Mathematics, Statistics, and Computer Science
axiomatic set theory, logic, proof, algebra, functions
As a general ﬁeld of study, logic isn’t really a branch of mathematics. It deals with conse-quential reasoning, something we do in all areas of our lives. It enters into daily conversation (“How can you believe that? Don’t you know that . . . ?”) and cooking decisions (“To modify this recipe to feed four instead of six, I need to . . . ”) as well as academic studies (“If poverty is a factor in systemic educational failure, then we should . . . ”). Any time we draw a necessary conclusion from something we already know, logical processes come into play.
So mathematics and computer science cannot lay exclusive claim to logic. Nonetheless, deductive reasoning is a crucial ingredient in all quantitative sciences. Moreover, mathematics and logic have had an ongoing intimate relationship since ancient times, and computer science has been closely allied with logic since it began in earnest in the twentieth century. In fact, the connections have become so close over the last century that portions of logic are diﬃcult to distinguish from mathematics, and computer science sometimes seems like applied logic. So it makes sense for us to spend some time here with logic, regardless of how it is classiﬁed.
In this ﬁrst section, we’ll begin putting this mathematics-logic-computer science nexus into historical perspective, and then we’ll discuss what sorts of things we can expect from logic for our study of discrete mathematics. In the process we’ll introduce some key notions that will be developed in more detail later in the book.
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Jongsma, Calvin, "Discrete Mathematics: Chapter 1, Sentential Logic" (2016). Faculty Work: Comprehensive List. 433.