Title

Discrete Mathematics: Chapter 0, Table of Contents and Preface

Document Type

Book Chapter

Publication Date

1-2016

Department

Mathematics, Statistics, and Computer Science

Keywords

axiomatic set theory, calculus, algebra, functions, computational complexity, probability, logic

Abstract

Discrete mathematics, you may be disappointed to discover, is not the sort of stuff you talk about discreetly, in secretive whispers behind closed doors. It can be discussed in public by anyone; it has lots of important everyday connections. The term discrete means separate or disconnected; its opposite is continuous. Discrete mathematics deals with non-continuous quantitative phenomena — activities as mundane as counting objects and as arcane as ana-lyzing the output of a Turing machine. It also includes familiar topics like functions, but it explores their structural algebraic features and examines them with respect to computational complexity; matters connected to continuity or differentiability are left for analytic geometry and calculus.

As a field of mathematics, discrete mathematics is both very old and very new. Counting and basic arithmetic, of course, go back to pre-historic times. The rise of discrete mathematics in recent decades, however, is a result of the increased power and ongoing development of computer technology. Concepts and results in discrete mathematics provide the mathematical foundation for computer science. In return, computer science supplies crucial stimuli and resources for important contemporary developments and applications in discrete mathematics.

Discrete mathematics is a field every computer scientist should know about, and one that today’s mathematicians should be familiar with as well. This textbook is written for students in both majors. While the primary focus here is on mathematics, we will investigate topics that are crucial for computer science as well.

Comments

This material is no longer available for download. A revised, improved version is now available as a chapter of Introduction to Discrete Mathematics via Logic and Proof (see https://www.springer.com/us/book/9783030253578), published by Springer as part of their Undergraduate Texts in Mathematics series.

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