Application

Applications are accepted from

June 1 - July 15 for the winter term (starting October 1st) and December 1 - January 15 for the summer term (starting April 1st) each year.

Universität Hamburg
MIN Fakultät, Fachbereich Mathematik
Studienbüro
Bundesstraße 55 (Geomatikum)
20146 Hamburg
Germany

Application Documents

To help the selection committee make its decision, your application should include the following documents:

• The signed printout of the online application form.
• A letter of motivation (about one page).
• Your Curriculum Vitae.
• A photocopy of your high-school diploma (In English, German or French. The photocopy and the translation need not be certified.)
• Your bachelor certificate in physics or mathematics displaying your grades (alternatively: Vordiplomszeugnis and grades of subsequent courses). Again, an uncertified photocopy is sufficient.

Scientific Prerequisites

For successful participation in the Master programme, you should have a good background knowledge in both mathematics and physics. Specifically, you should be familiar with the following topics from physics and mathematics.

Prerequisites in Physics:

A good background in quantum mechanics. This includes the following topics, which are part of the course content of a class in quantum mechanics according to our official handbook:

1. Hamilton-formalism, Poisson bracket
2. Schrödinger equation
3. Observables and operators
4. Eigenvalue problems for operators
5. Probability interpretation and uncertainty relations
6. One-dimensional problems
7. Angular momentum
8. Perturbation theory, Fermi's golden rule
9. Multiparticle systems, Fermi and Bose commutation rules

To students with a mathematics background, we recommend part 1 of the book Leon A. Takhtajan: Quantum mechanics for mathematicians, Graduate Studies in Mathematics Volume 95, American Mathematical Society.

It should be noted that without this background knowledge successful participation in a quantum field theory course would be extremely difficult. Additional background knowledge in theoretical electrodynamics and advanced quantum mechanics would be helpful. Most of our local students have taken an advanced class on quantum mechanics as well as a course on theoretical electrodynamics.

The content of our four-term class "mathematics for physicists" described below. Additionally, basic knowledge of elementary differential geometry, e.g. some familitarity with the notion of a manifold, and notions of Lie theory would be helpful.

1st Term:

1. Natural, rational, real and complex numbers
2. Vector spaces
3. Convergent sequences and series
4. Systems of linear equations
5. Continuity and differentiability of functions in one variable
6. Integration of functions in one variable

2nd Term

1. Sequences of functions
2. Hilbert spaces
3. Fourier series
4. Ordinary differential equations
5. Calculus in several variables

3rd Term

1. Integration in several variables
2. The classical theorems on integration (e.g. Gauss, Stokes)
3. Distributions and Fourier transforms
4. Partial differential equations

4th Term

1. Theory of complex functions
2. Linear operators on Hilbert spaces

It should be noted that our course "mathematics for physicists" is not limited to the applications of these topics in physics. It focusses on the mathematical concepts, abstract reasoning and proofs. Familiarity with mathematical reasoning as well as the ability to understand and conduct mathematical proofs are required for successful participation in the mathematics courses of our programme.

Proficiency in English

Your proficiency in English will be considered as proven if at least one of the following applies to you

1. You have successfully passed a university program taught in English.
2. You have passed the TOEFL test with 450 credits in the paper-based version (TOEFL PBT) or 130 credits in the computer-based test (TOEFL iBT)
3. You have passed the IELTS test with a score of at least 4.5
4. You have a high school diploma accepted at English language universities.
5. You have spent at least 6 months in an English speaking country.

or if you provide us with similar evidence or equivalent qualifications. In particular, we accept a certificate that proves that you have attended English classes in high school for at least 5 years.

Further comments:

• For applicants from outside the EU: if you anticipate problems in obtaining a visa or need our assistance to obtain one, please contact us well in advance. We will assist you, but the necessary procedures can take a lot of time.


• If you have problems sending the application documents by ordinary mail, e-mail submission is possible, except for the signed copy of your on-line application, which we need for legal reasons.


• If you have not yet received your bachelor certificate, please provide an up-to-date transcript of records and a written certification of your university that you are expected to have finished your studies by October 1st. In that case, please submit your bachelor certificate as soon as possible, by December 15 the latest.


• If your bachelor degree is neither in physics nor in mathematics, please contact us so that we can consider your case on an individual basis.


• A letter of recommendation from a professor of your home institution can be included in your application. The letter can also be sent from the professor's university email account to the Secretary or the Admissions Office


• There are semester/tuition fees, see the university's information on semester and tuition fees.


• Funding: Participants of the Master programme with a good knowledge of German are encouraged to apply for student jobs, either in computer maintenance (with interaction with users speaking only German, IT-Gruppe Mathematik - only in German) or for teaching undergraduate and service classes (knowledge of German at the level of being able to explain mathematics in German required, contact us). International students are encouraged to apply for grants to the DAAD (German Academic Exchange Service). The DAAD also runs an extensive database with information on funding opportunities from other organisations.

If you are interested in applying please feel free to contact us at any time.