Научный, научно-методический и организационный отчет "Институт теоретической математики и научных вычислений (ИТМиНВ) Евразийского национального университета имени Л.Н.Гумилева в 2019 году (Часть II)"

Abstract

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.