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A Walk through Combinatorics: An Introduction to Enumeration and Graph Theory (Third Edition), by Miklos Bona
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This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
- Sales Rank: #888137 in Books
- Published on: 2011-05-09
- Released on: 2011-05-09
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x 1.28" w x 6.00" l, 1.80 pounds
- Binding: Paperback
- 568 pages
Review
"It is extremely lively yet mathematically accurate, and the writing is lucid and very entertaining at the same time." -- Doron Zeilberger Rutgers University
"...A very inviting style of exposition, in which developments are always well motivated and illustrated by numerous examples." -- Zentralblatt MATH
"A very attractive textbook on Combinatorics." --Monatshefte fur Mathematik
"Bona's book is an excellent choice for anyone who wants an introduction to this beautiful branch of mathematics ... Plentiful examples illustrate each of the topics included in the book. Bona does a supreme job of walking us through combinatorics." --Choice
From the Inside Flap
This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.
Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.
The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity.
As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
About the Author
Miklos Bona received his PhD at Massachusetts Institute of Technology. He is a Professor of Mathematics at the University of Florida, where he has been inducted into the Academy of Distinguished Teaching Scholars. His research has been supported by the National Science Foundation, the National Security Agency, and the Howard Hughes Medical Institute. Miklos Bona has received teaching awards at the University of Florida and at the University of Pennsylvania. He is one of the Editor-in-Chiefs of the Electronic Journal of Combinatorics.
Most helpful customer reviews
3 of 3 people found the following review helpful.
Average
By Slydexic
I am a math major who is using this book for my combinatorics class. This book covers a lot of topics and I enjoy the author's use of math in the real world for his examples and exercises. However, the only thing I dislike about the book are his proofs. I don't enjoy reading his proofs because most of them seem too informal. He mixes in real life examples for his proofs of theorems. For example, Theorem 4.6 in the book. Overall, I don't like the dialogue he uses in his proofs. It doesn't feel like he's instructing me. It feels too casual, too informal, as if we're having a cup of coffee over the theorems and I continue to agree with everything he says and nod to him every minute. I understand as a math major I need to fill in the gaps he leaves behind because a proof DOES NOT have to provide reasoning. A proof only has to provide justification for each step.
2 of 2 people found the following review helpful.
Great book for undergrad level of combinatoric
By Ha Luu
I love this book. It's very interesting through out the book. Each section goes from very basic stuff to advance stuff which makes it's easy for you to follow.
Each chapter of the book, there are about 20+ problems with detail solutions in the book (Yes, I am not kidding-SOLUTION). It's perfect for people who want to practice and check their work or finding some hint when you are stuck.
It's a great way to learn how to solve combinatoric problems.
Moreover, it also have the supplementary problems ( this one with no solution), for people who want to challenge themselves more.
It's a great book for those who are new to combinatoric and want to find their way in. And it has so many difficult levels that you won't be bored. Recommended!!!
1 of 1 people found the following review helpful.
A great book for self-study
By Amazon Customer
A great book for self-study. It is a bit more time consuming though and around senior junior undergraduate level. Nice examples given throughout the text. Combinatorics is an important field in theoretical CS and discrete math.
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