# Department of Higher Mathematics and Mathematical Modelling

The first half of the department's title ? ?further mathematics? - integrates three profiles of educational work at pedagogical department: geometry, algebra, and mathematical analysis. The second part of the title ?mathematical modelling? indicates not only department's educational work profile but also the main idea of modern physical mathematical education and also department's scientific work direction. Geometry, algebra, and mathematical analysis are classical sections of further mathematics from which geometry is the most ancient of all and mathematical analysis is the youngest as it appeared in the XVIIIth century. Despite the fact that elements of mathematical modelling were exploited by scientists from the appearance of exact sciences, mathematical modelling as a separate science appeared not so long ago in the middle of the last century along with appearance of calculating machines and a large number of scientific technical projects.

Scientific schools

Two scientific schools could be distingushed at the department. The first fundamental highly productive school ?Classical and quantum statistical problems of general theory of relativity and gravitation? aims at mathematical modelling in the theory of gravitation, cosmology, and astrophysics. This school was founded at Kazan University in 1975 within the city scientific seminar organized by U.G. Ignatiev and G.G. Ivanov. Almost all prominent specialists in the field of gravitation and cosmology from Kazan and other cities and countries participated in this seminar. Among them are 9 Doctors and 32 Candidates of physical-mathematical sciences. Under the aegis of this concept permanent school-seminar ?Gracos? has been functioning on gravitation and cosmology since 2005. The participants usually gather at the end of August ? beginning of September on the shores of the lake Yalchik. The scientific leader of this school is U.G. Ignatiev. 2 Doctors and 14 candidates theses were defensed on this topic.

The second younger scientific school appeared in the process of the first concept's development as a natural result of its functioning ? ?Information Technologies in special mathematical education?. Development of the methods of computer modelling in computer mathematical systems (CMS) within the first concept has become the basis of this applied branch. Computer modelling in CMS and information technologies accompanying it were put into basis of scientific research works in the area of physical-mathematical formations informatization. The idea of such ?clever? informatization was supported by the development of multipapameter ruled program procedures in CMS. As a result, the user gets an opportunity to build visually equipped dynamical models studying which they are able to deeply understand the essence of the mathematical model studied. On the other hand, the system of analytical testing of mathematical knowledge on the basis of CMS Maple and its supplement Maplet is being developed at the department. The system of analytical testing (SAT) being developed aims at substitution of the methods of ?deep? testing by the methods of intellectual testing which makes it possible to estimate the level of mathematical knowledge of the one being tested. Within this approach regular seminars on computer modelling are held in Russia. Scientific leader of this approach is also professor U.G. Ignatiev. 4 Candidates' theses were defensed on this topic.