# Mathematics at the University of Ljubljana

Mathematics has had a long tradition at the University of Ljubljana. Ever since its founding in 1919, the university has been offering study programs in mathematics, following the high quality standards set by the existing study programs abroad. Nowadays, the mathematical studies at the Faculty of Mathematics and Physics (FMF) at the University of Ljubljana boast the highest quality levels.

At the establishment of the university in 1919, both a mathematical seminar and an institute for applied mathematics were founded. The seminar was meeting at the Faculty of Arts, and the institute was based at the Faculty of Technology. Dr. Josip Plemelj, who had previously held a full professorship at the University of Czernowitz (presently Chernivtsi, Ukraine), was appointed chair of the seminar, while Dr. Rihard Zupančič, who had previously lectured at the Vienna University of Technology, took over the direction of the institute. Plemelj and Zupančič also served, respectively, as the first and the second rector of the University of Ljubljana.

In the last few decades preceding World War I, some classical mathematical branches saw an exceptionally rapid development with active and creative contribution of Slovenian mathematicians. The achievements of Prof. Dr. Josip Plemelj were particularly important in the theory of integral equations, potential theory, and function theory, and the acquisition of such a renowned mathematician was a good basis for the evolution of the Slovenian mathematical science.

In between the World Wars, the mathematicians of the University of Ljubljana published a number of papers on algebra and differential geometry. The relatively young branches such as topology, functional analysis and modern algebra that brought fundamental changes to classical mathematics at the beginning of the twentieth century came to Ljubljana after World War II.

Mathematical studies have always been most deeply intertwined with physical studies. At the beginning, therefore, the Faculty of Arts offered two programs majoring in mathematics, namely mathematics with physics and mathematics with descriptive geometry. The latter was abolished in 1928. Instead, a program in pure mathematics and a program in applied mathematics were created. In the academic year 1949/1950, the departments of sciences and mathematics separated from the Faculty of Arts and created the Faculty of Sciences and Mathematics which existed from 1949 to 1954. In the academic years 1954/1955-1956/1957, the separated departments were reunited as the Faculty of Sciences, Mathematics, and Arts which in the academic year 1957/1958 ultimately split into the Faculty of Arts and the Faculty of Sciences. The latter existed from 1957 to 1960.

Prior to World War II, the following mathematical courses were offered: Fundamental course in mathematics I and II, Differential equations and variational calculus, The theory of analytical functions, Algebra with number theory, Differential geometry, Algebraic geometry, and A critical introduction to infinitesimal calculus. The curriculum did not vary much from World War II until the year 1959.

In 1960, mathematical studies underwent considerable changes when the Faculty of Sciences and the Faculty of Mining, Metallurgy, and Chemical Technology merged into the Faculty of Sciences and Technology (FNT). Then, mathematical studies were divided into two two-year programs; the Program in mathematics with physics and the Program in technical mathematics. In 1960, the university founded the Institute of Mathematics, Physics, and Mechanics (IMFM) which has since been giving to Slovenian mathematicians as well as physicists the possibility of scientific engagement. In the years 1994-1995, the University of Ljubljana was restructured, and that led to a splitting of the departments within the FNT. The mathematics and physics departments formed the present Faculty of Mathematics and Physics (FMF). Officially, the activities of the FMF started on 1st October 1995.

During the second half of the twentieth century, mathematics enjoyed tremendous growth resulting in creation of new branches and high-level specialization of the existing ones. Accordingly, those developments reflect on the variety of research activities of Slovenian mathematicians. The students will be able to get acquainted with this variety when they opt for elective courses offered within our second cycle study programs, newly designed to implement the principles of the Bologna declaration.