within mathematics. They are also listed on the Lecturers and Research Areas page.

In exceptional cases, a thesis may also be supervised by a professor or a private lecturer of another faculty or another university if this is done in agreement with a professor or a private lecturer of the Mathematical Institute of the University of Freiburg. Such external supervision must be applied for informally via the examination office and approved by the subject examination board.

Master of Education theses in didactics of mathematics can only be supervised externally, usually by professors of mathematics at the University of Education Freiburg. This is possible within the framework of the supervision capacity of the University of Teacher Education and requires the completion of the module "Fachdidaktische Forschung". Please register your interest with the Department for Didactics of Mathematics.
For the agreement with a professor of the Department of Mathematics of the University of Freiburg please contact either someone who is professionally close to the topic of the thesis, or to the Executive Director of the Department for Didactics of Mathematics.

A Bachelor's or Master's thesis can also be written in cooperation with a company. In this case, however, either the official supervision takes place at the Institute of Mathematics or the contact person in the company is by chance a habilitated professor or even a professor and the exception described in the previous section is possible. In the first case, experience has shown that a thorough consultation between the official supervisor of the thesis and the de-facto supervisor in the company is necessary.

It is best if you already have an idea of the direction in which your work should go or in which focus area you want to write your paper. Then you can specifically contact lecturers who work in this direction or are active in this focus area. Please have a look at the pages Lecturers and Research Areas and Typical Study Processes in the Focus Areas. It is best to make an appointment to speak with them. Lecturers with whom you are currently listening to a lecture or attending a seminar you are of course welcome to speak to them on the sidelines.

If you do not find anyone to supervise your work in this way, you can apply to the examination office for the assignment of a supervisor. However, this is rather unusual.

Two-Major Bachelor's:
Due to the fact that the curriculum leaves few choices, the topics for bachelor's theses are somewhat limited. You can connect to the advanced lectures in algebra and number theory, elementary geometry, numerics or stochastics, possibly also to the topic of the undergraduate seminar you have attended. Some instructors also assign topics that build on the basic lectures in calculus and linear algebra. Don't be afraid to approach lecturers; take advantage of office hours! If you would like to write your thesis in mathematics, but have no real idea who should supervise your work, it may also be useful to talk to the student advisory service of the Department of Mathematics.

Bachelor of Science:
In the course of your studies, through your required and elective courses, you will usually develop an idea of, in which focus area your work should be located. In this area you should then ideally also listen to an lecture and attend a seminar. Helpful is the page Typical study procedures in the focus areas. Feel free to approach the lecturers in this focus area early on. It may be advisable (as was still mandatory in the old examination regulations of 2012), to write the paper based on a seminar presentation. However, this does not have to be the case, especially if no suitable seminar is offered.

Master of Education:
You can write your Master's thesis in one of the two subjects in subject-specific science or subject-specific didactics, or in educational science. Interdisciplinary theses or theses combining subject-specific and subject-specific didactical aspects are also possible. (At times there was a rumor that you had to write your Master's thesis in the other subject than your Bachelor's thesis; this is not true).
If you want to write your thesis in mathematics, it is important to decide whether it should be in subject didactics or subject science, because the study plan depends on this:

• For a thesis in didactics of mathematics you have to complete the module "Fachdidaktische Forschung" at the PH Freiburg. Within the framework of this seminar you will then also find your supervisor.
• A specialized scientific paper can build well on the in-depth lecture or on a seminar taken in the module "Mathematische Ergänzung". If you already know in which area you would like to write your thesis, it is worthwhile to contact the lecturers of this area: Then you can take the module "Wissenschaftliches Arbeiten" instead of the in-depth lecture, in which you can familiarize yourself with the topic of the master's thesis.

Master of Education as an additional field:
For the "major subject variant" with 120 ECTS credits, the same applies as for the M.Ed. program; for the "minor subject variant" with 90 ECTS credits, one can orientate oneself on the specifications for the two-main subject bachelor.

Master of Science:
Students in the Master of Science program usually already have a good insight into mathematics and an idea of in which area they want to specialize. It is useful to have a look at the page Typical Study Sequences in the Focus Areas. Feel free to approach lecturers on the sidelines of lectures and seminars. Ideally, you should work your way into the topic of the Master's thesis in the specialization module or in the elective module in a reading course "Wissenschaftliches Arbeiten".

Registration must be made in writing at the Examinations Office using the form provided for this purpose (available online on the Examinations Office website under "Forms and Information Sheets"). The form must also be signed by the supervisor of the thesis. Then it must be handed in immediately to the Examinations Office (mailbox in front of the Examinations Office or by e-mail).
The processing time begins with the date of topic assignment noted on the registration form.

In the B.Sc. degree program Mathematics according to the "old" examination regulations of 2012, the registration of the thesis must be done at the latest on the day of the presentation in the Bachelor seminar. There are no requirements in the opposite direction: The presentation can take place as long as desired after the registration of the paper.

When registering for a Bachelor's or Master's thesis, one must confirm that one is familiar with the rules of good scientific practice. These rules are on the examination office website under "A to Z", keyword "Regeln wissenschaftlicher Redlichkeit".

When registering, the topic of the work is determined, the working title given for it can be adapted later. The topic may be changed once within certain deadlines (see under "New topic").

When registering the work, you can request, with the consent of the supervisor, to write the paper in English (or another language).

A topic for a thesis can be replaced once by a new topic, without it counting as a failed attempt, if the "return of the topic" happens within the following deadlines:

• Dual-Major Bachelor: two weeks
• B.Sc.: two weeks
• M.Ed.: four weeks
• M.Sc.: two months

The return of the topic must be communicated in writing to the examination office in due time (and of course this should be discussed with the supervisor beforehand). A new topic must then be assigned within four weeks; the processing time then begins anew.

In justified cases, the examination board can extend the processing time upon request, namely by the following maximum times:

• Dual-Major Bachelor: maximum six weeks
• B.Sc.: maximum one and a half months
• M.Ed.: maximum six weeks
• M.Sc.: maximum six weeks

If the extension is requested because of illness, a medical certificate "containing the medical facts necessary for the evaluation" must be submitted. If the extension is requested because the subject is too extensive for the time actually allotted, the supervisor must give a vote on the matter.

Theses must be written in German, unless, when registering the thesis, the student applies, with the consent of the supervisor, to write the thesis in another language. This must then be approved by the examination board, the review (with possibly second and third reviews) must be ensured and the thesis must contain a German abstract.
It is usually no problem to write a paper in English. French may also be possible; all other languages are likely to be difficult.

The examination regulations do not specify the number of pages or the formatting of a paper. (i.e. font size, line spacing, size of margins, citation style, etc.). Please discuss all these points with the supervisor of your paper. Depending on the topic, there will certainly be ideas from the supervisor about the size of the paper; In our experience, formatting issues are of secondary importance. However, it is usual to prepare the paper in DIN A4 format and to use the mathematical word processing program LaTeX. (LaTeX is not mandatory, but makes life easier).

This sample can be used for the title page. The name of the supervisor can, but does not have to be mentioned on the title page.
For Bachelor's and Master's theses as well as internal doctoral theses the title page with Unilogo may be used (however, without changes to the corporate design, i.e. in particular with regard to the size and position of the logo).

Two copies of the thesis - or three copies for the M.Sc. program in Mathematics - printed and bound must be submitted to the examination office of the Mathematics Department in due time (in person, in the mailbox in front of the examination office or by mail - in this case the date of the postmark is the date of submission).
In addition, the paper must be submitted (preferably by e-mail) as a pdf file. As a rule, the supervisor would also like to have the final version of the thesis as a pdf file by e-mail.

To meet the deadline, electronic submission is sufficient; the printed copies must then be subsequently delivered within the next two weeks together with a written assurance that the printed version matches the pdf version.

When submitting the work, one must assure in writing,

1. that one has written the submitted work independently,
2. that one has not used any sources or aids other than those indicated and that one has not copied any and that all content taken verbatim or in spirit from other works has been marked as such.
3. and that the submitted work is not or has not been the subject of any other examination procedure, either in its entirety of another examination procedure.

Be sure to read the exact requirements and the exact wording in the current version of the general part of the examination regulations; changes are possible! (The examination regulations are linked on the information pages for the study programs).

If the thesis contains a programming part, the corresponding programming code must be submitted electronically as a separate file together with the abstract of the thesis. You should clarify in advance with your supervisor whether this is sufficient, or whether a printout of the programming code (if necessary as part of the thesis) is required.

A presentation of the Bachelor's thesis is only required in the B.Sc. program according to the new examination regulations of 2021; a presentation of the Master's thesis only in the M.Sc. program. The presentations are ungraded study achievements of 1 ECTS point in the B.Sc. program and 3 ECTS points in the M.Sc. program.

There is no separate registration for the presentation, neither in writing nor via HISinOne.

The presentation of the bachelor's thesis should be about 30 minutes long, but can also be longer by mutual agreement. Beyond that, there are no formal and temporal requirements, especially not for the presentation of master's theses. A presentation may take place before the end of the submission of a thesis (sensibly not too early) and should not take place too late afterwards. At one extreme, it may be a discussion with the supervisor and the assessor in an office or, at the other extreme, it may consist of an ordinary presentation in a senior seminar or a project seminar. Both the date and the closer circumstances must be agreed upon with the supervisor.

A thesis is reviewed and evaluated by the official supervisor. In some cases there is also a second examiner, always in the M.Sc. Mathematics and in exceptional cases in the M.Ed. Mathematics.
(These exceptional cases are: in case of interdisciplinary work; in case of work with external supervision, unless it is a subject didactic paper supervised at the PH Freiburg, for which there is only one reviewer).
The second examiner is appointed by the responsible examination office, usually on the suggestion of the supervisor. Students do not have to take care of this.

The duration of the assessment should not exceed six weeks. If you need the assessment in a hurry (e.g. because of matriculation in a Master's program or starting a job), please discuss this with your supervisor as early as possible. If the assessment is delayed, please contact your supervisor and the examination office.

If there is only one expert opinion and it evaluates the thesis as passed, the grade of the expert opinion is the grade for the thesis. If the expert opinion evaluates the thesis as not passed, a second expert opinion is ordered by the examination board. If the second expert opinion also evaluates the thesis as not passed, the thesis is not passed. If the second expert opinion evaluates the work as passed with grade x, a third expert opinion is ordered by the subject examination committee, which determines the final grade y with x ≤ y ≤ 5.0 and thus in particular determines whether the thesis has been passed or not.
If there are two expert opinions, the arithmetic mean of the two individual grades, rounded down to one decimal place, is the grade for the paper, unless the two individual grades x1 and x2 differ by at least two grade levels. (Grade levels are"very good","good", etc. - so it is not about the difference of the two grades). In this case, a third opinion is ordered by the subject examination board, which determines the final grade y with min{x1,x2} ≤ y ≤ max{x1,x2} and, if applicable, thus determines in particular whether the thesis has been passed or not.

A thesis can be repeated exactly once in case of failure. For this purpose, the student must apply for a re-submission of the thesis within two months after the or submit an application for the assignment of a new topic.

The retake may be supervised by another person and the topic may be from a different area of mathematics concentration. However, the repetition of a thesis in the Dual-Major Bachelor or M.Ed. must be in the same subject.

A return of the topic is only allowed in case of a repetition if this possibility has not yet been used in the first attempt.

Master at the University of Freiburg

The general rule at the University of Freiburg is that in order to apply for a Master's program the underlying Bachelor's program does not have to have been completed. Important: The application deadline (in mathematics July 15 or January 15 - as of 2022) must not be missed under any circumstances, completely independent of the status of the Bachelor's thesis!
For matriculation, however, the Bachelor's program must have been completed. For Bachelor graduates from Freiburg, it is sufficient if the completion of the Bachelor program is documented in HISinOne; the certificate does not necessarily have to be available yet. (Applicants from other countries need the certificate for matriculation).
For matriculation, a deadline is normally set at the beginning of October for the winter semester or at the beginning of April for the summer semester. However, this deadline can be extended until approximately the end of the second week of lectures in consultation with the Student Secretariat, if, for example, the reports for the Bachelor's thesis are still outstanding.
(Matriculation under reserve is not possible - this only existed during the Corona pandemic in case, that the completion of the Bachelor's program was delayed for corona-related reasons).

In concrete terms, this means for Freiburg students who want to follow a Master's program at the University of Freiburg: If you are running short of time, you should re-register for the following semester in the Bachelor's program and plan the registration of the Bachelor's thesis in such a way, that the report is available at the beginning of the lecture period at the latest, so that you can then transfer to the Master's program. How much time the supervisor needs for the expert opinion should be discussed with him/her in advance. The examination office usually only needs one day to enter the grade in HISinOne, but may not be staffed every day.
If you would like to write the thesis in June, July and August, for example, the six weeks allotted for the assessment are sufficient, in order to be able to transfer to the master's program in mid-October. If, on the other hand, you would like to write the thesis in the months of July to September, the report must be prepared within two to three weeks, in order to be able to enroll or transfer in time: This is only possible after prior consultation with the supervisor!

Master at other universities

For matriculation at other universities, the certificate must usually be available and, of course, the matriculation deadlines of the respective university must be observed, which may end much earlier. It is therefore difficult to give a general timetable. In addition, the examination office also needs more time to prepare the certificate and have it signed, especially if the typical summer vacation period is involved. A few universities allow conditional matriculation; however, one must clarify this with the university.