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mathematical sociologythe use of mathematical procedures and mathematical models in sociology. The rationale for most mathematical sociology, as stated by James Coleman in Introduction to Mathematical Sociology (1964), is that: ‘Mathematics provides a battery of languages, which when carefully fitted to a set of ideas, can lend these ideas great power’. Usually mathematical sociologists do not operate with the expectation that high-level, mathematically expressed general laws will be established in sociology. Rather they have made more limited claims that mathematics can be employed to good effect in illuminating areas of social life.
Examples of mathematical approaches which have enjoyed some influence in sociology are:
- the THEORY OF GAMES, deriving from the work of Herbert Simon and others;
- probabilistic stochastic process models, e.g. Markov chains, used in the modelling of population processes and social mobility (see Coleman, 1964);
- CAUSAL MODELLING, arising especially from the work of Blalock (1961);
- applications of‘finite’ (‘non-quantitative’) mathematical models, as in Harrison White's analysis of the formal properties of kinship structures (Anatomy of Kinship 1953);
- applications of mathematical graph theory in the analysis of social networks (see P. Doreian, Mathematics in the Study of Social Relations, 1970).
The boundaries between mathematical sociology and STATISTICS AND STATISTICAL ANALYSIS are not easily drawn, but one distinction is that, while statistical analysis uses relatively standardized procedures, making standardized assumptions about the character of data, mathematical sociology uses a wider array of mathematical procedures and is more likely to involve the construction of theoretical models intended to achieve a more direct, more purpose-built, modelling of the area of social reality under analysis.