Academician Jonas Kubilius: works dedicated to the history of Lithuanian mathematics

The rise of the Lithuanian mathematical school in the second half of the 20th century is associated with the development of probability theory and its application, and the foundations of that school were insightfully laid by the famous Lithuanian mathematician Jonas Kubilius. However, the academician also had a second vocation – the history of mathematics. At the end of the 20th century, he purposefully researched the mathematical legacy of the poet, bishop A. Baranauskas, recognizing him as the first Lithuanian mathematician researcher of the second half of the 19th century. At the beginning of the 21st century, J. Kubilius undertook a detailed implementation of the idea of a work in the history of Lithuanian mathematics. For this purpose, an informal group of specialists was convened, the content of the work was planned, and the research-based book series ``From the History of Lithuanian Mathematics'' was published. The fourth book in this series, Mathematics in Lithuanian Higher Education Institutions in 1921–1944, presents the research of an academic who reveals the situation of mathematics in universities in Kaunas and Vilnius. In addition, the memoirs of mathematics history by J. Kubilius, dedicated to mathematicians Z. Žemaitis, G. Žilinskas and V. Statulevičius, should be mentioned. The article, at the end of which fragments of the author's memories are presented, is dedicated to the centenary of the birth of Academician J. Kubilius.

Nikolai Nikolaevich Luzin at the crossroads of the dramatic events of the European history of the first half of the 20th century

Nikolai Nikolaevich Luzin’s life (1883–1950) and work of this outstanding Russian mathematician, member of the USSR Academy of Sciences and foreign member of the Polish Academy of Arts and Sciences, coincides with a very difficult period in Russian history: two World Wars, the 1917 revolution in Russia, the coming to power of the Bolsheviks, the civil war of 1917–1922, and finally, the construction of a new type of state, the Union of Soviet Socialist Republics. This included collectivization in the agriculture and industrialization of the industry, accompanied by the mass terror that without exception affected all the strata of the Soviet society. Against the background of these dramatic events took place the proces of formation and flourishing of Luzin the scientist, the creator of one of the leading mathematical schools of the 20th century, the Moscow school of function theory, which became one of the cornerstones in the foundation of the Soviet mathematical school. Luzin’s work could be divided into two periods: the first one comprises the problems regarding the metric theory of functions, culminating in his famous dissertation Integral and Trigonometric Series (1915), and the second one that is mainly devoted to the development of problems arising from the theory of analytic sets. The underlying idea of Luzin’s research was the problem of the structure of the arithmetic continuum, which became the super task of his work. The destiny favored the master: the complex turns of history in which he was involved did not prevent, and sometimes even favored the successful development of his research. And even the catastrophe that broke out over him in 1936 – “the case of Academician Luzin” – ended successfully for him.

SMM-Promotion of Additional Education Services in the Aspect of Vocational Guidance for Schoolchildren

The article shows a number of problems of modern Russian education and outlines ways to solve them through additional education, which allows you to implement the professional orientation of schoolchildren. To select additional education courses, the younger generation turns, first of all, to Internet resources, often to social networks. SMM promotion technology can be applied in the field of education to popularize scientific knowledge, attract and inform consumers of educational services. The purpose of the article is to describe the effective experience of SMM-promotion of additional education services in the aspect of professional orientation for schoolchildren on the VKontakte social network. The functionality of this social network allows you to create conversations, thematic groups and place informational messages and educational media content in them. The article describes the community "Physico-mathematical school" Quantum"", representing the school of the same name, operating on the basis of physical and mathematical faculty of the federal state budgetary educational institution of higher education "Mordovian State Pedagogical Institute named after M. Ye Evseveva".

Spotkania Andrzeja Pelczara (1937–2010) z historią i filozofią nauki

Artykuł przedstawia postać Andrzeja Pelczara (1937–2010): jego rodowód genealogiczny, szkicową biografię naukową, listę pełnionych funkcji publicznych oraz dorobek z historii i filozofii nauki na tle dokonań krakowskiego środowiska matematycznego, a także uaktualnia informacje na temat stanu liczbowego krakowskiego środowiska matematycznego i matematycznej szkoły warszawskiej. Andrzej Pelczar’s (1937–2010) meetings with the history and philosophy of science The article presents the character of Andrzej Pelczar (1937–2010): his genealogical pedigree, sketchy scientific biography, list of performed public functions, achievements in the history and philosophy of science against the achievements of the Kraków mathematical environment, and also it updates the information on the numerical state of the Kraków mathematical environment and Warsaw mathematical school.

Research in the Field of Geometric Analysis at Volgograd State University

This article discusses the main directions of research in geometric analysis, which were conducted and are being carried out by the scientific mathematical school of Volgograd State University. The results of the founder of the scientific school, Doctor of Physics and Mathematics, Professor Vladimir Mikhailovich Miklyukov and his students are summarized. These results concern the solution of a number of problems in the field of quasiconformal flat mappings and mappings with bounded distortion of surfaces and Riemannian manifolds, the theory of minimal surfaces and surfaces of prescribed mean curvature, surfaces of zero mean curvature in Lorentz spaces, as well as problems associated with the study of the stability of such surfaces. In addition, the results of the study of various classes of triangulations — an object that appears at the junction of research in the field of geometric analysis and computational mathematics — are noted. Besides, this review discusses papers that use the Fourier decomposition method for solutions of the Laplace — Beltrami equations and the stationary Schr¨odinger equation with respect to the eigenfunctions of the corresponding boundary value problems. In particular, the authors give the results on finding capacitive characteristics that allowed for the first time to formulate and prove the criteria for the fulfillment of various theorems of Liouville type and the solvability of boundary value problems on model and quasimodel Riemannian manifolds. The role of the equivalent function method is also indicated in the study of such problems on manifolds of a fairly general form. In addition to this, the article gives an overview of the results concerning estimates of calculating error integral functionals and convergence of piecewise polynomial solutions of nonlinear variational type equations: minimal surface equations, equilibrium equations capillary surface and equations of biharmonic functions.

Scientific, scientific-methodological and organizational report “The Institute of theoretical mathematics and scientific computing (ITMSC) L.N.Gumilyov Eurasian National University in 2019 year (Part II)”

The article is the written on the constantly actual problem of \textit{understanding mathematic} which is even confessed by G.H. Hardy: "\textit{I learnt for the first time as I read it} ("Course of Mathematical Analysis" by Jordan - N.T.). Therefore, it is devoted to the question "\textit{To what extent and in what relation are the scientific environment and basic textbooks important for understanding mathematics?}". Although Hardy's case refutes, in any case does not make it unconditional, it is obvious that "\textit{A qualified environment makes up for the omissions of the textbook"}. This historical example in favor of the textbook shows that in mathematically incandescent Cambridge, an \textit{Englishman} with absolutely high mental abilities, Hardy \textit{understood mathematics} from the \textit{Frenchman} Jordan's textbook on mathematical analysis. On the other hand, during the heyday of the Moscow Mathematical School, all 5-year undergraduates and 3-year postgraduates were coming out from the Faculty of Mechanics and Mathematics of M.V.Lomonosov Moscow State University(MSU), with proper \textit{understanding Mathematics}. They were juniors with a powerful basic mathematical training without a single mandatory textbook, but with outstanding professors and three hundred seminars (a unique phenomenon of the USSR) where learners were introduced to Mathematics in their very early age, as the professor of Moscow State University Taras Pavlovich Lukashenko said to author of this article. In Kazakhstan the pioneer graduates from Moscow State University were the legendary Saduakas Bokaev and Askar Zakarevich Zakarin, post-war graduates were Kabdush Zhumagazievich Nauryzbaev, Marat Rakhimberdiev, Zhanbek Aubakirov, and now living Lyudmila Alekseeva, Nurlan Amanov, Nurlan Rakhmetov, Surgule Tanulkaev, Nurlan Zharkenov. The Kazakh position of Mathematics and Computer Science through IThMandSC is expressed in §§0-2 of this article. Further, the details of the implementation of Program A (Author's fundamentals of basic mathematical training as the Kazakh equivalent of general training in the PhD doctoral program of the USA from IThMandSC) are presented. The "Mathematical Analysis" book is made from the standpoint of self-sufficiency in providing the \textit{understanding of mathematics} without relying on a qualified environment. In the "§ 7 Introduction" the author acquaints the reader with everything developed in the \textit{understanding of mathematics} during the time of numerous conversations with many primarily outstanding mathematicians with their observations in the special mathematical environment of Moscow and personal conclusions in the process of their scientific research and reading mathematical literature of all levels. The theory of the Lebesgue measure is a separate topic of exceptional significance in the development of mathematics in 20th century and future, the mathematical understanding of which the author of these text received according to an individual program from Scientific Supervisor Pyotr Lavrentievich Ulyanov with the support of his fellow graduate student Dimitri Pechersky. According to the author, Probability theory is a specific discipline in which some points need more clarification.