General Problems of Mathematics – Field of study catalogue MU
General Problems of Mathematics“The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.” (G.K. Chesterton) 
The study programme of General Problems of Mathematics is intended for the graduates of the Master's degree programme of Upper Secondary School Teacher Training in Mathematics. The study programme consists of the following two subprogrammes: History of Mathematics and Upper Secondary and Tertiary School Teacher Training in Mathematics. The first subprogramme focuses on the development of mathematics in the 19th and 20th centuries, and especially on the Czech mathematics; however, the biographic and bibliographic aspects are also addressed. The History of Mathematics is closely related to the questions of teaching mathematics since the development of the branch is often based on the experience transferred by teachers and contained in textbooks. Abroad, the history and didactics of mathematics are often joined in one branch. It was the same in our country in the past  see the works of Q. Vetter (18811960) and F. Balada (19021961). The doctoral studies in the subprogramme of Teacher Training in Mathematics usually begins only after several years of teaching experience of the applicant, and it is mainly organized as the distance study mode (concurrent verification of the teaching practice). Therefore, writing a textbook can form one part of the doctoral thesis, as well as the collection of exercises, including the comments on methodology, explanation of difficult parts, and others. The work must be supported by an analysis of the results obtained in teaching practice and an informed summary of obtained results.
After successfully completing his/her studies the graduate is able to:
 explain the principles, methods, and procedures employed in teaching mathematics
 generate and advocate their methods of teaching mathematics for the secondary school pupils
 describe the main directions in the historical development of mathematics
 show positive selffulfilment, selfeducation, and selfreflection
The graduates are trained in the structure and history of mathematics and its teaching. They have knowledge and skills to become excellent teachers of mathematics at secondary schools.
The individual study plans for each academic year include lectures in advanced mathematics, studies of literature, assistance in instruction, foreign internships, and preparation of scientific publications related to the topic of the proposed doctoral thesis and the preparation of the thesis. Students must earn a total of 30 ECTS credits per semester.
To be admitted to the doctoral state examination the students must give at least one presentation in English (or a different foreign language) at an international conference or symposium.
The doctoral state examination consists of the oral examination in which the students answer three questions from the following areas: 1)Mathematics; 2)History of Mathematics; and 3) Didactics of Mathematics.
The studies are completed with the defence of the doctoral thesis.
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