Mathematical and Cartographic Modeling and Demographic Analysis of Rural Settlements

  • V. A. Rubtzov
  • N. K. Gabdrakhmanov
  • N. M. BiktimirovEmail author
  • M. R. Mustafin
  • R. R. Nurmieva
Conference paper
Part of the Springer Proceedings in Business and Economics book series (SPBE)


This chapter presents mathematical and cartographic methods used in the demographic research. Particular attention is paid to consider the issues of integrated presentation of spatially coordinated information on the population. This work discusses the possibility of organic integration of mathematical and cartographic models and the inexpediency of opposing them. It substantiates how modern methods and solutions in demographic analysis are influenced by time. As it turns out, modern cartography and geo-informatics have a unique method for presenting and analyzing information at all levels. That allows not only considering the current situation comprehensively, but also elaborating scenarios for its development. When conducting the research at the regional level, the geographical and cartographic components quite often become the major ones. The cartographic interpretation of mathematical calculations brings them to the form suitable for optimal use, which also serves for performing multilateral analysis of the mathematical modeling results. This work substantiates that any map is a strictly defined mathematically formalized model, the construction of which is carried out according to the canons of mathematical cartography. The study determines that a formalized cartographic image is well suited for mathematical analysis. It turns out that many areas of mathematics are applicable for processing and analyzing a cartographic image. Special attention is paid to the use of the main function of information theory, i.e., entropy. Comparison of maps of different subjects and different times allows making forecasts based on the identified relationships and trends in the development of a phenomenon. The analysis reveals that cartographic extrapolations are not universal. This work identifies the factors, on which the reliability of forecast maps depends.



The research was conducted with the financial support of the Russian Federal Property Fund and the Republic of Tatarstan, project No. 17–12-16005 “The forecast of Social and Economic Development of the Rural Settlements of the Republic of Tatarstan.”


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • V. A. Rubtzov
    • 1
  • N. K. Gabdrakhmanov
    • 2
  • N. M. Biktimirov
    • 1
    Email author
  • M. R. Mustafin
    • 1
  • R. R. Nurmieva
    • 1
  1. 1.Kazan Federal UniversityKazanRussia
  2. 2.Ural State University of EconomicsEkaterinburgRussia

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