The subject introduces the basic mathematical methods for statistics. It covers selected topics in classical analysis of functions that are essential for a proper understanding of the material in many statistics subjects. The limits of sequences and limits of functions are studied in this subject. We also study series and various tests are derived to determine the convergence or otherwise of these series. We then extend the basic idea of limit to include sequences of functions and sequences of sets in metric spaces. A powerful theorem called The Contraction Mapping Theorem will be derived. This theorem plays a fundamental role in analysis and its applications. We will use it to establish the existence and uniqueness of solutions to certain differential equations. Various applications in statistics will be discussed.

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