Add to ORKGThis thesis includes a brief review of the literature of methods of how partition identities may be derived. In the third and fourth chapters we introduce a totally new and different approach in partition theory. With the use of computers we will apply the method of sampling and simulation to estimate the number of partitions of an integer. We give an algorithm for generating partitions so that every partition is equally likely to be generated. We use Capture-Recapture method and an estimation technique of Boneh, Boneh, and Caron. In chapter five we give some new results in partition theory, using generating functions. The last chapter summarizes the findings of this thesis and compares these findings with known results.Dept. of Mathematics...