Mathematical methods are most widely used in systems research. At the same time, the decision practical problems mathematical methods are sequentially carried out according to the following algorithm:
mathematical formulation of the problem (development of a mathematical model);
choosing a method for conducting research on the resulting mathematical model;
analysis of the obtained mathematical result.
Mathematical formulation of the problem usually presented in in the form of numbers, geometric images, functions, systems of equations, etc. The description of an object (phenomenon) can be represented using continuous or discrete, deterministic or stochastic and other mathematical forms.
Mathematical model is a system of mathematical relationships (formulas, functions, equations, systems of equations) that describe certain aspects of the object, phenomenon, process or object (process) being studied as a whole.
The first stage mathematical modeling is formulation of the problem, object definition and research objectives, setting criteria (signs) for studying objects and managing them. Incorrect or incomplete formulation of the problem can negate the results of all subsequent stages.
The model is the result of a compromise between two opposing goals:
the model must be detailed, taking into account everything realistically existing connections and the factors and parameters involved in its work;
at the same time, the model must be simple enough to produce acceptable solutions or results in an acceptable time frame given certain resource constraints.
Modeling can be called an approximate scientific study. And the degree of its accuracy depends on the researcher, his experience, goals, and resources.
Assumptions made when model development, are a consequence of the modeling goals and the capabilities (resources) of the researcher. They are determined by the requirements for the accuracy of the results, and like the model itself, are the result of a compromise. After all, it is assumptions that distinguish one model of the same process from another.
Usually, when developing a model, unimportant factors are discarded (not taken into account). Constants in physical equations are considered constants. Sometimes some quantities that change during the process are averaged (for example, air temperature can be considered constant over a certain period of time).
Model development process
This is a process of consistent (and possibly repeated) schematization or idealization of the phenomenon under study.
The adequacy of a model is its correspondence to the real physical process (or object) that it represents.
To develop the model physical process it is necessary to determine:
Sometimes an approach is used when a low-completeness model of a probabilistic nature is used. Then, with the help of a computer, it is analyzed and clarified.
Model verification begins and takes place in the very process of its construction, when certain relationships between its parameters are selected or established, and the accepted assumptions are evaluated. However, after the formation of the model as a whole, it is necessary to analyze it from some general positions.
The mathematical basis of the model (i.e., a mathematical description of physical relationships) must be consistent precisely from the point of view of mathematics: functional dependencies must have the same trends of change as real processes; the equations must have a domain of existence that is no less than the range in which the study is being conducted; they shouldn't have singular points or ruptures, if they are not in real process, etc. Equations should not distort the logic of the real process.
The model must adequately, that is, as accurately as possible, reflect reality. Adequacy is not needed in general, but in the range under consideration.
Discrepancies between the results of the model analysis and real behavior objects are inevitable, since the model is a reflection, and not the object itself.
In Fig. 3. a generalized representation is presented that is used in constructing mathematical models.
Rice. 3. Apparatus for constructing mathematical models
When using static methods, the apparatus of algebra and differential equations with time-independent arguments.
IN dynamic methods differential equations are used in the same way; integral equations; partial differential equations; theory of automatic control; algebra.
IN probabilistic methods used: probability theory; information theory; algebra; theory random processes; theory Markov processes; automata theory; differential equations.
An important place in modeling is occupied by the question of the similarity between the model and the real object. Quantitative correspondences between individual parties to the proceedings flowing in real object and its models are characterized by scale.
In general, the similarity of processes in objects and models is characterized by similarity criteria. The similarity criterion is a dimensionless set of parameters characterizing this process. When conducting research, different criteria are used depending on the field of research. For example, in hydraulics such a criterion is the Reynolds number (characterizes the fluidity of the fluid), in thermal engineering - the Nusselt number (characterizes the conditions of heat transfer), in mechanics - the Newton criterion, etc.
It is believed that if such criteria for the model and the object under study are equal, then the model is correct.
Another method is adjacent to the theory of similarity theoretical research - dimensional analysis method, which is based on two provisions:
physical laws are expressed only by products of powers of physical quantities, which can be positive, negative, integer and fractional; the dimensions of both sides of the equality expressing the physical dimension must be the same.
In the history of mathematics, we can roughly distinguish two main periods: elementary and modern mathematics. The milestone from which it is customary to count the era of new (sometimes called higher) mathematics was the 17th century - the century of the appearance of mathematical analysis. By the end of the 17th century. I. Newton, G. Leibniz and their predecessors created a new apparatus differential calculus and integral calculus, which forms the basis mathematical analysis and even, perhaps, the mathematical basis of all modern natural science.
Mathematical analysis is a vast area of mathematics with a characteristic object of study (variable quantity), a unique research method (analysis by means of infinitesimals or by means of passages to limits), a certain system of basic concepts (function, limit, derivative, differential, integral, series) and constantly improving and a developing apparatus, the basis of which is differential and integral calculus.
Let's try to give an idea of what kind of mathematical revolution occurred in the 17th century, what characterizes the transition associated with the birth of mathematical analysis from elementary mathematics to what is now the subject of research in mathematical analysis, and what explains its fundamental role in the entire modern system of theoretical and applied knowledge .
Imagine that in front of you is a beautifully executed color photography a stormy ocean wave rushing onto the shore: a powerful stooped back, a steep but slightly sunken chest, a head already tilted forward and ready to fall with a gray mane tormented by the wind. You stopped the moment, you managed to catch the wave, and you can now carefully study it in every detail without haste. A wave can be measured, and using the tools of elementary mathematics, you can draw many important conclusions about this wave, and therefore all its ocean sisters. But by stopping the wave, you deprived it of movement and life. Its origin, development, running, the force with which it hits the shore - all this turned out to be outside your field of vision, because you do not yet have either a language or a mathematical apparatus suitable for describing and studying not static, but developing, dynamic processes, variables and their relationships.
“Mathematical analysis is no less comprehensive than nature itself: it determines all tangible relationships, measures times, spaces, forces, temperatures.” J. Fourier
Movement, variables and their relationships surround us everywhere. Various types of motion and their patterns constitute the main object of study of specific sciences: physics, geology, biology, sociology, etc. Therefore, precise language and corresponding mathematical methods for describing and studying variable quantities turned out to be necessary in all areas of knowledge to approximately the same extent as numbers and arithmetic are necessary when describing quantitative relationships. So, mathematical analysis forms the basis of the language and mathematical methods for describing variables and their relationships. Nowadays, without mathematical analysis it is impossible not only to calculate space trajectories, work nuclear reactors, the running of the ocean wave and the patterns of development of the cyclone, but also to economically manage production, resource distribution, organization technological processes, predict the course of chemical reactions or changes in the numbers of various interconnected species of animals and plants in nature, because all of these are dynamic processes.
Elementary math was mostly math constant values, she studied mainly the relationships between elements geometric shapes, arithmetic properties of numbers and algebraic equations. Its attitude to reality can to some extent be compared with an attentive, even thorough and complete study of each fixed frame of a film that captures the changing, developing living world in its movement, which, however, is not visible in a separate frame and which can only be observed by looking the tape as a whole. But just as cinema is unthinkable without photography, so too modern mathematics is impossible without that part of it that we conventionally call elementary, without the ideas and achievements of many outstanding scientists, sometimes separated by tens of centuries.
Mathematics is united, and the “higher” part of it is connected with the “elementary” part in much the same way as the next floor of a house under construction is connected with the previous one, and the width of the horizons that mathematics opens to us in the world around us depends on which floor of this building we managed to reach rise. Born in the 17th century. mathematical analysis has opened up possibilities for us scientific description, quantitative and qualitative study of variables and movement in in a broad sense this word.
What are the prerequisites for the emergence of mathematical analysis?
By the end of the 17th century. The following situation has arisen. Firstly, within the framework of mathematics itself over many years, some important classes of problems of the same type have accumulated (for example, problems of measuring areas and volumes of non-standard figures, problems of drawing tangents to curves) and methods for solving them in various special cases have appeared. Secondly, it turned out that these problems are closely related to the problems of describing arbitrary (not necessarily uniform) mechanical motion, and in particular with the calculation of its instantaneous characteristics (speed, acceleration at any time), as well as with finding the distance traveled for movement occurring at a given variable speed. The solution to these problems was necessary for the development of physics, astronomy, and technology.
Finally, thirdly, to mid-17th century V. the works of R. Descartes and P. Fermat laid the foundations analytical method coordinates (the so-called analytical geometry), which made it possible to formulate geometric and physical tasks in the general (analytical) language of numbers and numerical dependencies, or, as we now say, numerical functions.
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NIKOLAY NIKOLAEVICH LUZIN
N. N. Luzin - Soviet mathematician, founder Soviet school theory of functions, academician (1929). Luzin was born in Tomsk and studied at the Tomsk gymnasium. The formalism of the gymnasium mathematics course alienated the talented young man, and only a capable tutor was able to reveal to him the beauty and greatness of mathematical science. In 1901, Luzin entered the mathematics department of the Faculty of Physics and Mathematics of Moscow University. From the first years of his studies, issues related to infinity fell into his circle of interests. IN late XIX V. German scientist G. Cantor created general theory of infinite sets, which has received numerous applications in the study of discontinuous functions. Luzin began to study this theory, but his studies were interrupted in 1905. A student who took part in revolutionary activities, I had to leave for France for a while. There he listened to lectures by the most prominent French mathematicians of that time. Upon returning to Russia, Luzin graduated from the university and was left to prepare for a professorship. Soon he again left for Paris, and then to Göttingen, where he became close to many scientists and wrote his first scientific works. The main problem that interested the scientist was the question of whether sets containing more elements than many natural numbers, but less than the set of points on the segment (continuum problem). For anyone infinite number, which could be obtained from segments using the operations of union and intersection of countable collections of sets, this hypothesis was fulfilled, and in order to solve the problem, it was necessary to find out what other ways there are to construct sets. At the same time, Luzin studied the question of whether it is possible to imagine any periodic function, even having infinitely many discontinuity points, in the form of a sum of a trigonometric series, i.e. sums of an infinite set harmonic vibrations. Luzin obtained a number of significant results on these issues and in 1915 defended his dissertation “Integral and trigonometric series", for which he was immediately awarded the academic degree of Doctor of Pure Mathematics, bypassing the intermediate master's degree that existed at that time. In 1917 Luzin became a professor at Moscow University. A talented teacher, he attracted the most capable students and young mathematicians. Luzin's school reached its peak in the first post-revolutionary years. Luzin's students formed creative team, which was jokingly called the “Lusitania.” Many of them received first-class scientific results while still a student. For example, P. S. Alexandrov and M. Ya. Suslin (1894-1919) discovered new method construction of sets, which served as the beginning of the development of a new direction - descriptive set theory. Research in this area carried out by Luzin and his students showed that the usual methods of set theory are not enough to solve many of the problems that arise in it. Luzin's scientific predictions were fully confirmed in the 60s. XX century Many of N. N. Luzin’s students later became academicians and corresponding members of the USSR Academy of Sciences. Among them is P. S. Alexandrov. A. N. Kolmogorov. M. A. Lavrentyev, L. A. Lyusternik, D. E. Menshov, P. S. Novikov. L. G. Shnirelman and others. Modern Soviet and foreign mathematicians in their works develop the ideas of N. N. Luzin. |
The confluence of these circumstances led to the fact that at the end of the 17th century. two scientists - I. Newton and G. Leibniz - independently of each other managed to create a mathematical apparatus, summed up and generalized the individual results of his predecessors, including ancient scientist Archimedes and contemporaries of Newton and Leibniz - B. Cavalieri, B. Pascal, D. Gregory, I. Barrow. This apparatus formed the basis of mathematical analysis - a new branch of mathematics that studies various developing processes, i.e. relationships between variables, which in mathematics are called functional dependencies or, in other words, functions. By the way, the term “function” itself was required and naturally arose precisely in the 17th century, and by now it has acquired not only general mathematical, but also general scientific significance.
Initial information about the basic concepts and mathematical apparatus of analysis is given in the articles “Differential calculus” and “Integral calculus”.
In conclusion, I would like to dwell on only one principle of mathematical abstraction, common to all mathematics and characteristic of analysis, and in this regard explain in what form mathematical analysis studies variables and what is the secret of such universality of its methods for studying all kinds of specific developing processes and their interrelations .
Let's look at a few illustrative examples and analogies.
Sometimes we no longer realize that, for example, a mathematical relation written not for apples, chairs or elephants, but in an abstract form abstracted from specific objects, is an outstanding scientific achievement. This is a mathematical law that, as experience shows, is applicable to various specific objects. So, studying in mathematics general properties distracted, abstract numbers, we thereby study the quantitative relationships real world.
For example, from school course mathematics knows that, so in a specific situation you could say: “If they don’t give me two six-ton dump trucks to transport 12 tons of soil, then I can ask for three four-ton dump trucks and the work will be done, and if they give me only one four-ton dump truck, then she will have to do three flight." Thus, the abstract numbers and numerical patterns that are now familiar to us are associated with their specific manifestations and applications.
The laws of change in specific variables and developing processes of nature are related in approximately the same way to the abstract, abstract form-function in which they appear and are studied in mathematical analysis.
For example, an abstract ratio may reflect the dependence of a cinema's box office on the number of tickets sold, if 20 is 20 kopecks - the price of one ticket. But if we are riding a bicycle on a highway, traveling 20 km per hour, then this same ratio can be interpreted as the relationship between the time (hours) of our cycling trip and the distance covered during this time (kilometers). You can always say that, for example, a change of several times leads to a proportional (i.e., the same number of times) change in the value of , and if , then the opposite conclusion is also true. This means, in particular, to double the box office of a cinema you will have to attract twice as many spectators, and in order to ride a bicycle at the same speed twice longer distance, you will have to travel twice as long.
Mathematics studies and simplest addiction, and other, much more complex dependencies in a general, abstract form, abstracted from a particular interpretation. The properties of a function or methods for studying these properties identified in such a study will be of the nature of general mathematical techniques, conclusions, laws and conclusions applicable to everyone specific phenomenon, in which a function studied in abstract form occurs, regardless of what area of knowledge this phenomenon belongs to.
So, mathematical analysis as a branch of mathematics took shape at the end of the 17th century. The subject of study in mathematical analysis (as it appears from modern positions) are functions, or, in other words, dependencies between variable quantities.
With the advent of mathematical analysis, mathematics became accessible to the study and reflection of developing processes in the real world; mathematics included variables and motion.
FEDERAL AGENCY FOR EDUCATION
State educational institution of higher professional education “Ural State University named after. »
History department
Department of Documentation and Information Support of Management
Mathematical methods in scientific research
Course program
Standard 350800 “Documentation and documentation support management"
Standard 020800 “Historical and archival studies”
Ekaterinburg
I approve
Vice-Rector
(signature)
The program of the discipline “Mathematical methods in scientific research” is compiled in accordance with the requirements university component to the mandatory minimum content and level of training:
certified specialist by specialty
Documentation and documentation support for management (350800),
Historical and archival studies (020800),
in the cycle “General humanitarian and socio-economic disciplines” of the state educational standard higher vocational education.
Semester III
By curriculum specialty No. 000 – Documentation and documentation support for management:
Total labor intensity of the discipline: 100 hours,
including lectures 36 hours
According to the curriculum of specialty No. 000 – Historical and Archival Studies
Total labor intensity of the discipline: 50 hours,
including lectures 36 hours
Control activities:
Tests 2 people/hour
Compiled by: , Ph.D. ist. Sciences, Associate Professor of the Department of Documentation and information support Department of the Ural State University
Department of Documentation and Information Support of Management
dated 01.01.01 No. 1.
Agreed:
Deputy chairman
Humanitarian Council
_________________
(signature)
(C) Ural State University
(WITH) , 2006
INTRODUCTION
The course “Mathematical methods in socio-economic research” is designed to familiarize students with the basic techniques and methods of processing quantitative information developed by statistics. Its main task is to expand the methodological scientific apparatus of researchers, to teach how to use in practical and scientific research, in addition to traditional methods based on logical analysis, mathematical methods that help to quantitatively characterize historical phenomena and facts.
Currently, mathematical apparatus and mathematical methods are used in almost all areas of science. This natural process, it is often called the mathematization of science. In philosophy, mathematization is usually understood as the application of mathematics in various sciences. Mathematical methods have long been firmly established in the arsenal of research methods of scientists; they are used to summarize data, identify trends and patterns in the development of social phenomena and processes, typology and modeling.
Knowledge of statistics is necessary to correctly characterize and analyze the processes occurring in the economy and society. To do this, you need to master the sampling method, summarize and group data, be able to calculate average and relative values, indicators of variation, and correlation coefficients. Skills are an element of information culture correct design tables and graphs, which are an important tool for systematizing primary socio-economic data and visual representation quantitative information. To assess temporary changes, it is necessary to have an idea of the system of dynamic indicators.
Using the methodology sample survey allows you to study large amounts of information presented by mass sources, save time and labor, while obtaining scientifically significant results.
Mathematics -statistical methods occupy auxiliary positions, complementing and enriching traditional methods of socio-economic analysis, their development is necessary integral part qualifications modern specialist– document specialist, historian-archivist.
Currently, mathematical and statistical methods are actively used in marketing and sociological research, in collecting operational management information, drawing up reports and analyzing document flows.
Skills quantitative analysis necessary for preparation qualification works, abstracts and other research projects.
Experience in the use of mathematical methods shows that their use must be carried out in compliance with the following principles in order to obtain reliable and representative results:
1) the determining role is played by the general methodology and theory of scientific knowledge;
2) a clear and correct positioning research problem;
3) selection of quantitatively and qualitatively representative socio-economic data;
4) correct application of mathematical methods, i.e. they must correspond to the research problem and the nature of the data being processed;
5) a meaningful interpretation and analysis of the results obtained is necessary, as well as mandatory additional verification of the information obtained as a result of mathematical processing.
Mathematical methods help improve the technology of scientific research: increase its efficiency; they provide great time savings, especially when processing large amounts of information, and allow you to identify hidden information stored in the source.
In addition, mathematical methods are closely related to such areas of scientific information activities as the creation of historical data banks and archives of machine-readable data. The achievements of the era cannot be ignored, and information technology is becoming one of the most important factors development of all spheres of society.
COURSE PROGRAM
Topic 1. INTRODUCTION. MATHEMATIZATION OF HISTORICAL SCIENCE
Purpose and objectives of the course. Objective need for improvement historical methods through the use of mathematics.
Mathematization of science, main content. Prerequisites for mathematization: natural science background; socio-technical prerequisites. Boundaries of mathematization of science. Levels of mathematization for natural, technical, economic and human sciences. The main laws of mathematization of science: the impossibility of fully covering the areas of research of other sciences by means of mathematics; correspondence of the applied mathematical methods to the content of the science being mathematized. The emergence and development of new applied mathematical disciplines.
Mathematization historical science. Main stages and their features. Prerequisites for the mathematization of historical science. The significance of the development of statistical methods for the development of historical knowledge.
Socio-economic research using mathematical methods in pre-revolutionary and Soviet historiography of the 20s (, etc.)
Mathematical and statistical methods in the works of historians of the 60-90s. Computerization of science and dissemination of mathematical methods. Creation of databases and prospects for the development of information support for historical research. The most important results of the application of mathematical methods in socio-economic and historical and cultural research (, etc.).
Correlation of mathematical methods with other methods historical research: historical-comparative, historical-typological, structural, systemic, historical-genetic methods. Basic methodological principles of application of mathematical and statistical methods in historical research.
Topic 2. STATISTICAL INDICATORS
Basic techniques and methods statistical study social phenomena: statistical observation, reliability of statistical data. Basic forms of statistical observation, purpose of observation, object and unit of observation. Statistical document as a historical source.
Statistical indicators (indicators of volume, level and ratio), its main functions. Quantitative and qualitative side of a statistical indicator. Varieties of statistical indicators (volumetric and qualitative; individual and generalizing; interval and moment).
Basic requirements for the calculation of statistical indicators, ensuring their reliability.
Interrelation of statistical indicators. System of indicators. Summary indicators.
Absolute values, definition. Types of absolute statistical quantities, their meaning and methods of obtaining. Absolute values as a direct result of a summary of statistical observation data.
Units of measurement, their choice depending on the essence of the phenomenon being studied. Natural, cost and labor units of measurement.
Relative values. The main content of the relative indicator, the forms of their expression (coefficient, percentage, ppm, decimille). Dependence of the form and content of the relative indicator.
Base of comparison, choice of base when calculating relative values. Basic principles for calculating relative indicators, ensuring comparability and reliability of absolute indicators (by territory, range of objects, etc.).
Relative values of structure, dynamics, comparison, coordination and intensity. Methods for calculating them.
The relationship between absolute and relative values. The need for their complex use.
Topic 3. DATA GROUPING. TABLES.
Summary indicators and grouping in historical research. Problems solved by these methods in scientific research: systematization, generalization, analysis, ease of perception. Statistical population, units of observation.
Objectives and main contents of the summary. Summary - second stage statistical research. Varieties of summary indicators (simple, auxiliary). The main stages of calculating summary indicators.
Grouping is the main method of processing quantitative data. Grouping tasks and their significance in scientific research. Types of groups. The role of groupings in the analysis of social phenomena and processes.
The main stages of constructing a grouping: determination of the population being studied; selection of a grouping characteristic (quantitative and qualitative characteristics; alternative and non-alternative; factorial and effective); distribution of the population into groups depending on the type of grouping (determining the number of groups and the size of intervals), scale of measurement of characteristics (nominal, ordinal, interval); selecting the form of presentation of grouped data (text, table, graph).
Typological grouping, definition, main tasks, principles of construction. The role of typological grouping in the study of socio-economic types.
Structural grouping, definition, main tasks, principles of construction. The role of structural grouping in the study of the structure of social phenomena
Analytical (factorial) grouping, definition, main tasks, principles of construction, The role of analytical grouping in the analysis of the interrelations of social phenomena. The need for integrated use and study of groupings for the analysis of social phenomena.
General requirements for the construction and design of tables. Table layout development. Table details (numbering, title, names of columns and rows, symbols, number designation). Methodology for filling out table information.
Topic 4. GRAPHICAL METHODS FOR ANALYSIS OF SOCIO-ECONOMIC
INFORMATION
The role of schedules and graphic image in scientific research. Objectives of graphical methods: providing clarity of perception of quantitative data; analytical tasks; characterization of the properties of signs.
Statistical graph, definition. The main elements of a graph: graph field, graphic image, spatial reference points, scale reference points, graph explication.
Types of statistical graphs: line chart, features of its construction, graphic images; bar chart (histogram), definition of the rule for constructing histograms in the case of equal and unequal intervals; pie chart, definition, methods of construction.
Characteristic distribution polygon. Normal distribution sign and its graphic representation. Features of the distribution of features characterizing social phenomena: skewed, asymmetric, moderately asymmetric distribution.
Linear dependence between characteristics, features of a graphical representation of a linear relationship. Features of linear dependence in the characteristic social phenomena and processes.
Trend concept time series. Trend identification using graphical methods.
Topic 5. AVERAGE VALUES
Average values in scientific research and statistics, their essence and definition. Basic properties of average values as a generalizing characteristic. The relationship between the method of averages and groupings. General and group averages. Conditions for the typicality of averages. Basic research problems that solve averages.
Methods for calculating averages. Arithmetic mean - simple, weighted. Basic properties of the arithmetic mean. Features of calculating the average for discrete and interval distribution series. The dependence of the method of calculating the arithmetic mean depending on the nature of the source data. Features of the interpretation of the arithmetic average.
Median - average aggregate structures, definition, basic properties. Determining the median indicator for the ranked quantitative series. Calculate the median for a measure represented by interval grouping.
Fashion is an average indicator of the structure of a population, basic properties and content. Determination of mode for discrete and interval series. Features of the historical interpretation of fashion.
The relationship between the arithmetic mean, median and mode, the need for them integrated use, checking the typicality of the arithmetic mean.
Topic 6. INDICATORS OF VARIATION
Study of variability (variability) of attribute values. The main content of measures of trait dispersion, and their use in research activities.
Absolute and average variations. Variation range, main content, methods of calculation. Average linear deviation. Standard deviation, main content, calculation methods for discrete and interval quantitative series. The concept of trait dispersion.
Relative indicators variations. Oscillation coefficient, main content, calculation methods. Coefficient of variation, main content, methods of calculation. The significance and specificity of the use of each indicator of variation in the study of socio-economic characteristics and phenomena.
Topic 7.
The study of changes in social phenomena over time is one of the most important tasks socio-economic analysis.
The concept of a time series. Moment and interval time series. Requirements for constructing time series. Comparability in dynamics series.
Indicators of changes in dynamics series. The main content of the indicators of the dynamics series. Row level. Basic and chain indicators. Absolute increase in the level of dynamics, basic and chain absolute increases, calculation methods.
Growth rate indicators. Basic and chain growth rates. Features of their interpretation. Growth rate indicators, main content, methods for calculating basic and chain growth rates.
Average level of a series of dynamics, basic content. Techniques for calculating the arithmetic mean for moment series with equal and unequal intervals and for interval series at equal intervals. Average absolute increase. Average growth rate. Average growth rate.
Comprehensive analysis of interconnected time series. Revealing general trend trend development: moving average method, enlarging intervals, analytical techniques processing dynamics series. The concept of interpolation and extrapolation of time series.
Topic 8.
The need to identify and explain relationships to study socio-economic phenomena. Types and forms of relationships studied by statistical methods. The concept of functional and correlation connection. The main content of the correlation method and the problems solved with its help in scientific research. Main stages of correlation analysis. Peculiarities of interpretation of correlation coefficients.
Coefficient linear correlation, properties of features for which the linear correlation coefficient can be calculated. Methods for calculating the linear correlation coefficient for grouped and ungrouped data. Regression coefficient, main content, calculation methods, interpretation features. Determination coefficient and its meaningful interpretation.
Limits of application of the main varieties correlation coefficients depending on the content and form of presentation of the source data. Correlation coefficient. Coefficient rank correlation. Association and contingency coefficients for alternative qualitative characteristics. Approximate methods for determining the relationship between characteristics: the Fechner coefficient. Autocorrelation coefficient. Information coefficients.
Methods for ordering correlation coefficients: correlation matrix, pleiad method.
Methods of multivariate statistical analysis: factor analysis, component analysis, regression analysis, cluster analysis. Modeling prospects historical processes to study social phenomena.
Topic 9. SAMPLING RESEARCH
Reasons and conditions for conducting a sample study. The need for historians to use methods for partial study of social objects.
Main types of partial survey: monographic, main array method, sample study.
Definition of the sampling method, basic properties of the sample. Sample representativeness and sampling error.
Stages of conducting a sample study. Determining the sample size, basic techniques and methods for finding the sample size (mathematical methods, table large numbers). The practice of determining sample size in statistics and sociology.
Formation methods sample population: self-random sampling, mechanical sampling, typical and nest sampling. Methodology for organizing sample population censuses, budget surveys of families of workers and peasants.
Methodology for proving the representativeness of the sample. Random, systematic sampling and observation errors. The role of traditional methods in determining the reliability of sampling results. Mathematical methods for calculating sampling error. Dependence of error on sample size and type.
Features of interpretation of sample results and distribution of sample population indicators to the general population.
Natural sampling, main content, features of formation. The problem of representativeness of natural sampling. The main stages of proving the representativeness of a natural sample: the use of traditional and formal methods. The method of sign criterion, the method of series - as methods of proving the property of random sampling.
Concept small sample. Basic principles of using it in scientific research
Topic 11. METHODS FOR FORMALIZING INFORMATION FROM MASS SOURCES
The need to formalize information from mass sources to obtain hidden information. The problem of measuring information. Quantitative and qualitative characteristics. Scales for measuring quantitative and qualitative characteristics: nominal, ordinal, interval. The main stages of measuring source information.
Types of mass sources, features of their measurement. Methodology for constructing a unified questionnaire based on materials from a structured, semi-structured historical source.
Features of measuring information from an unstructured narrative source. Content analysis, its content and prospects for use. Types of content analysis. Content analysis in sociological and historical research.
The relationship between mathematical and statistical methods of information processing and methods for formalizing source information. Computerization of research. Databases and data banks. Database technology in socio-economic research.
Tasks for independent work
To secure lecture material students are offered tasks for independent work on the following topics course:
Relative indicators Average indicators Grouping method Graphical methods Dynamics indicators
Completion of assignments is controlled by the teacher and is prerequisite admission to the test.
Sample list of questions for testing
1. Mathematization of science, essence, prerequisites, levels of mathematization
2. Main stages and features of mathematization of historical science
3. Prerequisites for the use of mathematical methods in historical research
4. Statistical indicator, essence, functions, varieties
3. Methodological principles for the use of statistical indicators in historical research
6. Absolute values
7. Relative quantities, content, forms of expression, basic principles of calculation.
8. Types of relative quantities
9. Objectives and main content of the data summary
10. Grouping, main content and objectives in the study
11. The main stages of building a group
12. The concept of a grouping characteristic and its gradations
13. Types of grouping
14. Rules for constructing and designing tables
15. Time series, requirements for constructing a time series
16. Statistical graph, definition, structure, tasks to be solved
17. Types of statistical graphs
18. Polygon distribution of the characteristic. Normal distribution of the trait.
19. Linear dependence between characteristics, methods for determining linearity.
20. The concept of a trend in a time series, methods for determining it
21. Average values in scientific research, their essence and basic properties. Conditions for the typicality of averages.
22. Types of population averages. Interrelation of average indicators.
23. Statistical indicators of dynamics, general characteristics, kinds
24. Absolute indicators changes in time series
25. Relative indicators of changes in dynamics series (growth rates, growth rates)
26. Average indicators of the dynamic series
27. Indicators of variation, main content and tasks to be solved, types
28. Types of partial observation
29. Selective research, main content and tasks to be solved
30. Selective and population, basic properties of the sample
31. Stages of conducting a sample study, general characteristics
32. Determining sample size
33. Methods for forming a sample population
34. Sampling error and methods for determining it
35. Representativeness of the sample, factors influencing representativeness
36. Natural sampling, the problem of representativeness of natural sampling
37. Main stages of proving the representativeness of a natural sample
38. Correlation method, essence, main tasks. Features of interpretation of correlation coefficients
39. Statistical observation as a method of collecting information, the main types of statistical observation.
40. Types of correlation coefficients, general characteristics
41. Linear correlation coefficient
42. Autocorrelation coefficient
43. Methods of formalization historical sources: unified questionnaire method
44. Methods for formalizing historical sources: content analysis method
III.Distribution of course hours by topics and types of work:
according to the specialty curriculum (No. 000 – document management and documentation support for management)
Name
sections and topics
Auditory lessons
Independent work
including
Introduction. Mathematization of science
Statistical indicators
Grouping data. Tables
Average values
Variation indicators
Statistical indicators of dynamics
Multivariate analysis methods. Correlation coefficients
Sample study
Methods for formalizing information
Distribution of course hours by topics and types of work
according to the curriculum of specialty No. 000 – historical and archival studies
Name
sections and topics
Auditory lessons
Independent work
including
Practical (seminars, laboratory work)
Introduction. Mathematization of science
Statistical indicators
Grouping data. Tables
Graphic methods for analyzing socio-economic information
Average values
Variation indicators
Statistical indicators of dynamics
Multivariate analysis methods. Correlation coefficients
Sample study
Methods for formalizing information
IV. Final control form - test
V. Educational and methodological support course
Slavko methods in historical research. Textbook. Ekaterinburg, 1995
Mazur methods in historical research. Guidelines. Ekaterinburg, 1998
additional literature
Andersen T. Statistical analysis of time series. M., 1976.
Borodkin statistical analysis in historical research. M., 1986
Borodkin informatics: stages of development // New and recent history. 1996. № 1.
Tikhonov for humanists. M., 1997
Garskova and data banks in historical research. Göttingen, 1994
Gerchuk methods in statistics. M., 1968
Druzhinin method and its application in socio-economic research. M., 1970
Jessen R. Methods of statistical surveys. M., 1985
Ginny K. Average values. M., 1970
Yuzbashev theory of statistics. M., 1995.
Rumyantsev theory of statistics. M., 1998
Shmoilov study of the main trend and relationship in the dynamics series. Tomsk, 1985
Yates F. Sampling method in censuses and surveys / trans. from English . M., 1976
Historical information science. M., 1996.
Kovalchenko historical research. M., 1987
Computer in economic history. Barnaul, 1997
Circle of ideas: models and technologies of historical informatics. M., 1996
Circle of ideas: traditions and trends of historical informatics. M., 1997
Circle of ideas: macro and micro approaches in historical information science. M., 1998
Circle of ideas: historical information science on threshold of XXI century. Cheboksary, 1999
Circle of ideas: historical information science in information society. M., 2001
General theory of statistics: Textbook / ed. And. M., 1994.
Workshop on the theory of statistics: Proc. allowance M., 2000
Eliseeva statistics. M., 1990
Slavko-statistical methods in historical and research M., 1981
Slavko's methods in studying the history of the Soviet working class. M., 1991
Statistical Dictionary / ed. . M., 1989
Theory of statistics: Textbook / ed. , M., 2000
Ursul Society. Introduction to social informatics. M., 1990
Schwartz G. Selective method / trans. with him. . M., 1978