Article
Do we create mathematics or do we gradually discover theories which exist somewhere independently of us?
This is a preface to the paper A. Borel, "Mathematics: Art and Science" reprinted in EMS Newsletter, No. 103, March 2017.
Calendar of significant dates in the field of mathematics and mathematical education for 2018
This article provides an empirically grounded analysis for two fundamentally different models of mathematics teachers’ beliefs about student diversity in Russian secondary schools: exclusive and inclusive models. Although teachers’ beliefs are considered a central factor for the differentiated approach, teachers’ beliefs could be stereotyped and, consequently, the evaluation of a student’s ability would be systematically shifted and decisions about the possibility of teaching a student would be incorrect. Semistructured interviews with 30 mathematics teachers allowed us to investigate what criteria teachers claim to employ while classifying students in the classroom and what expectations they have for each group of students. It was found that within the exclusive model, teachers have an image of a “normal” student and use discrete categories for labelling students with reference to the “normality”. Within the inclusive model teachers tend not to match students with discrete categories; rather they prefer to compare a student only with herself or himself. Research findings are discussed in the context of a possible “fixed effect” on a student’s development. However, there is a need for further investigation of a connection between teachers’ belief systems, teaching practices, and student achievement.
This article consider The project of the scientific and educational Center for integration of multimedia technologies in science, education and culture, as spacetechnological environment for the implementation of innovative scientific and educational projects of the 21st century, which should become the support for the master's programs, especially interdisciplinary; at the intersection of science, art and information technologies, and implementation of innovative scientific and commercial projects, which are to become a master's thesis.
The three already traditional volumes of the WDS Proceedings you are holding in the hands are composed of the contributions which have been presented during the 21st Annual Conference of Doctoral Students that was held in Prague, at Charles University, Faculty of Mathematics and Physics from May 29 to June 1, 2012. In this year, 100 student manuscripts were submitted to publishing and 88 were accepted after the review process.
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 stateofthe 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.

Proceedings of the International Congress of Mathematicians 2018
The coursebook is designed for students to acquire, practice, and master their communicative competence in academic writing in English, the focus being on fundamental and applied mathematics and computer science. The target of the book is to teach students to write research project proposals of their term papers, senior theses, and dissertations in the format of a research article which could prospectively be published in a Scopus or WeofScienceindexed journals. The book covers both academic writing and academic speaking, i.e. presenting research at conferences and defences.
The materials employed in the book are research articles published in international peerreviewed journals, both fulltext and excerpts.
The target audience comprises undergraduate students majoring in IT, fundamental and applied mathematics, and cyber and information security. The book could also be of interest to students majoring in other STEM areas, both at the undergraduate and graduate levels.
The paper discusses in detail the scale of translation of primary points scored by school graduates in the unified state exam in mathematics, used from 2013 to the present time. Based on the analysis of the dynamics of these scales, a conclusion is made about the annual increase in the "average" 100point result, as well as the presence of a significant increase in the final grade compared with the linear scale. Additionally, the authors describe the effect of reducing the value of primary points as they approach the maximum.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnitedimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasisolutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasisolutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasisolutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasisolutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
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.
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 crosssection of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a crosssection 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 crosssection 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 crosssection 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 Wequivariant map T   >G/T where T is a maximal torus of G and W the Weyl group.