Kurt Gödel Research Center

Information for students of the Logik Master

This page contains information for (prospective) students of the Mathematics Master program with specialization (Schwerpunkt) on Mathematische Logik und Theoretische Informatik, which will be called Logik Master for short.

General information for foreign students

This paragraph is relevant mainly for foreign students who are interested to come to Vienna for a Logik Master. (Austrian students will know all the information provided here anyway.)

Admission

The KGRC is not involved in any way in questions of enrolement, admission, tuition fees etc. Please consult StudentPoint or the SCC or help.gv.at. In particular, the following points are not in the responsibility of the KGRC and provided for information only. Also, we cannot answer questions regarding the following points, please contact StudentPoint instead.

Tuition fees

The tuition fees are relatively low (maybe 350 to 700 EUR per semester). EU citizens might have this fee waived in certain situations.

Cost of living

Master students do not receive salaries, and there are hardly any fellowships or grants available for them. The parents are supposed to cover the living expenses and tuition fee of the student. Only in exceptional cases, for EU citizens, when the income of the student and the student's parents is very low, and the student's progress is very good (which is measured in a rather buerocratic and inflexible way), then a goverment grant is provided (up to 600 EUR per month, if the student's family does not live close to Vienna).

Duration

It is probably quite hard to finish a Logik Master in the official timeframe of 4 semesters, unless you already have a good education in mathematical logic to begin with. Note that it is not a problem to take longer than the 4 semesters, but of course you will then have to provide the cost of living for a longer period of time (and in the rare case that you get the goverment grant mentioned above, this grant will be only payed for up to 5 semesters).

Language

Basic German skills (or at least to take a German class once you arrive) are recommended, but probably not necessary: While admission to the master program in principle requires a proof of proficiency in German, this can be (and usually is) waived during the admission process. And it is probably possible to finish the Logik Master by attending classes in English only: All the lectures at the KGRC are held or can be held in English. You will also have to take courses outside th KGRC (at least for the Verbreiterung, see below, but possibly also for Wahlfach or for logic courses at TU). Some of these courses are in English anyway, and many more can be held in English if requested (just contact the lecturer and ask). But of course we can not guarantee anything for non-KGRC courses.

Courses of the Logik Master

As you know from the Studienplan, the following courses are required for the Logik Master, adding up to 120 ECTS:

Mandatory logic courses (Pflichtmodule: MLOL, MLOM, MLOI, MLOS), 30 ECTS

The mandatory courses are held at the KGRC every year. In the following table, W indicates that they are held in the winter semester, S in the summer semester. The exception is Einführung in die Theoretische Informatik: As we do not regularly offer this course, we recommend taking it at the Technical University. See the section on TU below.

Other logic courses (Vertiefungs LVAs: MLOV), 21 ECTS

For this part you can use every course with the code MLOV. At the KGRC we regularly give the following courses, but not all of them every year: Modelltheorie and Rekursionstheorie alternate in summer semesters. In addition, Anwendungen der Mathematischen Logik is held every second year or so (sometimes at TU). The Forschungsseminar is held every semester (it is an advanced seminar suitable for PhD students and advanced Master Students). Note that there are many courses at TU that can be used (angerechnet) as MLOV, see the section on TU.

Courses from other areas (Verbreiterung), 24 ECTS

Every course from the Mathematics master program will do, provided it does not have a code starting with MLO. Note that you do not have to choose all these courses from a single non-Logik Schwerpunkt. I.e., you can use courses from more than one non-Logik Schwerpunkt.

Free choice of courses (Wahlfach), 15 ECTS

Every course from the Mathematics master program will do, including courses at the KGRC that you do not use for Pflicht or Vertiefung. Note that you can also use TU courses, see below.

Thesis (Masterarbeit), 30 ECTS including exam

A master thesis can be supervised by faculty with Habilitation (at the KGRC currently S. Friedman and J. Kellner). In practise we can offer topics from set theory and to some degree model theory and recursion theory. If you would prefer a thesis in a research area that is represented at TU (such as proof theory or automatic theorem proving), it will be necessary to get a supervisor from TU. It is theoretically possible to have an external advisor, but this is cumbersome and uncommon for Master theses (but you have to discuss it with the SPL Mathematics). As alternatives, the thesis can still be supervised at the KGRC if you can get a secondary supervisor from TU.

Recommended timeplan

In the following, let us assume that your aim is to write a Master thesis at the KGRC, in set theory or maybe in model theory. It is required that you already know some very basic logic as covered, e.g., by the Bachelor course Grundbegriffe der Mathematischen Logik. Ideally, you already took Einführung in die Logik and Mengenlehre 1 while studying for the Bachelor. In this case, a possible schedule for the remaining Logic courses would be the following:

This will cover the mandatory courses, give you the 21 ECTS required for Vertiefung and another 18 ECTS you can use for Wahlfach (which is actually more than the 15 you need, so you could, e.g., drop one of Beweistheorie, Modelltheorie or Rekursionstheorie).

Notes:

• Don't forget that you additionally need 24 ECTS worth of Verbreiterung courses, i.e., non-logic courses.
• You can take the reading course twice (as suggested in the timeplan above), or even three times, provided of course that the contents is different (and suitable) each time. So the first time you will learn, e.g., about forcing and measurable cardinals; the next course about descriptive set theory and mor advanced forcing techniques, etc.
• If you did not do the Logik and Mengenlehre during the Bachelor program, you will obviously have to compress the master a bit.
• Of course many variations are possible. E.g. you can take many additional courses at TU. You definitely should do that if you are interested in the computational side of logic.
• Or if you do not want to write a master thesis in set theory, then the set theory reading courses should be subsituted by courses from the area of the thesis.

Mathematical Logic at the University of Technology (TU Wien)

At the Technische Universität Wien (TU for short), there are several active research groups and many interesting courses on mathematical logic and theoretical computer science. You are strongly encouraged to enroll at TU in addition to the Universität Wien (univie for short).

How to enroll at TU and what TU curriculum to choose

• For general information, contact the TU Studienabteilung.
• You can enroll in any additional curriculum at TU you want, or just choose Mitbelegung:
• The simplest version is Mitbelegung: You do not enroll in a TU program, but rather just register your univie Logik Master curriculum at TU. A page at the TU Studienabteilung (German) has more information.
• Alternatively, you can enroll for any curriculum offered at TU. For this, you need to provide the usual documents: Reifeprüfung for a Bachelor program and a Bachelor Diploma for a Master Program, which might be complicated for foreigners. Again, you can find more information (in German) at the Studienabteilung. Natural choices for curricula would be:
  Master program Computational Logic
  Master program Technische Mathematik
  Master program Computer Science
• Usually, additional enrollment at TU should not incur any fees nor should it interfere with any potential financial support you might be eligible for, such as Familienbeihilfe; but please check this yourself!

When you should enroll

• You should enroll as soon as possible, and in every semester, even in semesters in which you do not plan to attend any courses at TU.
• The reason: To be able to take an exam for a course at TU, you have to be enrolled at TU both in the semester of the course as well as in the semester of the exam. So if you decide near the end of the Master program that you would like to take an exam for a TU course that was given in a previous semester, it is necessary that you have been enrolled in that semester.

How you can use the TU courses for the univie Master program

• Whether a TU course can be used is not decided by the KGRC, but rather by the SPL Mathematics (i.e., as of 2011 by A. Cap). The SPL decides on an individual basis whether a course from another curriculum will be accepted (angerechnet) for the univie Master.
• Theoretically, you can (or even should) ask the SPL whether a TU course will be accepted before taking it (otherwise your effort might be wasted). However, the SPL is probably not very interested in such questions, and we never had any problems getting reasonable courses accepted. (Of course it has to be a specialized course on logic or theoretical computer science; an easy general introduction to logic will not be accepted as a MLOV course, since it would add redundancy to the Bachelor and Master courses Grundbegriffe and Logik.)
• So while we (the KGRC) cannot guarantee anything, we would recommend to just take any reasonable course at TU and you can be sure that it will be accepted by the SPL.

Why you should enroll, what courses you should take

While the KGRC offers most mandatory courses for the (Logic part of the) Logik Master, there are good reasons to take some additional courses at TU:

• The mandatory course Einführung in die theoretische Informatik (5 ECTS) is not given at the KGRC regularly. It is recommended to take the TU course Theoretische Informatik (for Master Program Mathematics) (4 ECTS). If the SPL demands another course for the 1 missing ECTS point, we can provide an appropriate mini-course at the KGRC. (Alternatively, you could take theoretical computer science courses for computer scientists, at TU or at univie, but this is not recommended, since the contents is probably too simple while your effort is higher, due to mandatory attendance and the great number of students.)
• The KGRC offers enough ECTS to cover the mandatory and Vertiefungs part of the Logik Master, but there is not much left for the Wahl part. So while you are of course welcome to take courses from other parts of mathematics, it might be less effort and/or more interesting for you to take logic courses at TU. (In particular, since you will have to write a Master thesis, you will have to learn a lot about your area of spezialisation anyway. For example if you write a thesis in set theory, Martin Goldstern's courses will be interesting for you.)
• The KGRC specializes on the semantic part of logic (set theory, model theory, a bit of recursion theory etc). There is a different side to logic as well, leaning more towards syntax and computer science, containing subjects such as nonclassical logics, proof theory, automatic theorem proving, model checking. All these subjects are represented in research and teaching at the TU. In particular, we recomment to take Beweistheorie at TU, one of the four classical branches of mathematical logic, which is currently not represented at the KGRC. (But even if you are only interested in set theory, you should check out Martin Goldstern's courses at TU, as already mentioned.)

TU Research groups in (or close to) mathematical logic

(The following list is probably not complete)

• Algebra Group, led by Martin Goldstern, emphasis on set theory and universal algebra.
• Computational Logic Group, led by Matthias Baaz, emphasis on proof theory and non-classical logics.
• Theory and Logic Group Group, led by Alexander Leitsch, emphasis on proof theory and theoretical computer science.
• Database and Artificial Intelligence Group, led by Georg Gottlob and Reinhard Pichler
• Knowledge-Based Systems Group, led by Thomas Eiter
• Formal Methods in Systems Engineering, led by Helmut Veith, emphasis on Model Checking