PřF ALGB Algebra, Number Theory and Mathematical Logic
Name in Czech: Algebra, teorie čísel a matematická logika
doctoral combined specialized
Included in the programme: PřF D-MA_ Mathematics and Statistics

Final state doctoral examination and defence of the doctoral thesis

Before submitting an application for a state doctoral exam, the doctoral candidate must have fulfilled all the obligations set out in the individual study plan to this milestone.

The Doctoral Board will select three of the following courses for the exam:

- classical algebra,
- algebraic structures,
- number theory,
- discrete mathematics,
- theoretical computer science,
- linear algebra.

A deep understanding of content and context is required.

The dissertation must include the original and published results or the results received for publication.

Requirements of the study

The student has at least four semester subjects during the course of study outside of the dissertation's focus (5-15% of the total workload).
Upon agreement with the supervisor, a separate study will focus on broadening the knowledge of the given field and on the special parts required for the dissertation.

Research activities:
- Dissertation preparation - takes place during the whole study period and constitutes 60-70% of the workload
- Publishing activity - consists of at least one article in an impacted journal, accounts for 10-15% of the workload
- Pedagogical activities (participation in teaching) - Ph.D. student can take part in conducting bachelor's theses, conducting seminars, etc., up to a maximum of 150 hours per study (5-10% of the workload)
- Throughout the course, PhD students continuously report on their project and results at international workshops and seminars (domestic and foreign), including international conferences. The expected extent of this activity is about 5-15% of the total workload
- Active participation in one of the algebraic seminars at the institute (5-10% of the workload)

Part of the study in this doctoral study program is the completion of a part of the study at a foreign institution lasting at least one month or another form of direct student participation in international cooperation.

The basic form of doctoral study is a full-time form. It is expected that if the student will properly fulfill all his / her duties, he / she will successfully complete his / her studies after four years of standard study period (he / she will present the application for defense and defend in the following period). The combined form should be used exceptionally, especially in cases where, for serious reasons, the student fails to finish his studies after 4 years, although he has fulfilled his ISP duties properly. The only task within the combined form is the work on the dissertation project.

Suggestion of theses topics and the topics of defended theses

5 defended disertationsi:

Lattice effect algebras
Jiří Janda (školitel Jan Paseka)
https://is.muni.cz/auth/th/qxrr3/?fakulta=1431

Triads in ordered sets
Radek Šlesinger (školitel Jan Paseka)
https://is.muni.cz/auth/th/b04l9/?fakulta=1431

On Categories of Algebras
Jan Pavlík (školitel Jiří Rosický)
https://is.muni.cz/auth/th/os4lf/?fakulta=1431

Washington's group of circular units
Milan Werl (školitel Radan Kučera)
https://is.muni.cz/auth/th/jbpxt/?fakulta=1431

On constructions of left determined model structures
Marc Olschok (školitel Jiří Rosický)
https://is.muni.cz/auth/th/xhch5/?fakulta=1431


Recommended progress through the study plan

Warning:

The study plan does not contain any courses.