Discrete Mathematics with Applications [Hardcover]

Susanna S. Epp (Author)

Book Description

ISBN-10: 0534359450 | ISBN-13: 978-0534359454 | Publication Date: December 22, 2003 | Edition: 003

Susanna Epp's DISCRETE MATHEMATICS, THIRD EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

Editorial Reviews

About the Author

Susanna S. Epp received her Ph.D. in 1968 from the University of Chicago, taught briefly at Boston University and the University of Illinois at Chicago, and is currently Vincent DePaul Professor of Mathematical Sciences at DePaul University. After initial research in commutative algebra, she became interested in cognitive issues associated with teaching analytical thinking and proof and has published a number of articles and given many talks related to this topic. She has also spoken widely on discrete mathematics and has organized sessions at national meetings on discrete mathematics instruction. In addition to DISCRETE MATHEMATICS WITH APPLICATION, she is co-author of PRECALCULUS AND DISCRETE MATHEMATICS, which was developed as part of the University of Chicago School Mathematics Project. Epp co-organized an international symposium on teaching logical reasoning, sponsored by the Institute for Discrete Mathematics and Theoretical Computer Science (DIMACS), and she was an associate editor of MATHEMATICS MAGAZINE from 1991 to 2001. Long active in the Mathematical Association of America (MAA), she is a co-author of the new set of curricular guidelines for undergraduate mathematics programs: CUPM CURRICULUM GUIDE 2004.

Product Details

• Hardcover: 928 pages
• Publisher: Brooks Cole; 003 edition (December 22, 2003)
• Language: English
• ISBN-10: 0534359450
• ISBN-13: 978-0534359454
• Product Dimensions: 10.4 x 8 x 1.3 inches
• Shipping Weight: 3.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (35 customer reviews)
• Amazon Best Sellers Rank: #6,222 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

53 of 54 people found the following review helpful:

5.0 out of 5 stars Great text on discrete mathematics especially for non-math majors, August 9, 2006

By 

calvinnme - See all my reviews
(HALL OF FAME REVIEWER)    (VINE VOICE)    (TOP 50 REVIEWER)   

This review is from: Discrete Mathematics with Applications (Hardcover)

I used an earlier edition of this textbook in a discrete mathematics class that was required for those of us with a non-CS background enrolled in a MSCS program at Virginia Tech, and I found this to be an excellent and complete book on the subject. If you find yourself enrolled in a class using this book, you can be sure of two things - your instructor knows how to select good textbooks and also it won't matter if your instructor is a good teacher since this book does all of the work for him/her.

If you are enrolled in a class on discrete math and this textbook is not assigned, might I suggest you get a used copy of the previous edition. It is just as good as this current edition and used copies can easily be found dirt cheap. If you buy a copy of a previous edition the topics you'd be missing that are new to this edition would be expected value, conditional probability, Bayes' theorem, modular arithmetic, Fermat's little theorem and the Chinese remainder theorem, and RSA cryptography.

The author has included illuminating examples of all concepts throughout the textbook, defined all terms, and makes sure that each new concept introduced builds on previously explained material. Subjects covered include the logic of computation, including the predicate logic that is necessary for fully understanding artificial intelligence, methods of proof including the method of induction and also the terminology of sequences, number theory and combinatorics, O-notation and the calculation of the efficiency of algorithms, graph theory and discrete structures, and an introduction to concepts from the theory of computation. There are many exercises included, with the solutions to selected exercises in the back of the book.

This book only assumes mathematical maturity at the level of precalculus, excluding trigonometry. I highly recommend this text especially to students who are transitioning to computer science from some other discipline and need a firm foundation in the basics of that field. You'll find it useful as a foundational text for studying artificial intelligence, the theory of algorithms, mathematical models of computation, and the theory of computation. Another useful book on this subject is the "Schaum's Outline of Discrete Mathematics".

The table of contents are as follows:
1. The Logic of Compound Statements
2. The Logic of Quantified Statements
3. Elementary Number Theory and Methods of Proof
4. Sequences and Mathematical Induction
5. Set Theory
6. Counting
7. Functions
8. Recursion
9. O-Notation and the Efficiency of Algorithms
10. Relations
11. Graphs and Trees
12. Finite State Automata and Applications

22 of 22 people found the following review helpful:

5.0 out of 5 stars Comparison of the top 3 Discrete Math Texts, May 24, 2009

By 

Michael Yasumoto - See all my reviews
(REAL NAME)   

This review is from: Discrete Mathematics with Applications (Hardcover)

I have read "Discrete Mathematics" by Epp, Rosen and Ross which are the three most common discrete math texts that I encounter at university.

Of these three, I would rate Epp's book as my favorite because it has the clearest explanations and is so easy to read that you can't help but feel like you understand all of the content completely. The only failing that Epp's book might have is that it is not as thorough in its coverage of the material as some of the more technical books. I would say that it covers about 90% of the material and leaves out some of the more obscure topics.

Rosen's book would be the most thorough, covering every topic in meticulous detail and offering a jumping point for other texts in cryptography and number theory. Although this book is more complete than Epp's, it is also less readable and requires more effort to get through. Ideally you would use Epp's book to learn the material and then go to Rosen's book for a technical reference.

For those of you who are considering Ross's book, I have one thing to say and that is don't. Although I have read this book and done a lot of the problems in the first 3/4 of the text, this book is neither clear in its explanations like Epp nor is it as complete as Rosen's book. If you are assigned this book for a course, my suggestion would be to buy Epp's book and photocopy the Ross homework problems from a friend's textbook.

Take the advice of someone who has read all three books. If you have to buy just one, then get the Epp book. It is better to understand 90% of the material completely rather than 100% of the material partially.

31 of 33 people found the following review helpful:

5.0 out of 5 stars Almost perfect....., October 22, 2004

By 

Black-Dove (3rd from the sun) - See all my reviews

This review is from: Discrete Mathematics with Applications (Hardcover)

For anyone having a bit of a problem getting used to formal proofs and number theory, this book is the best I've seen for the beginner, hands down. If you've gotten into one of the top math programs in the country, you will do OK without this book; but as for the rest of us, this book may prevent a lot of grief. It moves slowly and clearly through basic methods of proof and number theory, and it builds confidence quickly. Dr. Epp has written a great book, and the only drawback (which isn't her fault) is the price. If you are pretty good at math through Calculus but got thrown for a loop trying to understand proofs and more formal mathematics, this is probably the book for you (as it was for me).