Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (3Rd Edition)

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.

Great textbook

My gut feeling about your book A walk through Combinatorics -- All I can say is, I just want to extend my deepest gratitude and admiration for this great book. Your book is a true gem—an extraordinary blend of clarity, depth, and mathematical elegance. It is rare to encounter a text that not only presents combinatorial concepts with such rigor but also makes them come alive with engaging problems, insightful explanations, and an intuitive flow that guides readers through the subject with ease and precision. Beyond its technical excellence, what sets your book apart is its pedagogical brilliance. The way you illuminate intricate combinatorial structures, providing both fundamental intuition and advanced insights, fosters not just understanding but an enduring appreciation for the beauty of discrete mathematics. Your careful attention to detail, your knack for anticipating readers’ thought processes, and your ability to untangle complex ideas with elegance make this book an indispensable resource for anyone serious about combinatorics. Simply put, A Walk Through Combinatorics is not just a textbook—it’s a masterclass in mathematical thinking. For this, and for your meticulous correctness in addressing the nuances of combinatorial reasoning, I sincerely thank you. With the highest respect and admiration, Adam

it is very good.fast and excellent

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.

He does a short explanation in each chapter and few examples after that. Then at end of the chapter the author bomb you with problems, that if you don't have anyone to ask then will be nearly impossible to solve. So guess what, you pay $60 just to google the material anyway.

Just for disclosure, I'm a senior undergraduate in mathematics. This will suggest something about my background, which is always an important factor in how a work is received. It seems to be a general trend that participants in Olympiads write texts with a lot of problems -- as opposed to none or just exercises. This is the kind of text Bona has written. There are hundreds of problems and they range in technique and difficulty. Personally, I think these are the best kinds of textbooks because they ask you to spend a lot of time on a few problems and this really helps you get in there and see what's happening at a deeper level. But one thing unique about Bona's text that is especially nice is the inclusion of detailed solutions to all of the problems not given in the supplementary sections. Writing a clear and instructive textbook is a great skill. But writing solutions to difficult problems is probably a more difficult skill to develop, yet Bona has it. All of the material here is very helpful for developing a strong base for future work in combinatorics. Another additional topic that I'm very happy he included is the section on complexity. Historically, combinatorics and complexity have been closely related, which is something that has only increased in recent decades. But Bona's text is the only one I've seen that is introductory and includes a discussion of computational complexity. This is a wonderful feature to an already outstanding textbook. I've given the text four stars because I've read just three or four chapters. They've all been great, but this is less than half of the textbook.

I bought this paper book(3rd) because MIT OCW recommends it, but after read several chapters, I find it is not as good as amazon comments. at least for the beginner. I really recommend Richar Brunaldi's Introductory Combinatorics.