Discrete Mathematics with Applications

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The author states in the preface that “the feature that most distinguishes this book from other discrete mathematics texts is that it teaches—explicitly but in a way that can be understood by typical freshman and sophomore college students—the unspoken logic and reasoning that underlie mathematical thought.” She pays considerable attention to logic and proof, blending well-selected examples and exercises with appropriate levels of abstraction, all designed to teach students to understand mathematical arguments and create their own proofs.

There are no problems here at all. The book uses terms and concepts consistently throughout the book/No problems at all. I find the author's mechanics very good and his style is a joyful and as stated above enthusiastic. The framework seems totally consistent. I don't see any problems. From what I know of the subjects involved, the terminology seems appropriate and consistent Predicates and Quantified Statements I. Predicates and Quantified Statements II. Statements with Multiple Quantifiers. Arguments with Quantified Statements. The material in the book was well-edited and proof-read. I didn’t encounter obvious mistakes or omissions in my first reading of the text, and only a few typos (e.g. “bijectitve”).

The chapters are very well organized. However, I would prefer the number theory chapter to appear earlier in the book so that the number theory concepts and examples can be used throughout the book. When I introduced equivalence relations to my students, I had to explain the congruence relations (to provide a good example) before we covered the number theory chapter. The text is well organized and structured, allowing the material to flow and be built up in an accessible manner. The use of the introductory Investigate! sections through-out the text is an excellent tool to motivate students to think about topics before getting into the details.The text has a comprehensive index, and has both a PDF version and a well-designed interactive online format, with a contents tab and expandable solutions (allowing students to attempt a question before unveiling the solution). The text has several features that I found quite innovative and helpful. The presentation takes an inquiry-based approach, and most topics start with an “Investigate!” section that poses a number of questions or problems to help motivate students to understand the context for the topic they’re about to start – for example, the Combinatorial Proofs topic is preceded by an Investigate! Section that uses the Stanley cup tournament rules to make students think about how many ways a team can win, and how to generalize the problem space. The text also approaches mathematical proofs in a friendly, non-intimidating manner and provides different approaches to proving a given identity or theorem, helping students to broaden their mathematical toolkit.

Oscar Levin is an Associate Professor at the University of Northern Colorado in the School of Mathematical Sciences. He has taught mathematics at the college level for over 10 years and has received multiple teaching awards. He received his Ph.D. in mathematics from the University of Connecticut in 2009. The text is generally less difficult than some competing textbooks; as mentioned previously, however, the book is written to be used even by first-year, first-semester students. The fundamentals in many interesting areas are so well developed that they lead to significant depth within the text itself and allow the instructor to easily extend the coverage in many directions if desired. Extensive use is made of material at progressively deeper levels through a spiral approach. Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH 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.This is the part I very much like in the book. One can easily move from one part of the book to another. The figures drawn to illustrate graphs etc., are appropriate. This subject is essentially timeless because the principles are mathematical and will always be true and valid. There is one problem involving Continental Airlines that no longer exists, but that is a minor quibble. This does not make the text obsolete.