# 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 combinated form of 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.

The apllicant is required to pass the entrance examination and to get at least 60/100 points as follows:

- knowledge of mathematics − 30/ 50 points,
- knowledge of math history or didactics − 20/30 points,
- knowledge of a forein language – 10/20 points.

### Study requirements and completion of studies

**Individual Study Plan**

In the **present **form of study, the student has to go through at least four regular one-semester faculty courses in mathematics which are inidicated individually by the supervisor. The student is obliged also to regularly attend seminars in the history and didactics of mathematics, to assist in the teaching/preparing undergraduated courses and exams and to review bachelor theses (by enrolling the course *Teaching Assistance *each semester).

Both in the **present** and **combined** form of study, based on regular consultations with the supervisor, the student concentrates on intensive self-study to gain more knowledge in the field and to consider special aspects needed to write a good dissertation (by enrolling the courses *Literature study*, *Literature research* and *Preparation of Ph.D. Thesis*).

To complete the doctoral study, the student has to prepare at least two original papers on subject of the intended Ph.D. thesis and to give a talk or a lecture in the foreign language during an international scientific meeting (by enrolling the courses *Scientific publications writing* and *Lecture in the foreign language*) .

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

Before to apply for the State doctoral exam, the student has to prepare at least one original paper on subject of the intended Ph.D. thesis.

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 some branches of mathematical analysis
- Contributions of Czech personalities to the development of modern mathematics
- Teaching algebra and geometry at colleges
- Mathematical population dynamics - history and development
- Development of complex analysis or theory of ordered structures.

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

### Individual study plan

List of members of doctoral committee

List of supervisors

Commission for state doctoral exams and defenses

List of current doctoral topics

Department pages