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 Lecture 1. Definition of system and structure Hierarchy of systems in the environment. Model and environmental modeling. Generally speaking, a system is a unity of objects connected with each other in a certain way. Properties of the system are determined by interconnections between objects which are parts of the systems. Objects forming a system are called elements or subsystems in the event they will be in their turn further considered as systems. The main feature of a system is a property of emergentness. Emergentness feature is a demonstration of the system unity ensured by interconnection of all its elements by definite types of connections and relations. The totality of connections and relations between elements of the system is the structure of the system. Definition of multiple, hierarchic and united vision of a system. Function of an element. Functional and processing vision of a system. Formal point and formal space. Elementary formal space.  2
 Laboratory № 1. Study of structure and possibilities of а Spreadsheet of Statistica program. study the structure of a Spreadsheet. study functional abilities of a Spreadsheet. study forms of variables in a Spreadsheet. Determining of indicators of variables and brief review. Transition between numeric and text form of representation of variables. Editing names of variables. Commentary for variables.  2 
22  Model. Different approaches to determination of properties and functions of a model. Models of objects and processes of environment. Types of models (material and imaginary). Groups of models. Peculiar features of different types and groups.

 Laboratory № 2. practicing main operations with variable in electronic table. study ways of performing main commands.. recalculation of variables connected to primary formula. shift of variable value for n number of cases. distribution of variables by order. recoding of variables. calculation of main statistics and design of diagrams using the window of current certifications.

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3 2 34  Lecture 2. collection and preliminary evaluation of initial information on environmental conditions. Types of information on environmental conditions. Scale for measuring parameters: nominal, ordinal, interval and scale of relations. ^ hypothetic, existing, verified. Accuracy and reliability of test results. Point and interval statistic evaluations. Trusted possibility or reliability. Boundaries of trusted interval. Average square deviation from test results. Average square deviation. Methods of creation of trusted intervals.

2  Laboratory № 3. Study of the Structure of specialized module of Data Management. create a new file using the data from current file. sort the data. study global operations for working with variables. check the name and formats of variables in the current file. standardization of variables values replace missing values for average value of correspondent variable. creation of megafile. study of specific operations with megafiles. changing of regular file with extension *.sta into a megafile with extension *.mfm

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 combine two files with data. record macro command using keyboard. record commentary of a macro command. record a macro command containing steps recorded by a mouse. creation of a new button on instrument panel. 

15  Lecture 3. Random values and types of their subdivisions. Normal subdivision. Its characteristics and importance of data verification selection in light of correspondence to normal distribution in processing of ecological and geological information. Rules of 2х and 3х standard deviations. Even distribution. Gamma – distribution. Lognormal distribution. Хі – square – distribution Binormal distribution. Separable binormal distribution Distribution of Poisson Geometric distribution Hypergeometric distribution Polinominal distribution Beta distribution Student distribution

2  Laboratory № 4. determination of type of distribution of variable. Study algorithm for determination of type of distribution of variable using Statistica package of programs. Visualizing distribution of variable with the help of histogram. Grouping data. Diagrams of dispersion. Diagrams of dispersion and histograms. Diagrams of dispersion and diagrams of swing. Normal and probability diagrams. Diagrams of diapasons. Diagrams of swing. Columnar diagrams. Linear diagrams (diagram of variables and observation profile). Circular diagrams. Diagrams with omitted values and intervals. Diagrams of user functions. study of methods of transition of variables. (normalization, logarithmization, etc.) 
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 Importance of determination of the type of distribution for modeling problems and forecast of environmental conditions. Principles of ascertaining of necessary volume for specific evaluation of general unity.
  fundamentals of 3dimensional visual analysis  
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2  Laboratory № 5. calculation of optimal quantity of trials for ecological geological shooting with the scale 1 : 25000
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678  Lecture 4. Multidimensional random values. System of two random values. Multiplication correlation. On one and the same site of elementary event, for example on the site for ecological geological shooting, it is possible to distinguish several random values. There may exist possibility of connections between these values ascertaining which makes it possible to optimize ecological geological research. System of two discrete random values (X, Y) and their numeric characteristics. Basic numeric characteristics for random values X, Y forming the system (X, Y). Covariation. 
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 Laboratory № 6. Calculation of coefficients of correlation for systems of data on environmental conditions. Calculate coefficients of correlation using Statistica package of programs. Visualize and edit received results of correlation analysis. Interpretation of correlation analysis results in light of the aims of research. 
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7  Correlation moment. Coefficient of correlation, its properties. Conditional laws of division of systems of two discrete random values and their numeric characteristics. Pairs of coefficients of correlation. Partial coefficients of correlation. Correlation regressive analysis of actual data of environmental conditions.
   
89  Lecture 5. Forecast of environmental conditions using method of regressive analysis. Mathematical fundamentals of regressive analysis. Peculiarities of application of regressive analysis for forecasts of environmental conditions. Exponential regressive model. Normal regressive model. Lognormal regressive model. 
2  Laboratory № 7. Design of linear regressive model of a process on the basis of data obtained by many years’ monitoring of environmental conditions. Formulation of tasks for design of a regressive model. Selection of variable for analysis and calculation of regressive model. Processing of results of regressive analysis. Analysis of “remainders”. Transfer of results into reporting file. 
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 Laboratory № 8. Design of multiple regressive process model on the basis of data obtained from many years’ monitoring of environmental conditions. Formulation of a task for design of a regressive model.

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 Creation of electronic table with outcome data. Transformation of outcome data. Selection of variable for analysis and calculation of a regressive model. Processing results of regressive analysis. Analysis of “remainders”. Transfer of results into reporting file.  
111  Lecture 6. Nonparametric statistics. FI – coefficient. Criterion хі – square of McNemar. Correlation of Speerman. Correlation of tau Kendel. Correlation of Gamma. Criterion of ValdaVolfovitz series. U – criterion of Mann  Vitni. Criterion of Kolmogorov  Smirnov. ANOVA of Craskel – Vollis and median test. Criterion of indicators. Criterion of Villcockson. 
2  Laboratory № 9. Comparison of distribution of chemical elements in different horizons of soil profile for ecological geochemical research. Comparison of contents of chemical elements in two horizons of soil profile by method of Kolgomorov Smirnov. Comparison of contents of chemical elements in three or more horizons of soil profile by method of KolgomorovSmirnov.

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1213  Lecture 7. Design of models using the method of main components. Mathematical fundamentals of method of main components. Main components and factor analysis. Setting a task of environmental conditions with the purpose of solving it by means of factor analysis. Mathematical fundamentals of factor analysis. Calculation of initial estimates of factor loads. Rotation of vectors. Peculiarities of applications of factor analysis to solving problems of environmental conditions.  2  Laboratory №10. Analysis of time rows and forecast for process under research. Study of mathematical fundamentals of analysis of standard time rows. Selection of data for analysis Study of the structure of dialogue ARIMA. Transformation of a time row. Design of a time row, type INTERRUPTED ARIMA. Conduction of exponential smoothing of a time row. Conduction of a forecast. Analysis of a forecast.  4 
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 Laboratory № 11 Determination of paragenetic associations of chemical elements using factor analysis. Preparation of selection for factor analysis. Determination of optimal quantity of factors depending on ecological geological tasks. Calculation of factor loading table and its interpretation. Visualizing data of factor loading table. Interactive graphic analysis of data.
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15  Lecture 8. Analysis of space changes. Space changes and level of dependability of particular values of space variables from space coordinates. Mathematical fundamentals of studying laws of objects spreading on the basis of chain theory of Markov. Division and correlation of crosssections according to complex of features. Application of Radionov criterion for solving problems of decomposition of a crosssection. Peculiarities of application of methods of space changes analysis when solving ecologicalgeological problems.
 2  Laboratory № 12 Determination of territories for revealing factors of geochemical process by method of factor analysis. Calculation of factor scores table. Separation of abnormal sites. Visualizing results in the form of diagrams and maps. Ascertaining main agents of geochemical process.  2 
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  Laboratory № 13 Determination of geochemical barrier with the help of results obtained by factor analysis and space changes analysis. Determination of strong geochemical paragenetic associations in horizons of soil profile. Analysis of characteristics of soil profile using Radionov’s criterion. Comparison of results of both types of statistics analysis and determination of geochemical barriers.  2 