Throughout the long history of the library, there have been many examples of methodical approaches to creating techniques, tools and knowledge that contribute to creating the library profession as we know it today. Collection arrangement and book labelling represent skills that are built into the very foundations of librarianship.With the opening of each new library, with collection merging or moving, or when building open access to a collection from scratch, librarians continue to question the methods they inherited. Librarians have to have a good understanding of the details and functions of book labelling in order to make an informed decision on how much of the work required for book labelling and re-shelving can be saved or replaced by other methods of locating and presenting documents.

The purpose of this paper is to construct the real number system. The foundation upon which the real number system will be constructed will be the system of counting numbers.

In this thesis our goal is to study pseudorandom numbers. We  will investigate how to produce pseudorandom samples from the uniform distribution with a method called the linear congruential method. Another method we will look at is the inverse sampling method which gives us the possibility to generate samples from other distributions that are not the uniform distribution. When generating pseudorandom samples quality is an important aspect, therefore we are going to take a look at a discrepancy which is a tool to determine quality of uniformly distributed samples. We implement the methods in Python and perform numerical experiments to test some quality aspects of the output.

This thesis covers the development of the natural numbers by means of the peano postulates.

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

Product densities have been widely used in the literature to give a concrete description of the distribution of a point process. A rigorous description of properties of product densities is presented with examples to show that in some sense these results are the best possible. Product densities are then used to discuss positive dependence properties of point processes. There are many ways of describing positive dependence. Two well known notions for Bernoulli random variables are the strong FKG inequalities and association, the strong FKG inequalities being much stronger. It is known, for example, from van den Berg and Burton, that the strong FKG inequalities are equivalent to all conditional distributions being associated, which is equivalent to all conditional distributions being positively correlated. In the case of point processes for which product densities exist, analogs of such positive dependence properties are given. Examples are presented to show that unlike the Bernoulli case none of these conditions are equivalent, although some are shown to be implied by others. / Graduation date: 1988

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The purpose of this composition is to develop a rigorous, axiomatic proof of the comparability of the cardinals of infinite sets.