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... focuses on both the human method of cognition in general [CPR, B 25] and certain types of cognition aimed at justifying their objective significance. This article aims to explicate Kant’s understanding (resp. justification) of the abstract nature of mathematical knowledge (cognition) as the “construction of concepts in intuition” (see: “to construct a concept means to exhibit a priori the intuition corresponding to it”; [CPR, A 713/В 741], which is “thoroughly grounded on definitions, ...

This review of contemporary discussions of Kantian philosophy of mathematics is timed for the publication of the essay Kant’s Philosophy of Mathematics. Volume 1: The Critical Philosophy and Its Roots (2020) edited by Carl Posy and Ofra Rechter. The main discussions and comments are based on the texts contained in ...

This article considers the features of mathematical education in Russia in the 18th-19th centuries. The focal point is the significance of children’s physical activity for the development of spatial perception and mathematical thinking. The author makes recommendations on the development ...

... Maton, J. R. Martin and Y. J. Doran, eds. Teaching Science . London; New York, pp. 105—133. Ebert, Ph. A., 2016. A framework for implicit definitions and the a priori. In: Ph. A. Ebert and M. Rossberg, eds. Abstractionism: Essays in Philosophy of Mathematics . New York, pp. 133—160. Esmonde, I., 2009. Explanations in mathematics classrooms: A discourse analy­sis. Canadian Journal of Science, Mathematics and Technology Education , 9 (2), pp. 86—99, https://doi.org/10.1080/14926150902942072 ...

This article describes possible applications of the resources of the Mathematica programming environment (version 7.0.1.0) in teaching mathematics as a means of the automatic control of initial data input, input data generator, and a means to improve the visibility of mathematical problem solving. The author offers examples of Mathematica codes for each case and identifies the sequence ...

... of science necessitates addressing Kant’s theory of science when searching for a truly philosophical understanding of science, which can be only of metaphysical nature. The experience of building a system of transcendental metaphysics combined with mathematics and physics shows that philosophy of science is necessary for solving the most important problems of the humanity rather than analysing or synthesising scientific knowledge or development it. Philosophy of science proper should be based on ...

Further development of theoretical pedagogy and the theory of learning is closely connected to the use of mathematical and digital techniques in learning process simulations. This article explores formal methods for studying a didactic system as well as difficulties in employing them. The author describes key stages of simulation development and presents ...

Didactic systems relate to poorly structured and poorly formalizable ob­jects that function under conditions of uncertainty and lack of information about the state of the student, the teaching methods used, etc. The article con­siders the application of mathematical and computer modeling methods for the study of didactic systems and various approaches to the construction of math­ematical and computer models of the student. The following models are dis­cussed: linear and nonlinear learning models; multicomponent ...

... to the innovative concept of managing modern industrial enterprises as economic systems, namely, integrated controlling. The author presents a methodological framework for the implementation of the integrated controlling theory. Possible uses of the mathematical apparatus in studying integrated controlling are shown. Static and dynamic characteristics of integrated controlling as a complex system are described. A mathematical model of such system is constructed. 1. Акимова И. В., Ермолаева ...

This article analyses different mathematical models of the process of postmortem heat transfer in an adult cadaver based on postmortem temperature dynamics. A model of heat transfer in a newborn cadaver presented as a finite cylinder is examined in detail. An important factor in constructing ...

Apart from biomedical and organizational issues, the emergence of the new coronavirus COVID-19 (SARS-CoV-2) pandemic, set large-scale tasks for creating and improving mathematical and information technologies that operate spatial data in statistical analysis and forecasting. The regional level is seen as a suitable choice for spatial analysis of COVID-19 morbidity and mortality due to the availability of statistics,...

... nineteenth and early twentieth centuries: German Neo-Kantianism and Vladimir Solovyov’s school of all-unity. Second, Frank himself and the German Neo-Kantians considered Nicholas of Cusa to be one of their forerunners and pointed out the importance of his mathematical ideas for their mathematical studies. Thirdly and lastly, Frank paid particular attention, especially in his formative period as a philosopher, to the leading trend in the early twentieth century, namely German Neo-Kantianism, which led some ...

... (3) assessing and utilizing the meaning (initially functional significance, relevance) of the forms and modes of actuality. The latter ability is precisely the basis of semiotics and semiosis. The first two are metretics or organon for computational mathematics and statistics, as well as morphetics or organon for a wide variety of morphologies, comparative studies, discrete mathematics, topology, etc. Avdonin, V. S., 2015. Methods in the "vertical" dimension (metatheory and meta­languages-organons)....

.... Tsikly deyatel'nosti i ideal'nye ob"ekty [Cycles of activity and ideal objects]. Moscow (in Russ.). Krenke, N. P., 1933—1935. Fenogeneticheskaya izmenchivost' [Phenogenetic varia­bility]. Vol. 1. Moscow (in Russ.). Kudrin, B. I., 2002. Mathematics of cenoses: specific, rank-specific, rank-by-para­me­ter hyperbolic H-distributions and the laws of Lotka, Zipf, Pareto, Mandelbrot. Filosofskie osnovaniya tekhnetiki. Matematicheskii apparat strukturnogo opisaniya tsenozov i giperbolicheskie ...

... management, and destruction or reality. We demonstrate the need for a constructive model of a special event—a model taking into account the temporal factor in the development of reality. The second problem concerns the development of theoretical (mathematical) tools to describe such dynamics. In this connection, we identify the mathematical semantics of event processes. To build the necessary model, we use the methods of maxima/ minima and infinitesimal calculus and carry out an analysis of the ...

Debates over Kant’s famous postulate about the existence of synthetic a priori judgements in mathematics, formulated in the Critique of Pure Reason, have been raging for over two centuries. On the one hand, it was fiercely criticised by neo-positivists in the early 20th century. On the other hand, Kant’s ideas on constructive nature of mathematics ...

... Kantovskiiy sbornik [The Kantovsky sbornik], no. 2 (48). P. 10—25. 31. Katrechko, S. L. 2014b, Transcendental'nyiy analiz matematicheskoiy dejatel'nosti: abstraktnye (matematicheskie) ob"ekty, konstrukcii i dokazatel'stva [Transcendental analysis of mathematical activity: abstract (mathematical) objects, structures and proofs], in: Dokazatel'stvo: ochevidnost', dostovernost' i ubeditel'nost' v matematike (Proceedings of the Moscow Seminar on the Philosophy of Mathematics). M. : «LIBROKOM», P. 86—120....

... political disciplines thus creating a basis for social forecasting. The methods he developed made it possible to predict the results of political elections and formed the basis for the theory of social choice. However, Condorcet’s ideas on the limits of mathematical constructs’ application in social and moral sciences opened up opportunities for social philosophy to go beyond the borders of speculative metaphysics and develop as a ‘practical’ science serving both the individual and the community....

... is to identify the elemental operations of mind and the underlying laws. These laws serve as the basis for critique, which is aimed against the critique of reasoning and is of logical nature. However, according to Jungius, it is not traditional but mathematical logic — which he interprets inthe manner of constructivism — that should be the instrument of critique. Traditional logic is a reflective science and thus cannot serve as the basis for the whole system of knowledge. It itself requires ...

... Wien : Julius Springer, 1955. 14. Quine, 1953: Quine W. V. O. Two Dogmas of Empiricism. Reprinted in: Quine W. V. O. From a Logical Point of View. Cambridge (Mass.) : Harvard University Press, 1953. 15. Ramsey,1931: Ramsey F. P. The Foundations of Mathematics and Other Logical Essays. L. : Kegal Paul, Trench, Trübner & Co., 1931. 16. Ramsey, 1991: Ramsey F. P. Notes on Philosophy, Probability and Mathematics / ed. by M. C. Galavotti. Napoli : Biopolis, 1991. 17. Rescher, 1973: Rescher N. The ...

... Analytic Philosophy. N. Y., 1949. 13. Pap A. Analytische Erkenntnistheorie. Wien, 1955. 14. Quine W. V. O. Two Dogmas of Empiricism. Reprinted // Quine W. V. O. From a Logical Point of View. Cambridge (Mass.), 1953. 15. Ramsey F. P. The Foundations of Mathematics and Other Logical Essays. L., 1931. 16. Ramsey F. P. Notes on Philosophy, Probability and Mathematics / ed. by Galavotti M. C. Napoli, 1991. 17. Rescher N. The Coherence Theory of Truth. Oxford, 1973. 18. Rorty R. Philosophy and the Mirror ...

The authors analyse various types of non-standard tasks, identifies their main characteristics related to the formation of cognitive competence in mathematical education. The article explores ways of solving heuristic, research, and creative problems. A comprehensive approach to the definition of the nonstandard task is proposed. The proposed structure of the problem is based on the following scheme: ...

... indi-vidual work of students (IWS) in the formation of creative competence and the requirements for its organization, contributing to the formation of creative competence are identified. The case of organizing individual work when studying the Basis of Mathematical Information Processing is examined. 1. Пичкова Л. С. Организация самостоятельной работы студентов как фактор формирования профессионально значимых ...

Through the case of general educational institutions of the Kaliningrad region, the authors consider the methods for increasing the level of students’ preparation for the Unified State Examination in mathematics through using the system of distance learning for training and monitoring the level of preparation. The authors describe the approach, which makes it possible not only to present the content and function of computer-assisted testing, but also ...

This article addresses the problem of training specialists in elasticity theory. The author suggests parallel studying of mathematics and mechanics, in particular, elasticity theory. The author considers the case of organizing training process for solving a two-dimensional problem of the theory through an inversed method. It is shown that the analysis of inversed problems ...

This article stresses the need to use a mathematical model of the space of mental images in psychology, medicine, and other sciences. The author identifies the relation between such space and the space-time of physics. The article shows opportunities for structuring the space and introducing ...

One of the features distinguishing human being from the outer world is the ability to set goals and motivation, which are closely connected with the processes of emergence and development of needs. On the basis of mathematical modelling, the author analyses the dynamics of development of need state for major types of needs. 1. Ильин Е.   П. Мотивация и мотивы. СПб., 2003. 2. Леонтьев А.   Н. Потребности, мотивы ...

This article deals with the role of mathematical information in teaching. The author emphasizes the need for the development of informational and activity mobility. The author offers an excerpt from students’ individual work triggering the activity component of informational mobility....

... Пространство и Время. 2013. Т. 3, вып. 2. URL: http://www.j-spacetime.com/actual%20content/t3v2/3206.php (дата обращения: 15.10.2015). 2. Boole M. E. Collected works : in 4 vols. / ed. by E. M. Cobham. L., 1931. Vol. 2. 3. Boole G. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. Cambridge ; L., 1847. 4. Boole G. An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities. L. ; Cambridge,...

... dominated by the supreme monad-hero vested with the theurgic grace of deciding the fates of people. Florensky plays the role of a “social engineer” who develops the concept of a good state, whereas the human being serves as material for this social and mathematical structure. 1. Андроник (Трубачев), иеродиакон. К 100-летию со дня рождения свящ. Павла Флоренского (1882—1943) // Богословские труды. М., 1982. Сб. 23....

The research problem of increasing the effectiveness of marketing activities and the management of business units and institutional structures serves as a framework for describing current trends in applied research on the basis of statistical and economic-mathematical (SEM) modeling. The authors explore the possibilities of using modern information technologies in applied economics and management studies, the prospects of economic agreement studies based on SEM modeling in STATISTICA ™ and MATLAB...

... atmosphere above it are considered as an integral continuous environment. At the water-air surface, the density changes abruptly from ρ = ρwater = 1000 kg/m3 for water to ρ = ρair = 1.2 kg/m3 for air. The solution to model equations is generalised. The mathematical mechanism of equation solving suggests automatic smoothing of density in the area of wave breaking and formation of a thin fluid layer with an intermediate density. 1. Пелиновский Е. Н. Гидродинамика волн цунами....

The analysis of multidimensional raw data on the state of aquatic ecosystems often requires the use of modern analytical tools capable of identifying hidden patterns. The purpose of this study is to analyze long-term water quality monitoring data for the Pregolya River (Kaliningrad) in order to identify the main factors determining variability in the hydrochemical regime and to assess their temporal dynamics. To analyze data on indicators of the nitrogen and phosphorus cycles, methods of multivariate...

... improperly used "white noise". The purpose of this analysis is to identify the specifics of political communication under conditions of international bifurcations. The methodology of the analysis is based on the symbiosis of modern theories: mathematical modeling of communication by C. Shannon and W. Weaver, political cybernetics by D. Easton, political communication by D. J. Lilleker and P. Lazarsfeld, crisis communication by R. Ulmer, T. Sellnau and M. Seager, and game theory with opposing ...

The need for integration and digitization in the field of mathematical education for bache­lor students in pedagogical disciplines is being actualized during the transition from the SPOD (Stable, Predictable, Orderly, and Democratic) world to the VUCA (Volatile, Uncer­tain, Complex, and Ambiguous) world. The ...