Unofficial English translation of the examination regulations

Examination Regulations
for the International Master's Program
in Mathematics
at the Ludwig-Maximilians University
of Munich

From the 5th of November, 2001





In accordance with article 6, article 81 paragraph 1 clause 1, and article 86a of Bavarian University Law (BayHSchG) as well as § 51 paragraph 1 of the qualification regulations (BayRS 2210-1-1-3-UK/WFK), the Ludwig-Maximilians University Munich issues the following statutes:



Table of Contents

I. General Regulations

§ 1    Qualification
§ 2    Type of study and examination, academic degree
§ 3    Length of study, semesters abroad
§ 4    Examination board
§ 5    Examiners
§ 6    Crediting study periods, courses and examinations
§ 7    Evaluation of exam results
§ 8    Withdrawal, failing, deception, violation
§ 9    Flaws in the examination procedure, inspection of records

II. Master's Exam

§ 10    Sections of the master's exam, exam subjects
§ 11    Admission to the master's exam
§ 12    Oral final exam
§ 13    Electives
§ 14    Free attempts
§ 15    Passing and retaking the oral final exam
§ 16    The master's thesis
§ 17    Evaluation of the master's thesis
§ 18    Graduation, failing and repetition of the master's exam
§ 19    Certificate
§ 20    Master's diploma
§ 21    Deprivation of the master's degree

III. Concluding Notes

§ 22    Effective date

I. General Regulations

§ 1

(1) To qualify for the mathematics master's program, the student must

1.a) provide the first job-qualifying academic degree in a mathematics course of studies aquired from a university in Germany and completed with a grade of at least "good" or provide an equivalent foreign degree, or
b) provide the first job-qualifying academic degree in a different course of studies than mentioned under a) acquired from a university in Germany and completed with a grade of at least "good" or provide an equivalent foreign degree, and have s uccessfully participated in a selection interview according to paragraph 4;
2. possess a good knowledge of the English language.


(2) 1The university admissions department determines the presence of qualification requirements pursuant to paragraph 1 within the framework of the enrollment procedure, and, in case of uncertainty, in agreement with the examination boa rd. 2Should uncertainty arise over the equivalence of foreign academic degrees, the examination board can consult the central department for foreign studies.

(3) Applicants whose first language is not English must provide proof of knowledge of the English language through the "Test of English as a Foreign Language" (TOEFL, at least 207 points).

(4) 1The purpose of the selection interview is to verify that the applicant has sufficient basic knowledge in the field of mathematics to correspond to the requirements of an intermediate examination and allow successful participation in the studies. 2Carrying out the selection interview is incumbent on the examination board; the test requires persons from the professional teaching circle who participate in the studies to carry out the selection interview. 3The selectio n interview lasts approximately 30 to 60 minutes per candidate.

(5) Applicants from a non-German-speaking background should have a good command of the German language to an extent that allows them to participate in second-year German-speaking seminars in mathematics as well as in their minor.


§ 2
Type of study and examination, academic degree

(1) The master's exam forms the conclusion of the master's program in mathematics.

(2) 1The master's program encloses

1. the attendance of lectures and seminars
- in two compulsory subjects (Pure Mathematics and Applied Mathematics) and
- in a subsidiary subject (minor);
2. the completion of a master's thesis;
3. the completion of an oral final exam in the two compulsory subjects, in an area of emphasis (major) and in the subsidiary subject (minor).

2The master's exam should determine whether the necessary background knowledge was obtained for transition into the professional field, whether the connectivity of the subject has been grasped, and whether the student is capable of working independently on academic principles.

(3) Upon passing the master's exam, the Department of Mathematics, Computer Science, and Statistics for the Ludwig-Maximilians University of Munich grants the academic degree of "Master of Science" (abbreviated to "M.Sc.").


§ 3
Length of study, semesters abroad

(1) The regular length of study amounts to four semesters.

(2) The workload for required seminars and lectures amounts to at most 48 semester hours.

(3) Students who did not receive their qualifying degree for the program at a foreign university pursuant to § 1 paragraph 1 clause 1 no. 1 are recommended to complete one semester of the program at a foreign university.


§ 4
Examination board

(1) 1To organize the examinations and fulfill the tasks designated by the examination regulations, an examination board is formed. 2The board consists of six members. 3The term of office is three years. 4Members may be reappointed.

(2) 1The chairperson, his or her deputy and the other members of the examination board are appointed by the department council. 2Members must be professors.

(3) 1The examination board is decision-capable if all members are properly invited and a majority is present and entitled to vote; it decides with a majority of cast votes in a sitting. 2In the event of parity of votes, the chairperson casts the deciding vote. 3Abstention, secret voting, and transfer of the right to vote are not permissible. 4A member may be expelled by means of deliberation and voting pursuant to article 50 BayHSchG.

(4) 1The examination board ensures that the provisions of the examination regulations are observed. 2The board regularly reports to the department council about the examinations and study times and stimulates the reform of curricula and examination regulations.

(5) The exam board members have the right to be present at the exams.

(6) 1The examination board is responsible for carrying out exams. 2It makes the necessary decisions to do this, insofar as other authorities are not declared responsible within these examination regulations. 3The chairperson issues invitations to exam board sittings. Upon demand of at least two board members, the chairperson must call a sitting within a period of two weeks.


§ 5

(1) 1The chairperson of the exam board determines the examiners, whereby the candidate's requests are most likely to be taken into consideration. 2The chairperson of the exam board is not bound to these requests.

(2) 1For mathematics partial exams, all professors employed full-time by the Mathematics Institute as well as professorial holders of teaching permits for mathematics that belong to full-time personnel of the mathematics institute are permitted to be examiners. 2The exam board can impose restrictions. 3Under special circumstances and in accordance with university examiner regulations in the pertaining effective version, the exam board can also accept emeritus professors and retired professors as well as PhD-holding academic employees of the Department of Mathematics, Computer Science, and Statistics for individual exams or as regular examiners. 4If an individual that is entitled to take the exam withdraws from the university, the exam board can decide that the individual may retain this right for a limited period of time.

(3) 1For exams within subsidiary subjects (minors), the approved examiners are determined in consultation with the responsible department. 2Candidates include faculty members that represent the relevant subject as well as other faculty active within this subject who have been approved for the exam in accordance with the university examiner regulations.


§ 6
Crediting of study periods, courses, and examinations

(1) Relevant semesters of study at university-level institutions in Germany and results from studies and exams at these institutions are awarded credit.

(2) 1Pertinent semesters of study at other university-level institutions and the results of studies and exams at these institutions are awarded credit insofar as an equivalent level of study can be proven. 2Equivalence is determined by approved agreement of equivalence from the Conference of Secretaries for Cultural Affairs and from the Conference of University Rectors of the Federal Republic of Germany. 3In cases of doubt of equivalence, the Central Office for Foreign Education may be consulted. 4Certificates acquired in nationally recognized correspondence degree programs (Fernstudium), insofar as they are equivalent, are credited just like the length of study. 5Equivalence is determined in accordance with article 51 paragraph 3 clause 5 BayHSchG.

(3) 1Upon application, complete or partial credit is awarded for semesters of study in related fields of study and the related accomplishments, insofar as equivalence can be proven. 2The decision is made by the chairperson of the exam board, who consults an additional department representative before refusing credit.

(4) Certificates in a language other than German or English must be presented in a certified translation in German.

(5) 1The crediting of exam results as a master's thesis or within the scope of the oral final exams is precluded in accordance with paragraphs 1 through 3. 2The exam board determines recognition according to paragraphs 1 through 3.


§ 7
Evaluation of exam results

(1) 1The individual exam results in the master's exam including the master's thesis are evaluated with the following grades:

"very good" (1)    outstanding work
"good" (2)    work which considerably exceeds the normal requirements
"satisfactory" (3)    work that corresponds to the normal requirements
"sufficient" (4)    work that, despite its shortcomings, still fulfills the requirements
"insufficient" (5)    work that, due to considerable insufficiencies, is no longer acceptable

2Only these grades may be used in a certificate. 3The grades can however be lowered or raised 0.3 points in the record for a distinguished evaluation and are in this form used to calculate the overall grade. 4Grades of 0.7 and 4.3 are not possible.

(2) 1The grades for the exam results are determined by the respective examiner(s). 2In the case of different evaluations, the examiners should come to an agreement on one grade. 3If this is not possible, the grades are averaged.

(3) 1The overall grade for the master's exam is the unrounded mean of the oral exam results in the individual subjects plus the doubly-weighted grade for the master's thesis. 2The overall grade of a passing exam is:

with a mean of up to 1.5:    very good
with a mean from 1.5 to 2.5:    good
with a mean from 2.5 to 3.5:    satisfactory
with a mean from 3.5 to 4.0:    sufficient

2If the grade for the master's thesis is 1.0 and if the overall grade is better than 1.1, the "passed with honors" distinction is granted.


§ 8
Withdrawal, failure, deception, violation

(1) 1If a withdrawal happens after registering for a fixed exam without a convincing excuse, the respective exam is scored as "insufficient" (5.0). 2Failure to attend a fixed, registered exam without a convincing excuse is treated as an unexcused withdrawal. 3The same is true if written exam results are not produced within the provided working time.

(2) 1Plausible grounds for excusable withdrawal must be promptly reported in writing to the chairperson of the exam board. 2In case of sickness, the chairperson can request a medical certificate from a doctor of his/her choice.

(3) 1An attempt to influence the results of an exam to one's personal advantage or to that of another by deception or the use of unpermitted aids will result in a score of "insufficient" (5.0) for the respective exam. 2Mere possession of unpermitted aids during and after the distribution of the exam documents is also regarded as deception. 3Whether an offense has been committed is determined by the exam board. 4As long as this decision has not been made, the exam can be continued.

(4) A student who disorderly disrupts the exam can be disqualified by the examiners or supervisors in charge; the respective exam results are scored as "insufficient" (5.0).

(5) 1If the requirements for admission to an exam were not fulfilled without intentional deception, and if this fact is first recognized after the distribution of the master's exam certificates, this shortcoming is remedied by passing the exam. 2If admission was intentionally and unfairly achieved, the exam board decides in compliance with the administrative legal principles whether to revoke illegal administrative acts.

(6) 1If after the issuance and handing out of exam certificates it follows that unpermitted aids were used during the exam or deception was present, the exam board can later adjust the respective grades and declare the entire exam or part of the exam as not passed. 2The incorrect exam certificate is confiscated and, if necessary, a new one is issued. 3Such a decision is first precluded after a period of 5 years from the date of the exam certificate.

(7) Before a decision pursuant to paragraph 3, 5, or 6, the opportunity is granted to make an open statement.


§ 9
Flaws in the examination procedure, inspection of records

(1) If it can be demonstrated that the examination procedure was significantly flawed in a way that could have influenced the exam results, upon application from the respective persons or department, a retaking of the exam in whole or in part must be arranged.

(2) 1Alleged flaws in the examination procedure must be notified to the exam board or to the examiner immediately - before the release of exam scores at the latest. 2Such notification is no longer possible after one month has passed since the exam results were provided.

(3) Six months after the end of the exam, regulations pursuant to paragraph 1 may no longer be questioned by a department.

(4) 1After the production of all exam results, the respective records may be inspected upon application. 2The chairperson of the exam board determines the time and place of inspection. 3The production of copies or photocopies is not permitted.



II. Master's Exam

§ 10
Sections of the master's exam, exam subjects

(1) The master's exam consists of:

  1. the oral final exam

  2. the completion of a master's thesis.

(2) As per paragraph 1, participation in the exams must be timely so that the master's exam has been taken before the end of the fourth semester.

(3) Should the period of time pursuant to paragraph 2 exceed two semesters without good reason, the untaken portion of the master's exam is counted as taken and not passed.

(4) 1Any reasons that should justify exceeding the period of time pursuant to paragraph 3 must be asserted and substantiated at the examination office before the end of the period of time. 2In case of sickness, the submission of a certificate from a doctor selected by the examination board is requested. 3The examination board decides whether to acknowledge the reasons and determines the length of the time extension. 4The decision results in written notification that, which in the event of rejection, informs the student of the reasons and provides information on applicable remedies.


§ 11
Admission to the master's exam

(1) 1The application for admission to the master's exam must be submitted in writing using the prescribed forms to the examination board by the deadline specified in a notice. 2The application must include the following:

  1. proof of enrollment in the master's mathematics program at the Ludwig-Maximilians University of Munich;

  2. a written declaration that no final exam in the field of mathematics at a German university or at an equivalent university has been conclusively failed and that the student did not leave the university due to loss of qualification for the exam;

  3. the submission of certificates pursuant to paragraph 3;

  4. a written declaration of the selected major and minor pursuant to § 12 paragraph 1.

(2) 1If the documents are not complete in accordance with paragraph 1 clause 2, admission is refused. 2In this case, a notice of rejection is issued to show the reasons for rejection and provide information on applicable remedies.

(3) 1As certification, evidence is required of successful participation in:

  1. two mathematics seminars; seminar certificates are normally acquired by actively participating and by holding a two-hour lecture in a mathematics seminar;

  2. three four-hour lectures with two-hour exercise courses; the fields of Pure Mathematics and Applied Mathematics must be represented with at least one lecture each;

  3. an exercise course or a seminar or advanced practical training according to the conditions of the selected minor.

2The stated certificates are acquired by work such as homework, in-class exercises, and written or oral exams. 3Details are settled by the member of the teaching staff who is responsible for the respective lecture or seminar. 4Any attempt to acquire certificates can be repeated several times in observance of § 10 paragraphs 2 and 3.


§ 12
Oral final exam

(1) 1The oral final exam covers the following subjects:

  1. Pure Mathematics;

  2. Applied Mathematics;

  3. the area of emphasis (major);

  4. the subsidiary subject (minor).

2The major, from which the master's thesis should develop, is freely chosen by the candidate. 3Detailed knowledge will be tested on a branch within the major. 4The minor may not be a branch of Mathematics. 5It must be offered within the frame of a diploma or master's program at the Ludwig-Maximilians University of Munich. 6Valid minors are Applied Statistics, Experimental Physics, Computer Science, Theoretical Physics, Actuarial Theory (mathematics of finance and insurance), and Economics. 7The examination board can admit additional minors generally or upon application.

(2) 1In consultation with the examiner, the candidate can declare fields in which he or she is particularly prepared; the exam primarily includes these fields. 2The right of the examiner to touch on related fields remains unrestricted. 3In particular, the exam subject should be considered in sufficient breadth. 4With every exam subject, a range of the material must be taken as a basis that corresponds to roughly 12 semester hours of lectures, seminars, and exercise courses.

(3) 1The exam lasts approximately 30 minutes for each exam subject. 2It can be held in English upon application by the candidate, which is to be included with the application for admission to the master's exam.

(4) 1In justified special circumstances, a single examiner can administer at most 2 of the exam subjects. 2An examiner in the minor may not also be an examiner for one of the other exam subjects at the same time.

(5) 1All partial exams must -- in principle -- be taken in a time span of four weeks and within seven months after admission to the exam. 2The chairperson of the exam board may allow exceptions if examiners are not present, the candidate becomes sick, or there is another convincing reason. The candidate arranges the exam dates with examiners and informs the examination office accordingly.

(6) 1Each candidate is examined individually. 2The exam procedure is recorded by an expert observer. 3The record is signed by the examiner and the observer. 4The results of the exam are then shared with the candidate.

(7) 1In the partial exams, students in the same field of study are admitted as listeners according to the number of seats available. 2Listeners may not be present when the exam result is announced, and may also be denied admission by objection from the candidate. 3The dates of public exams are announced with a notice from the examination office.


§ 13

(1) 1The candidate can, upon request, take more than the prescribed subjects of an oral exam (electives). 2The examination board decides on the application. 3More than two electives are not allowed.

(2) The exam results in these subjects can be included in the certificate upon request from the candidate but will not be included in the assessment of the overall grade.


§ 14
Free attempts

(1) Free attempts can be made on the oral subject exams according to paragraphs 2 and 3.

(2) Oral subject exams not passed the first time are not considered taken if they were taken after uninterrupted study no later than the end of the fourth semester.

(3) 1Passed oral subject exams that were taken after uninterrupted study no later than the fourth semester can be repeated once on the next regular date to try to improve the grade; the better score counts. 2In this case, notification of a free attempt, including which oral exam results the free attempt applies to, must be submitted in writing to the examination board at least four weeks after the announcement of the exam scores.


§ 15
Passing and retaking the oral final exam

(1) The oral final exam has been passed if the results in all subjects have received a grade of "sufficient" (4.0) or better.

(2) 1The oral final exam has not been passed if the results in one subject have received a grade of "insufficient" (more than 4.0). 2An oral final exam that was not passed can within a semester be retaken once in the subjects that were not passed. 3The repeat examination has been passed if the oral repeat exam receives a grade of "sufficient" (4.0) or better. 4A second retake of the oral final exam is then only permitted when for every subject exam that has not been passed there is at least one subject exam that was passed with a grade of 3.0 or better; the second repeat examination must be taken within a semester.


§ 16
The master's thesis

(1) 1In the master's thesis, the candidate should show adequate mastery of the subject and an ability to work independently on academic principles. 2The master's thesis may be written in German or English.

(2) 1The master's thesis can be given out by anyone qualified for the exam according to § 5. 2Under special circumstances, the thesis can also be handed out with the approval of the examination board by a different member of the university teaching staff, provided it does not conflict with the rules of the university examiner regulations in the pertaining effective version.

(3) 1The chairperson of the examination board must be notified of the handing out of a master's thesis by the task assigner. 2Upon special request from the candidate, the chairperson of the examination board can see to it that the candidate timely receives the topic for his or her master's thesis. 3The time from the handing out of the thesis to the delivery of the thesis amounts to six months. 4The choice of a topic should be adapted to fit this time frame. 5The writing and editing period can under justified special circumstances be extended with the approval of the examination board by at most three months; the grounds for extension must be substantiated. 6Proven sickness affects the writing and editing time.

(4) 1The master's thesis must be provided with a statement that the candidate independently wrote the thesis and used no sources or aids other than those indicated. 2The thesis must be bound, paginated, and provided with a summary. 3The master's thesis is to be handed in within the agreed time limit in duplicate in the examination office; the time of handing in is to be recorded.

(5) If the creation of the master's thesis is intended to collaborate with a company in the industry, then an internship with this company is strongly recommended.


§ 17
Evaluation of the master's thesis

(1) 1The master's thesis is to be evaluated by the topic provider and an additional examiner determined by the chairperson of the examination board within a time frame determined by the chairperson of the examination board. 2If the master's thesis is evaluated as "insufficient" by one of the two examiners or if the evaluations deviate from each other by more than two grades, the examination board will determine a third examiner. 3The overall grade is established by arithmetical means of assessment, whereby only the first decimal place is taken into consideration.

(2) 1The master's thesis has been passed if it was marked with a grade of at least "sufficient" (4.0). 2If the master's thesis, without valid justification, was not handed in to the chairperson of the examination board within the agreed time limit, it receives a grade of "insufficient".

(3) 1If the master's thesis has received a grade of "insufficient", it can be repeated once with a new topic within one semester from the announcement of the grade. 2A second repetition is not permitted. 3The repetition of a master's thesis with a grade of at least "sufficient" (4.0) is not permitted.


§ 18
Graduation, failing and repetition of the master's exam

(1) The master's exam has been passed when the oral final exam and the master's thesis have each received a grade of at least "sufficient" (4.0).

(2) If the master's exam is considered not passed the first time according to § 10 paragraph 3, it can be retaken one time within the next six months.

(3) The master's exam is considered conclusively not passed and cannot be repeated, if

  1. one or more of the subject exams of the oral final exam have been evaluated as "insufficient" (more than 4.0) after all opportunities to retake the exam have been exhausted;

  2. the master's thesis has been evaluated as "insufficient" (more than 4.0) after all opportunities to repeat the thesis have been exhausted;

  3. a deadline for repeat exams has been exceeded due to unjustified circumstances.

(4) 1If the master's exam was not passed or if it is considered to be not passed, a written notice is sent indicating the corresponding rules of these exam regulations. 2The notice will also inform the candidate whether the master's exam can be repeated, to which extent, and within which period of time.


§ 19

(1) 1If a candidate has passed the master's examination, he or she obtains a certificate about the results which includes the grades obtained in the individual subjects, the names of the examiners, the grade for the master's thesis with information about the task assigner as well as the overall grade. 2The certificate is signed by the chairperson of the examination board and is provided with the seal of the examination board. 3The certificate is written in German as well as English.

(2) Notification of the conclusively failed exam is to be provided with information on applicable remedies.


§ 20
Master's diploma

(1) 1A diploma is delivered to the candidate at the same time as the certificate that records the granting of the academic master's degree and contains the overall grade for the master's exam. 2The date indicated on the diploma is the day on which all exam requirements were fulfilled.

(2) 1The diploma is signed by the chairperson of the examination board and by the dean of the Department of Mathematics, Computer Science, and Statistics and is provided with the seal of the department. 2The diploma is written in German as well as English.

(3) Moreover, a supplementary description (Diploma Supplement) is handed out that describes the primary underlying study content of the degree, the program, and the qualifications acquired with the degree.


§ 21
Deprivation of the master's degree

The withdrawal from the academic master's degree complies with the statutory regulations.



III. Concluding Notes

§ 22
Effective date

This statute becomes effective on the day after its announcement.



Issued on the basis of the resolutions of the senate of the Ludwig-Maximilian University of Munich from the 17th of May, 2001; on the basis of the resolutions of the Board of Trustees of the university from the 19th of September, 2001; and on the basis of the approval of the Bavarian Minister of Science, Research, and Art in writing from the 24th of October, 2001, No. X/5-5e65(LMU)-10b/45 327.

Munich the 5th of November, 2001




Professor Dr. Andreas Heldrich



The statute was put into writing on the 7th of November, 2001, at the University of Munich. The writing of the statute was announced by notice on the 8th of November, 2001. The day of announcement is thereby the 8th of November, 2001.