generatingfunctionology: Third Edition 3rd Edition by Herbert S. Wilf (PDF)

Description

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in – Combinatorics – Probability Theory – Statistics – Theory of Markov Chains – Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is not an entry level book. The notation could be clearer. It assumes you know alot about series and some calculus. But the topic and methods are useful analytic tools I’ve seen nowhere else.

⭐Wonderful, friendly introduction to generating functions. Wilf has a great writing style. In particular, his presentation of the exponential formula in terms of cards, hands, and decks made it much more digestible than in the abstract. My only criticism is that his treatment of series occasionally lacks rigor, especially concerning the algebraic aspects of formal power series (namely convergence in the ring of formal power series).

⭐This is simply the best mathematics book I have ever read.

⭐This book is freely available online, but it is so good that it is worth buying a hard-copy of, and it’s reasonably priced too. I would advise potential buyers to check it out online; you’ll probably find that you like it, and you’ll probably buy it after you get tired of staring at your screen or making printouts.Wilf is an outstanding writer, among the best writers in mathematics; this book is a true pleasure to read. His explanations are lucid and he has a great sense of humor. This book is not particularly advanced, although it is one of those texts that you can keep coming back to; it takes quite some time to exhaust the material in it and I have certainly not come close to doing so. It covers generating functions in the form of ordinary power series, exponential power series, and Dirichlet series, and it touches on a few other types of generating functions as well. There is a chapter on the exponential formula and a chapter which explores a more systematic approach to counting. The last chapter is on analytic methods to study asymptotic approximations to counting functions. The book is well organized; topics flow naturally, and yet it is easy to skip topics and move around freely. The exercises are immensely useful. They start simple, but there are many of them and they become progressively more difficult in a natural way.This book would be suitable for an undergraduate course in combinatorics, and it also makes a good supplementary text for anyone studying combinatorics or possibly complex analysis at the graduate level. I find this book is excellent for self-study at any level as well. Check it out for yourself!

⭐A good introduction to the theory of generating functions and their uses. In fact, the only readable introduction I could find. It is NOT one of those many generation functions books written by mathematicians for mathematicians.Shows lots and lots of neat tricks that become available for a “generatingfunctionologist” in the fields of combinatorics and probability.All the material is presented in a very clean, organized way, with good examples. I use it as a hands-on reference book.

⭐This book may actually become less useful the more experience the reader has with mathematics. Certainly, if you want to build your skills with manipulating generating functions, this book is good. So in that sense, it’s a book for beginners. Those with more mathematical training would benefit from more connections to other areas of mathematics, e.g. formal power series over the rationals as an integral domain. The “cards and decks” theory is much more completely developed elsewhere (with different terminology), and some students may find the discussion of it in generatingfunctionology difficult to grasp. For more information on generating function asymptotics, see Flajolet and Sedgewick. Chapter 4 and the exercises are perhaps the most valuable parts of the book.

⭐I did download this book for free from Dr. Wilf’s homepage, but I’ve dog-eared my printouts so many times I thought I would buy a hard-bound copy. If you enjoy mathematical puzzles and games, if modern algebra seems too abstract (and possibly pointless) or if you have always wanted to study combinatorics, then I am sure you will love this book. It is advances, Dr. Wilf is a master, but it is written in a friendly, motivated manner that sucks you in and pushes you along.

⭐This is a delightful book about generating functions; normal – exponential, …The author clearly explains what generating functions are and what they can be used for. He is clearly a master of the field. He often applies the wizardry to counting (and other) problems. When you read his solutions they are so very clear that you wonder why you can’t do it yourself like this.Not only is the coverage very deep, the book is also beautiful, very handy to put near you and read where you are.

⭐An absolutely fascinating book delivered before the expected arrival. Thanks!

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