ABSTRACT
Many of the most common mathematical systems, including the integers, the rational numbers, and the real numbers, have an underlying algebraic structure. This chapter examines the structure and properties of various types of algebraic objects. These objects arise in a variety of settings and occur in many different applications, including counting techniques, coding theory, information theory, engineering, and circuit design. Simple groups arise as a fundamental part of the study of finite groups and the structure of their subgroups. Boolean expressions that appear to be different can yield the same combinatorial circuit. A Boolean expression is minimal if among all equivalent sum-of-products expressions it has the fewest number of summands, and among all sum-of-products expressions with that number of summands it uses the smallest number of literals in the products.
