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## Современные образовательные технологии обучения математике и информатике в высшей и средней школе: Материалы 3-ей Всероссийской научно-практической конференции. 27-28 марта 2009 г.

Articles and theses of reports on use of educational and information technologies in teaching and educational process of the higher and high school are presented in the collection. In work requirements according to which standards and curricula in the Applied Mathematics and Informatics direction are developed are formulated

The brochure presents the curriculum for third- and fourth-year students of Higher School of Economics, studying English as a second language at the Department of World Economy and International Affairs.

the article discusses the development algorithm of the undergraduate program in Applied Mathematics based on the determination of the demanded educationaloutcomes in accordance with the international standards.

The article describes the experience of designing project-based learning courses as part of the educational program "Applied Mathematics" in MIEM NRU HSE. The features of the organization of project-based learning for educational programs for mathematical sciences are considered. The results of the annual survey of employers, concluded that the need for various forms of project-based learning to achieve the learning outcomes claimed by employers. We suppose a sequence of the project-based workshops and seminars, as well as their approximate content. An important feature of the practice-oriented courses in the educational program "Applied Mathematics" is its interdisciplinary focus, including the projects carried out in a foreign language.

Coming at the cusp of twenty years of social work training in Russia, this article analyses why education in universities is still so disconnected from the field of social work practice. Our attention focuses on institutional dynamics that shape the national regulation of social work education, limited practice content in curricula and the mixed impact of international co-operation. The research highlights that achieving broad agreement on the need for practice skills, service user prioritisation and a strong values base must be the key focus when developing training in contexts where social work is relatively new.

This book aims to present the newest research in the fields of mathematics and mechanics. Theories of mathematics and mechanics are the basis of modern technological improvements and, therefore, interest towards them are increasingly important.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.