Document Type

Book Chapter

Publication Date

1-2016

Department

Mathematics, Statistics, and Computer Science

Keywords

axiomatic set theory, logic, proof, algebra, functions

Abstract

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.

Comments

  • From Discrete Mathematics: An Integrated Approach, a self-published textbook for use in Math 212
  • © 2016 Calvin Jongsma

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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