Educational and Scientific Profile of the Department

The Department of Geometry is one of the oldest at the Faculty of Mathematics, Physics and Informatics. It was established in 1960. It provides education for teachers of mathematics and descriptive geometry for secondary schools and grammar schools and trains specialists in the fields of computer geometry and computer graphics.

The department is divided into two sections: the Section of Geometry and Topology and the Section of Descriptive Geometry and Computer Graphics.

For all students in teacher training, the department offers lectures, exercises, and seminars in various areas: linear algebra, fundamentals of constructive and analytical geometry, and the history of mathematics. For students in specialised mathematics studies, the department provides specialised courses and seminars: geometry, topology, geometric modelling, and CAGD. It also plays a significant role in doctoral education and teaching within supplementary studies.

Scientific Work

The scientific and research activities of the department focus primarily on algebraic and differential geometry and topology, applied geometry and computer graphics, history and didactics of mathematics. Within these activities, more than 25 students have obtained the academic title of PhD and over 100 students have earned the academic title RNDr.

Members of the department are authors or significant co-authors of 4 university textbooks and about 10 mathematics textbooks for secondary schools and grammar schools. Several monographs and encyclopaedic works have also originated at the department.

The department is actively involved in extensive cooperation with several domestic and foreign institutions (Germany: Halle, Leipzig, Potsdam, etc.; Austria: Vienna, Graz; Hungary: Budapest; Italy: Bologna, Palermo). It is also a member of the system for international cooperation in science and education.

Department staff are invited to lecture at international symposia and conferences (Austria, Germany, Czech Republic, etc.) and have spent extended periods working at foreign universities on several occasions.

Graduates find employment as teachers at secondary schools, grammar schools, or universities. They are also frequently employed in various industrial sectors (design), services, financial institutions, etc.

Selected Publications

Monographs:

• V. Svitek:
  Logical Foundations of Geometry. Bratislava, SPN 1969
• J. Čižmár, V. Zaťko (co-authors):
  Encyclopaedia of Mathematics. Bratislava, Obzor 1967 (1st edition), 1978 (2nd edition), 1981 (3rd edition)
• J. Čižmár:
  Groups of Geometric Transformations. Bratislava, Alfa 1984

Textbooks:

• V. Zaťko (co-author):
  Geometry 1 (university textbook). Bratislava, SPN 1985
• M. Božek (co-author):
  Geometry 2 (university textbook). Bratislava, SPN 1987
• V. Piják, V. Zaťko (co-authors):
  Constructive Geometry (university textbook). Bratislava, SPN 1985
• T. Hecht, Z. Sklenáriková:
  Methods of Problem Solving (university textbook). Bratislava, SPN 1992
• M. Božek (co-author):
  Mathematics 2 (textbook for grammar schools). Bratislava, SPN 1985-1990
• J. Čižmár (main author):
  Mathematics 6. I, II, SPN, Bratislava-Prague 1989-1996
• J. Čižmár (co-author):
  Mathematics 7. I, II, SPN, Bratislava-Prague 1990-1996
• Š. Solčan:
  Projective Geometry (script). Comenius University Bratislava, 1994
• M. Božek:
  Mathematics 2 (volume 3) (textbook for grammar schools). Bratislava, Orbis Pictus, 1998
• P. Chalmovianský (co-author):
  Complexity of Geometric Algorithms (script). Comenius University Bratislava, 2001
• Z. Sklenáriková, J. Čižmár:
  Elementary Geometry of the Euclidean Plane (script). Comenius University, Bratislava 2002