ABSTRACT
This chapter covers material usually referred to as the foundations of mathematics, including logic, sets, and functions. In addition to covering these foundational areas, the chapter includes material that shows how these are applied to discrete mathematics, computer science, and electrical engineering. The chapter covers methods of proof, program verification, and fuzzy reasoning. Logic is the basis for distinguishing what may be correctly inferred from a given collection of facts. Propositional logic, where there are no quantifiers is called zero-order logic. Sets are used to group objects and to serve as the basic elements for building more complicated objects and structures. Counting elements in sets is an important part of discrete mathematics. The asymptotic growth of functions is commonly described with various special pieces of notation and is regularly used in the analysis of computer algorithms to estimate the length of time the algorithms take to run and the amount of computer memory they require.
