Applied Combinatorics

Reviewed by Greg Conradi Smith , Professor , William & Mary on 11/20/18

Comprehensiveness rating: 4 see less

Overall, the scope and topics of the book were excellent. There are a few places where figures and other material are "to be added later."

Content Accuracy rating: 5

I read Ch 16 on Pólya’s Enumeration Theorem carefully and found no significant errors.

Relevance/Longevity rating: 5

The mathematics of combinatorics will not need to be updated often, but I look forward to future revisions.

Clarity rating: 5

The writing of this textbook was approachable, appropriate to undergraduate readers and students approaching combinatorics without much mathematics background. The text is engaging and not patronizing.

Consistency rating: 5

The notation was appropriately consistent throughout.

Modularity rating: 5

The chapter arrangement (number and content) was well-chosen.

Organization/Structure/Flow rating: 5

The overall organization was excellent. There is a clear gradual increase in complexity and depth with each passing chapter.

Interface rating: 5

The figures were very nice.

Grammatical Errors rating: 5

The writing was clear and grammatically correct.

Cultural Relevance rating: 5

The text is not culturally insensitive or offensive in any way.

Comments

As 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. It would be perfect as an introduction to combinatorics for students using these techniques for the first time. I've already made several students aware of the resource.

Reviewed by Sebastian Cioaba, Associate Professor, University of Delaware on 2/1/18

Comprehensiveness rating: 5 see less

This is a book used at Georgia Tech for a junior level course targeted primarily at students pursuing a B.S. in Computer Science. The purpose of this course is to expose students to combinatorics using applications to emphasize the key concepts and methods. This course is also required for the student s getting a B.S. in Mathematics at Georgia Tech. In a typical semester, 250 Georgia Tech students would be enrolled in this course. 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. 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.

The book contains almost all the topics I would usually cover in the first discrete mathematics course. 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. 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\'{o}lya's enumeration theorem.

Content Accuracy rating: 5

The authors are well respected and important researchers in the area of discrete mathematics. The book is correct and up to date with the latest research.

Relevance/Longevity rating: 5

I really like the book and I think it should and will be used by many schools for introductory undergraduate discrete mathematics.

Clarity rating: 5

The book is very well written. The authors use a friendly and informal tone throughout the book and employ an interesting cast of characters: Alice, Bob, Carlos, Dave, Xing, Yolanda and Zori, who are all undergraduate students at Georgia Tech taking the 8.05am section of Math3012 Applied Combinatorics. The mathematics presented in the book is mixed with dialogues between these characters discussing the current topics of the course and their relevance in their lives, interests and future plans. I really liked this idea of incorporating student-like characters in the textbook and I would think this would go well with students studying the book on their own who will find their own questions and comments among the ones brought up by Alice, Bob, Carlos, Dave, Xing, Yolanda and Zori.

Consistency rating: 5

The tone used by the authors of the book is clear and consistent. The writing and the pictures are neat and tidy. I like the fact that the authors use SageMath throughout the book.

Modularity rating: 5

The modularity is very good. I think that individual chapters can be used separately if necessary.

Organization/Structure/Flow rating: 5

The structure is different from what I am used to seeing in a introduction to discrete mathematics, but I really like it. As mentioned in the preface, the authors confess that they wrote their book to use it in an introductory undergraduate course to discrete mathematics aimed mostly at computer science and mathematics majors. I think they did a great job

Interface rating: 5

Everything is very neat and it seems like the authors have spent a lot of time polishing this material.

Grammatical Errors rating: 5

The grammar and language are fine.

Cultural Relevance rating: 5

The text is not offensive in any way.

Comments

I really liked the book and I hope to use it at my university soon. It is much better than many expensive books used in introductory undergraduate courses and I hope it will be adopted by more departments and instructors.