# Spiral Workbook for Discrete Mathematics

Harris Kwong, State University of New York (SUNY) Fredonia

Pub Date: 2015

ISBN 13: 978-1-9423411-6-1

Publisher: Open SUNY

## Read This Book

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

This book covers the main topics in a discrete mathematics text. It does not include an analysis of algorithms, graphs, trees, and other topics that … read more

The book does not cover graphs, discrete probability, random variables and expectations. It also does not cover some counting problems like … read more

## Table of Contents

Preface

1 An Introduction

1.1 An Overview

1.2 Suggestions to Students

1.3 How to Read and Write Mathematics

1.4 Proving Identities

2 Logic

2.1 Propositions

2.2 Conjunctions and Disjunctions

2.3 Implications

2.4 Biconditional Statements

2.5 Logical Equivalences

2.6 Logical Quantifiers

3 Proof Techniques

3.1 An Introduction to Proof Techniques

3.2 Direct Proofs

3.3 Indirect Proofs

3.4 Mathematical Induction: An Introduction

3.5 More on Mathematical Induction

3.6 Mathematical Induction: The Strong Form

4 Sets

4.1 An Introduction

4.2 Subsets and Power Sets

4.3 Unions and Intersections

4.4 Cartesian Products

4.5 Index Sets

5 Basic Number Theory

5.1 The Principle of Well-Ordering

## About the Book

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

Open SUNY Textbooks is an open access textbook publishing initiative established by State University of New York libraries and supported by SUNY Innovative Instruction Technology Grants. This initiative publishes high-quality, cost-effective course resources by engaging faculty as authors and peer-reviewers, and libraries as publishing service and infrastructure. The pilot launched in 2012, providing an editorial framework and service to authors, students and faculty, and establishing a community of practice among libraries. Participating libraries in the 2012- 2013 pilot include SUNY Geneseo, College at Brockport, College of Environmental Science and Forestry, SUNY Fredonia, Upstate Medical University, and University at Buffalo, with support from other SUNY libraries and SUNY Press. More information can be found at http://textbooks.opensuny.org.

## About the Contributors

### Author(s)

**Harris Kwong** is a mathematics professor at SUNY Fredonia. He was born and raised in Hong Kong. After finishing high school there, he came to the United States to further his education. He received his B.S. and M.S. degrees from the University of Michigan, and Ph.D. from the University of Pennsylvania. His research focuses on combinatorics, number theory, and graph theory. His work appears in many international mathematics journals. Besides research articles, he also contributes frequently to the problems and solutions sections of Mathematics Monthly, Mathematics Magazine, College Journal of Mathematics, and Fibonacci Quarterly. He gives thanks and praises to God for his success.