# Applied Discrete Structures

Alan Doerr, University of Massachusetts Lowell

Kenneth Levasseur, University of Massachusetts Lowell

Copyright Year: 2017

Last Update: 2021

ISBN 13: 9781105559297

Publisher: Alan Doerr & Kenneth Levasseur

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

The text covers all areas in our Discrete Mathematics course appropriately and provides a useful index. read more

The text covers all areas in our Discrete Mathematics course appropriately and provides a useful index.

This book is well written and rigorous while at the same time does a good job of motivating the material.

Content is up-to-date and revised often.

Well written and all notations are introduced before using them.

The text is consistent and follows the logical outline of most Discrete Math courses.

The text is well organized. The clickable expandable examples and exercises provide options for different reading levels.

The flow is logical, except maybe with the exception of the chapter on Matrix Algebra that could be moved to the appendices at the end.

The text is free of significant interface issues, including navigation problems. There are some distortion of some images in the Graphs chapter. The book may benefit from a more standardized way to unify the representations of graphs, Hasse diagrams, lattices, etc.

I did not find grammatical errors.

I did not find the text culturally insensitive or offensive in any way.

The inclusion of SageMath notes in this textbook when Sage was first released was the reason for which I chose this book originally many years ago. It is an excellent example of successful integration of open source software in an open source textbook. With the different editions, these SageMath Notes have been expanded and they populate now most of the chapters of this book. It is great addition that rounds and expands its content.

The material adequately covers the subject and there is a reliable glossary and index. As a text for an entry level survey class, it includes more than would generally be expected of a beginning college freshman. read more

The material adequately covers the subject and there is a reliable glossary and index.

As a text for an entry level survey class, it includes more than would generally be expected of a beginning college freshman.

There are no major contextual errors in the text. There are places where concepts are assumed to be in possession of the students without benefit of coverage

No discussion of parallel or perpendicular lines in linear equations; the notation 3/2x is confusing for slope, (3/2)x would be better

Terminology of matrices (rows and columns) is assumed

Assumes familiarity with graphing linear inequalities with no development and doesn’t address “test points”

Does not address any finance operations involving unknown times or number of periods of awarding interest

Uses three separate, unrelated notations for complements of sets

Error on page 221 – P(E | F is missing a closing parenthesis

Error on page 225 – centering for P(E | F) = P(E) for consistency

Error on page 279 – P(Walked Wednesday | Bicycled Monday) is not 3/5/16 and Bicycled misspelled in the next line (Bicycleed)

The material is up-top-date with only minor references to “dated” entities in applications (Ma Bell and Pa Bell in Markov Chains); the necessary changes would be quickly and easily made

As far as a mathematics text goes, it is remarkably readable; there is minimal use of “technical jargon” beyond what is necessary to the material

Language and content are consistent with other traditional texts; the framework and presentation, except where noted above flow well and topics are tied together as necessary

There is little need to artificially subdivide given that the material is already fairly well sectioned out with topics appropriately arranged and flow from topic to topic is logical and developmentally arranged

As discussed in previous sections, the material builds logically with necessary material covered adequately in most places to build new concepts.

There is no real “artwork” in the presentation, no pictures or photographs. Generally the tables and diagrams are well laid out (the exception being many pixilated tree diagrams and Venn diagrams in the material on Sets and Counting and Probability)

One noted spelling error, as noted above (page 279);

I find nothing in this presentation that would be offensive to anyone on the basis of race, creed, color, gender, religious or sexual preference

I chose to look at this text because I regularly teach a Finite Mathematics class to entry level freshmen. For my institution this is a survey course. Some of the latter topics are well beyond the scope that would be covered, but I find them very interesting, nonetheless.

Personally, I would like to see some “artwork” added to the presentation, but it works fine without it. I like there being both exercises and solutions for the exercises. The presentation of solutions on a separate line, sometimes centered, sometimes not, doesn’t bother me but if I was paying for printing this book, I’d like to see a different layout that would reduce the number of pages,

I am pleased with the coverage of material that is needed for our COSC 312 (Discrete Structures) course. Index and glossary are fine. The chapters on Matrix Algebra are not really needed for our one semester course. That material is covered in a... read more

I am pleased with the coverage of material that is needed for our COSC 312 (Discrete Structures) course. Index and glossary are fine. The chapters on Matrix Algebra are not really needed for our one semester course. That material is covered in a linear algebra course offered by the Math Department.

Content appears accurate but I did not evaluate all expressions in great detail.

I am not convinced having the Sage programming examples is all that helpful. Our Computer Science students are taking this course the first semester of their junior year and they are already well versed in C++ and C. I think it might be more useful to have a version of the book that does not have explicit programming examples. You could generate different versions based on what open source programming languages/environments the instructor has available.

I had no concerns with the clarity of the text I read.

The text is internally consistent in terms of terminology and framework.

There are alignment issues with some of the equations extending way outside of the text margins. Looks like LaTeX might have been used to create the pdf file for the book. Perhaps the margins could be widened a bit so that more text would appear per line within the PDF viewer.

Yes, although I think the Matrix Algebra chapters could be more supplemental or even in an Appendix.

Figures seem fine - just the margin issues I alluded to before.

The text contains no grammatical errors from my reading.

No problem whatsoever with cultural insensitivity.

I appreciate the creation of this book for material that is still very needed for computer science curricula.

## Table of Contents

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

## Ancillary Material

## 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 atCasper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).

## About the Contributors

### Authors

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

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