Master's program in mathematics – core modules and elective courses in Mathematical Logic and Theoretical Computer Science

This page contains information for (prospective) students of the mathematics master's program with specialization (Schwerpunkt) on Mathematische Logik und Theoretische Informatik. Note that nearly all of the information listed here (admission, curriculum etc) is not in our responsibility. This information is provided for your convenience, but we cannot take any responsibility that it is correct, complete or still up to date. Please make sure to check with the authoritative sources, e.g.

General information for foreign students

This paragraph is relevant mainly for foreign students who are interested to come to Vienna to specialize in mathematical logic and theoretical computer science. (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 SSC Mathematik or help.gv.at. In particular, the following points is 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 (363.36 to 726.72 euros 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 bureaucratic 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 study program 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 paid 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's 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 study program 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 (courses from other areas of specialization; see below), but possibly also for Wahlfach (electives) 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 specialization in mathematical logic and theoretical computer science

As you know from the curriculum, the following courses are required for the master's program with specialization in logic, adding up to 120 ECTS:

Core modules in mathematical logic and theoretical computer science (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 and S/W in either semester.

ModuleWhenECTSSStTypeName
MLOL W 6 4 VO Introduction to Mathematical Logic
MLOL W 3 2 PS PS Introduction to Mathematical Logic
MLOM S 5 3 VO Axiomatic Set Theory 1
MLOM S 3 2 PS PS Axiomatic Set Theory 1
MLOI W 5 3 VO Introduction to Theoretical Computer Science
MLOS S/W8 4 SE two seminars (SE), 4 ECTS and 2 SSt each

Electives from your chosen area of specialization, mathematical logic and theoretical computer science (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: Model Theory and Computability and Complexity alternate in summer semesters. The Research Seminar 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 credited (angerechnet) as MLOV, see the section on TU.

ModuleWhenECTSSStTypeName
MLOV(S)32VOModel theory
MLOV(S)32VOComputability and Complexity
MLOVW72VOSet Theory (reading course)
MLOVW42VOSelected Topics in Mathematical Logic
MLOVS42VOSelected Topics in Set Theory
MLOVW & S42SEResearch Seminar (Mathematical Logic)

Courses from other areas of specialization (Verbreiterung), 24 ECTS

You need courses from other areas of specialization in mathematics master programs, i.e. courses that have a code not starting in MLO. Note that you do not have to choose all these courses from one single non-logic area of specialization; you can use courses from more than one. Of these 24 ECTS, at least 15 ECTS have to be from the Standardausbildung, and at most 4 ECTS from seminars.

Further electives (Wahlfach), 15 ECTS

Any course from the Mathematics master program will do, including courses at the KGRC that you do not use for core modules or electives in mathematical logic and theoretical computer science. Note that you can also use TU courses, see below.

Thesis (Masterarbeit), 30 ECTS including defense

A master thesis can be supervised by faculty with habilitation (at the KGRC currently S. Friedman, B. Miller, V. Fischer, L. Zdomskyy and M. Müller). In practice 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 time plan

In the following, let us assume that your aim is to write a master thesis at the KGRC. It is required that you already know some very basic logic as covered, e.g., by the Bachelor course Grundzüge der Mathematischen Logik (Basic Concepts of Mathematical Logic). Ideally, you already took Grundbegriffe der mathematischen Logik (Basic Concepts of Mathematical Logic) and Axiomaische Mengenlehre 1 (Axiomatic Set Theory 1) while studying in the bachelor's program. In this case, a possible schedule for the remaining Logic courses would be as follows:

TO DO: GIVE EXAMPLE PATH THROUGH MASTER'S PROGRAM

Notes:

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 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

When you should enroll

How to get credit using TU courses for the univie master program

Why you should enroll, what courses you should take

While the KGRC offers all mandatory courses for logic and theoretical computer science as an area of specialization in your master's program, as well as sufficiently many ECTS points for the electives in mathematical logic and theoretical computer science (MLOV) part, there might be good reasons to take some additional courses at TU:

TU Research groups in (or close to) mathematical logic

(The following list is probably not complete)

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2017-01-27, 14:58.