# Applied Discrete Structures

Alan Doerr, University of Massachusetts Lowell

Kenneth Levasseur, University of Massachusetts Lowell

Pub Date: 2017

ISBN 13: 978-1-1055592-9-7

Publisher: Independent

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

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## Table of Contents

- Chapter 1: Set Theory
- Chapter 2: Combinatorics
- Chapter 3: Logic
- Chapter 4: More on Sets
- Chapter 5: Introduction to Matrix Algebra
- Chapter 6: Relations and Graphs
- Chapter 7: Functions
- Chapter 8: Recursion and Recurrence Relations
- Chapter 9: Graph Theory
- Chapter 10: Trees
- Chapter 11: Algebraic Systems
- Chapter 12: More Matrix Algebra
- Chapter 13: Boolean Algebra
- Chapter 14: Monoids and Automata
- Chapter 15: Group Theory and Applications
- Chapter 16: An Introduction to Rings and Fields

## About the Book

In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach andmove them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked.

The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics.

To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs.

Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete.

The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.

An Instructor's Guide is available to any instructor who uses the text. It includes:

- Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid;
- Suggested coverage times;
- Detailed solutions to most even-numbered exercises;
- Sample quizzes, exams, and final exams.

This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).

## About the Contributors

### Author(s)

**Alan Doerr**, Professor of Mathematical Science at University of Massachusetts, Lowell.

**Kenneth Levasseur**, Professor and Chair, Department of Mathematical Sciences, University of Massachusetts Lowell.