ABSTRACT
This chapter discusses the study of some mathematical analysis involving discrete variables which take on integer values only. The mathematical theory of equations in integers is not very fully developed, even when attention is confined to linear equations. The chapter devotes to systems of simultaneous linear equations in integer variables. In general, the chances of such a system having a solution or solutions are rather less than if the same set of equations involved continuous variables. Although the integer requirement generally reduces the number of solutions compared with the corresponding case for continuous variables, it does not necessarily lead to a unique solution or to no solution at all. In many social science contexts involving non-negative integer variables, the problem is not so much one of solving a set of linear equations but rather one of finding which point or points in a feasible region (determined by linear inequalities) maximizes/minimizes some function of the variables.
