The book is correct and up to date with the latest research.
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The authors are well respected and important researchers in the area of discrete mathematics. In addition, there are several other interesting topics covered involving topics closer to the authors such as posets, generating functions, probability, probability and some its applications to combinatorics, graph algorithms, networks flows and applications, P\'lya's enumeration theorem. Other than congruences (which appear as Exercise 2 in Section 6.10 on page 134), everything that I would teach in an introductory discrete mathematics course is covered: sets, counting, inclusion-exclusion, permutations, binomial coefficients, integers, divisibility, greatest common divisor, recurrence relations, graphs. The book contains almost all the topics I would usually cover in the first discrete mathematics course. The authors confess that in designing the Georgia Tech course, they needed a textbook that would go a bit deeper into combinatorics than the available textbooks. As mentioned in the preface of the book, the authors want to show the students the beauty of combinatorics and how combinatorial problems arise naturally in computer science and other fields. In a typical semester, 250 Georgia Tech students would be enrolled in this course. This course is also required for the student s getting a B.S. The purpose of this course is to expose students to combinatorics using applications to emphasize the key concepts and methods. This is a book used at Georgia Tech for a junior level course targeted primarily at students pursuing a B.S. Reviewed by Sebastian Cioaba, Associate Professor, University of Delaware on 2/1/18 I've already made several students aware of the resource. It would be perfect as an introduction to combinatorics for students using these techniques for the first time. The text is not culturally insensitive or offensive in any way.Īs an applied mathematical scientist with undergraduate students entering my lab from a variety of backgrounds, I greatly appreciate the level and scope of this text. The writing was clear and grammatically correct. There is a clear gradual increase in complexity and depth with each passing chapter. The chapter arrangement (number and content) was well-chosen. The notation was appropriately consistent throughout. The text is engaging and not patronizing. The writing of this textbook was approachable, appropriate to undergraduate readers and students approaching combinatorics without much mathematics background. The mathematics of combinatorics will not need to be updated often, but I look forward to future revisions.
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I read Ch 16 on Pólya’s Enumeration Theorem carefully and found no significant errors. There are a few places where figures and other material are "to be added later."
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Overall, the scope and topics of the book were excellent. Reviewed by Greg Conradi Smith, Professor, William & Mary on 11/20/18 Journalism, Media Studies & Communications.