# Doctoral Studies

## General Problems of Mathematics - Field

### Brief description of field

The field of General Problems of Mathematics has two sub-divisions:

- History of Mathematics
- Teaching Mathematics in secondary schools and universities

The subdiscipline *History of Mathematics * is focused mainly on the 19th and 20th century and especially on the history of Czech mathematics; but biographical and bibliographical aspects are also dealt with. History of Mathematics is closely linked to teaching mathematics, because its development is conditioned by the transfer of knowledge by teachers and textbooks. Abroad, didactics and history of mathematics are often merged into one field. This is how we used to teach it as well (Q. Vetter / 1881-1960 /, F. Balada / 1902-1961 /).

Doctoral studies in the subdiscipline of *Teaching Mathematics* are usually commenced by students who have had several years of teaching experience, and are usually undertaken in the form of off-campus (distance) studies. During this programme the students will often examine the practical knowledge that they have gained as teachers. One part of the dissertation may be, for example drafting a textbook, an exercise book, etc. However, such books must be tested in practice and the findings (such as methodological commentary, analysis difficult and problematic parts of the book etc. ) must be included in the dissertation along with a professional summary of the conclusions obtained.

### Objectives of the study

The field of *General Problems of Mathematics* is designed primarily, but not exclusively, for graduates of teacher training in mathematics. The aim is to produce knowledgeable secondary or tertiary mathematics teachers capable of independent creative work. Therefore, the field includes extensive mathematical training (which well exceeds the level of training obtained from a Masters degree), high quality education in didactics of mathematics, and education about the history and philosophy of mathematics.

### Profile of a typical graduate

Graduates will be well educated in their field and will find employment as high school, college, or university teachers.

### Requirements for applicants

For admission to the field of General Problems of Mathematics one is required to have a deeper knowledge of high school and basic university math courses. One will also be required to have general knowledge of the history of mathematics, good skills in solving high school level math problems, and knowledge of at least one foreign language.

### Study requirements and completion of studies

### Individual Study Plan

The student will need to completes six one-semester courses appointed for doctoral studies.

After consultation with the supervisor, self-study will focus on gaining more knowledge in the field and on special aspects needed to write a good dissertation. The student will also regularly attend seminars and help with preparing/teaching undergraduate courses.

### Content and scope of the state doctoral examination, required knowledge

The State doctoral exam will be from the following three areas:

- Mathematics
- History of mathematics
- Teaching mathematics

Particular emphasis is put on areas that are related to the topic of the dissertation.

### Requirements for a doctoral dissertation

The thesis must contain original and published results or results accepted for publication.

**General Topics for PhD theses: **

- History of graph algorithms
- Contributions of Otakar Borůvka to the development of modern algebra
- Creating mathematics textbook for “víceleté gymnazium” (i.e. a special type of secondary school which starts at grade 6 or grade 8; but finishes with grade 13 same as other secondary schools)
- Teaching algebra at colleges
- Computational linguistics - history and development
- Development of lattice theory

**A List of current dissertation topics for the academic year is found on the page below.**

### Individual study plan

The student will need to completes six one-semester courses appointed for doctoral studies.

After consultation with the supervisor, self-study will focus on gaining more knowledge in the field and on special aspects needed to write a good dissertation. The student will also regularly attend seminars and help with preparing/teaching undergraduate courses.

List of members of doctoral committee

List of supervisors

Commission for state doctoral exams and defenses

List of current doctoral topics

Department pages