It is very difficult as well as unsatisfying to speak on the uses of mathematics in accounting for two main reasons. Firstly, because discussions of this nature convey the somewhat false impression that the only impetus toward changes, if any progress is evident in the use of mathematics in accounting instruction and research, has originated from without rather than from within the accounting profession, and that progress has been forced upon the accounting discipline by outsiders. Secondly, because the potential uses of mathematics in accounting are so many, within the time limitations of a meeting one can at best only survey the area. The author in this article did not attempt to explore fully the reasons accountants have not taken advantage of the existing body of mathematical knowledge earlier, but, according to him, he cannot help speculating briefly on this issue. It appears to him that the demands of management for new quantitative criteria of efficiency of operations and decisions both aggregative and partial, are presenting opportunities and pressures that accounting cannot ignore. Mathematical simulation, which has grown to maturity in the last few years, has had a pronounced influence on the design of feedback-control systems.

This article focuses on the "mathematics" of accounting variance analysis. It seems that the managerial significance of accounting data is a rather controversial matter and consequently it should not be left completely to the imagination of the reader. The purpose of this note is to suggest an alternative, and what is believed to be a simpler way of getting the overhead variances and then point out some of the significance of the results. One of the most striking features of present accounting literature may be said to lie in the growing interest paid to the mathematics of variance analysis. This development began in 1953 when Gilbert Amerman published his very famous article on the subject. The variation analysis may be easily tied to an effective budgetary control system by comparing the standard and actual costs of a period with the corresponding budgeted costs. On these lines it is possible to discern the influence that important activity and production mix variations had on the direct materials and labor costs. The budget variance is defined by the difference between the actual costs of the period under investigation and the flexible budget allowance for the actual hours worked.