Generatingfunctionology

by Herbert S. Wilf

Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

Genres: Mathematics, Textbooks, Academic, Nonfiction, Science, Reference

184 pages, Kindle Edition

First published January 1, 1990

Reviews

[Alan Bu · Rating 5 out of 5]

Read it earlier, was very interesting. Personally, generating functions are one of my favorite parts of mathematics as it is an almost perfect method (a bit bashy) of algebrizing some combinatorics questions, and is a very powerful trick. I'm not sure there's really a theme, since it's nonfiction, and there isn't really any bias since it's mathematics, so... Anyways, I really enjoyed it, so five stars out of five for not making the subject too confusing.

[Allison · Rating 5 out of 5]

Generatingfunctionology is a masterpiece. If you read this book, I promise you will not only understand generating functions, but you will develop a profound appreciation for them.
Very well explained, very passionate book. Would recommend, especially for people who haven't seen generating functions before.

[Riley Holmes · Rating 5 out of 5]

This book gives a great tour / exhibition of some really cool techniques. Every other page I was saying "wow.... you can do that?!". Highly recommended if you've seen the basics of combinatorics and formal power series.

[Dmitry Zinenko · Rating 5 out of 5]

A good introduction to the theory of generating functions and their uses. In fact, the only readable introduction I could find. Shows many neat tricks that become available for a "generatingfunctionologist" in the fields of combinatorics and probability.

[Bethany Epstein · Rating 5 out of 5]

one of my favorite mathematical texts, and one i return to regularly. the utility of generating functions is incredibly widespread, and having these tools ready in your toolkit will allow you to cut through otherwise difficult calculations like butter.

[Robert Katz · Rating 5 out of 5]

Brilliant

[anneinus · Rating 5 out of 5]

Has some funny remarks, yayy (which isn't often the case for a hard-core math book)!
Cool stuff =)

[Andriansyah , · Rating 5 out of 5]

Full of elegant techniques, the practicality of this book is off the charts

[George · Rating 4 out of 5]

For me, this is a rather quirky book that taught me more than I will probably ever need to know about generating functions. It is not an easy read, because it is a rather tough subject, but you are learning from a grandmaster of generating functionology. The style is engaging and the author's enthusiasm for the subject really shines through. In particular, he really wants to give you a practical mastery of generating functions, so that you can go out into the world and solve problems with them.

If you are interested in the topic, have a browse though this book to see if you like the style. I suspect you'll either love it or hate it.

[Ivan · Rating 5 out of 5]

Very good introduction to combinatorial applications of generating functions. Explanations are very concise, each chapter contains a set of exercises.

[Lulu]

Combinatorics