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Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games

October 2005, ©2006
Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games (EHEP000485) cover image
These active and well-known authors have come together to create a fresh, innovative, and timely approach to Discrete Math.  One innovation uses several major threads to help weave core topics into a cohesive whole.  Throughout the book the application of mathematical reasoning is emphasized to solve problems while the authors guide the student in thinking about, reading, and writing proofs in a wide variety of contexts.  Another important content thread, as the sub-title implies, is the focus on mathematical puzzles, games and magic tricks to engage students.
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1. Puzzles, Patterns, and Mathematical Language.

2. A Primer of Mathematical Writing.

3. Sets and Boolean Algebra.

4. Functions and Relations.

5. Combinatorics.

6. Probability.

7. Graphs and Trees.

Appendix A: Rules of the Game.

Appendix B: Matrices and Their Operations.

Selected Answers and Hints.

References and Further Reading.

Index.

 

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Doug Ensley is a full professor at Shippenshburg University with a Ph.D. from Carnegie Mellon.  He is an active participant in national and regional committees determining the future of the discrete math curriculum, and he regularly speaks at Joint Math and MathFest.

Winston Crawley is a full professor and chair of the math department at Shippensburg University.  He has a Ph.D. from University of Tennessee-Knoxville.  Crawley developed the undergraduate computer science curriculum at Shippensburg.

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-Text is replete with “real world excursions” reinforcing the utility of discrete mathematics. 
-Online applications help improve students’ mathematical reasoning with intriguing, interactive flash-based applications which illustrate key mathematical concepts and help develop students’ ability to reason mathematically, solve problems and work with proofs.  Explore More Icons in the text direct the student to online activities at www.wiley.com/college/ensley.
- Every section contains a number of practice problems and at the conclusion of each chapter a section review outlines the major terms, concepts and skills covered in that chapter.
-Over 1,000 exercises ranging from routine reinforcement to conceptual challenges. 
-Appendices on basic matrix operations as well as an appendix explaining the basic rules and terminology for many of the games used for examples in the book. 
-Answers and hints are given in the back of the book and more detailed solutions to those exercises are found in a supplementary student solutions manual. 
 
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"I like the book's approach to Discrete Math - consider it a set of puzzles we have to solve. This makes a supposedly "dry" subject quite interesting."

 -Saurabh Bagchi, Purdue University

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Instructors Resources
Wiley Instructor Companion Site
http://www.wiley.com/college/ensley
contains details and helpful advice on how to use this book.
Instructor's Solutions Manual to accompany Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games
Provides complete solutions to all the exercises in the book.
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Students Resources
Wiley Student Companion Site
Student Website
containing web based activities with online versions of the problems in the book and interactive activities, which aid in developing ideas. (Web based material relating to mathematical proof was funded through a grant from the National Science Foundation.)
Available Materials
by Douglas E. Ensley, J. Winston Crawley
978-0-471-76097-9
January 2009, ©2006, Paperback
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Purchase Options
Hardcover   
Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games
ISBN : 978-0-471-47602-3
704 pages
October 2005, ©2006
$204.95   BUY

Hardcover   
Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games, Textbook and Student Solutions Manual
ISBN : 978-0-470-08642-1
May 2006, ©2006
$257.95   BUY

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