Mathematical sociology uses mathematics (including logic and information science) to formalize theoretical propositions and model empirical social processes. Examples include the algebraic formalization of measurement theory; use of graph theory and finite mathematics in sociometry, social network analysis, and studies of kinship; and the extensive use of probabilistic Markov chains for modelling social mobility and stratification. The specialist Journal of Mathematical Sociology covers the field.
The work of the American sociologist Leo A. Goodman is typical of this approach. Goodman, who has substantive interests in demography, social mobility, and stratification generally, has pioneered the use of loglinear and latent structure techniques in the analysis of contingency tables. Analysing Quantitative/Categorical Data (1978), a collection of ten articles published between 1970 and 1975, is a representative collection of his writings. For a more recent example see The Analysis of Cross-Classification Having Ordered Categories (1984). See also neo-positivism.