## Doctoral Studies## Algebra, Number Theory and Mathematical Logic - Field## Brief description of fieldThis field of study focuses on certain areas of algebra, number theory, and mathematical logic such as the category theory, semigroup theory, universal algebra, ordered sets and ordered algebraic structures, algebraic number theory, linear algebra, mathematical logic, and the application of these disciplines in theoretical computer science.
The aim is to achieve important results in the studied field and also to obtain a sufficiently broad knowledge of mathematics. Also one should master the scientific methodologies used in mathematics. ## Profile of a typical graduateThe graduate of this programme will have acquired an overview of mathematics. Within his field of study he should have deep knowledge and understanding of current trends in research. The graduate should have also proven his/her creative abilities at an international level. Graduates may find employment in general or applied research in the fields of mathematics and computer sciences, in designing software, or as university teachers. ## Requirements for applicantsThe basic requirement is completion of a master's degree in the field of mathematics or computer science. One should at least have completed: - linear algebra,
- algebra,
- combinatorics and graphs,
- logic.
The candidate should also have sufficient knowledge of the English language and the candidate’s ability to communicate in English will be verified at the oral entrance examination. The apllicant is required to pass the entrance examination and to get at least 60/100 points as follows: - knowledge of mathematics − 50/ 80 points,
- knowledge of the English language – 10/20 points.
## Study requirements and completion of studies
By the end of the student’s studies he/she will have attended six one-semester courses designed for doctoral studies (each in the length of one semester). Upon consultation with the supervisor, students will choose courses aimed at expanding knowledge in the field of focus, and special courses needed to write a dissertation. The student will regularly attend seminars, and help in teaching undergraduate courses. In the combined form these obligations can be modified by the supervisor.
Before applying to the exam the student has to fulfil all requirements specified by the supervisor. The exam will be from three of the six following subjects. The candidate will choose three and propose them for approval to the Doctoral Board: - Classical Algebra,
- Algebraic Structures,
- Number Theory,
- Discrete Mathematics,
- Theoretical Computer Science,
- Linear Algebra.
Deep understanding of the content and context will be required.
The thesis must contain original and published results or results accepted for publication.
- Circular units in abelian bodies
- Characteristics of ordered sets
- Morita equivalence for lattice ordered structures
- Equational logic of semigroups and its applications
- Accessible categories and their applications
- The use of category theory in number theory
- The use of computers in number theory
- Different types of generalized inverse matrices - computation algorithms and their applications
## Individual study planList of members of doctoral committee Commission for state doctoral exams and defenses |

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