These notes are short papers that may be helpful to students studying statistics. More complete treatments certainly exist on any topic represented here. They are to be considered as work in progress and not complete. Comments and suggestions are appreciated.

Some Facts about the Real Numbers.(DVI) The purpose of these notes is to provide a review of some facts and propositions about real numbers that may be useful in the study of mathematical statistics. In particular, they are intended to provide a background review for the first course in measure theory encountered at UNC. The material can be found in many advanced calculus or real analysis books.

Some Facts about Complex Variables.(DVI) The purpose of these notes is to provide a review of some facts and propositions about complex variables that will be useful in the study of time series analysis. This is not a complete review but only enough to help understand some facts concerning the polynomials and rational functions that occur in the study of parametric time series models. This development follows Chapters 2 and 3 of Conformal Mapping by Zeev Nehari. In this version the proofs are omitted, although they are typically not very difficult. Nothing is said here about complex integration, a review of which could also be useful to statistics students for the purpose of inverting characteristic functions. These notes are most definitely ``in progress'' so please tell me of any errors or clarifications that you believe would be helpful.

The Periodogram.(PS) Discusses the use of the periodogram for detecting periodic components and it's role in the estimation of spectral density.

Herglotz' Theorem.(DVI) A proof using the Helly theorems.

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