Abstract
This chapter describes different topics in algebra that involves the set of natural numbers. Mathematical induction provides a means of proving certain theorems involving the natural numbers that appear to resist other means of proof. Probability theory enables one to state the likelihood of occurrence of a given event and has obvious applications to games of chance. The theory of permutations and combinations, which enables counting the ways in which a set of objects or select a subset of the original set can be arranged, is necessary background to a study of probability theory. An infinite sequence is a function whose domain is the set of all natural numbers. The series associated with an arithmetic sequence is called an arithmetic series. The choice of which formula to use depends on the available information. In a geometric sequence, the terms between the first and last terms are called geometric means.
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