Integer Partitions [Paperback]

George E. Andrews (Author), Kimmo Eriksson (Author)

Book Description

Publication Date: October 11, 2004 | ISBN-10: 0521600901 | ISBN-13: 978-0521600903 | Edition: 2nd

The theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.

Editorial Reviews

Review

"...until now there has not been a good introduction to the subject at an elementary level. Integer Partitions...is written at a level that most undergraduates, and even many high school students, could follow quite easily."
-MAA Reviews, Darren Glass, Columbia University

"This book is written in a very easy and friendly style. The authors start from scratch and lead the readers from the easy to the unsolved problems. It is really a pleasure to read."
-Mathematical Reviews

Book Description

The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics.The aim in this introductory textbook is to provide an accessible and wide ranging introduction to partitions, without requiring anything more of the reader than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.

See all Editorial Reviews

Product Details

• Paperback: 152 pages
• Publisher: Cambridge University Press; 2nd edition (October 11, 2004)
• Language: English
• ISBN-10: 0521600901
• ISBN-13: 978-0521600903
• Product Dimensions: 8.9 x 6 x 0.5 inches
• Shipping Weight: 7.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,224,045 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

5.0 out of 5 stars A Beautiful Presentation of Mathematical Reasoning, June 22, 2009

By 

Charles Neuhauser (Sunnyvale, CA USA) - See all my reviews
(REAL NAME)   

This review is from: Integer Partitions (Paperback)

This is a wonderful little book about a very simple mathematical object known as the "integer partition". The concept is simple: a partition of a positive integer is the set of positive integers that when summed give that number. (i.e. one integer partition of 6 is [5, 1] another is [3, 2, 1]). Order is unimportant so [5,1] and [1,5] are the same partition.

Amazingly this simple idea gives rise to many rich investigations that are the basis for this book. Many of these relate to "counting" the number of partitions with a given property and relating the number of partitions with various properties to one another. In fact, the mere counting of the number of partitions of a large integer, like 200, requires a foray into generating functions, an extremely important area of combinatorics. The formal properties of integer partitions have been investigated for over 200 years by some of the brightest lights in the mathematical constellation, such as Euler and Ramanujan. One of the authors (Andrews) is probably the current leading expert in this field.

Using integer partitions as a starting point the authors take the reader into many areas of mathematics (for example, generating functions, bijective proofs, Ferrers graphs and partially ordered sets). Each chapter also provides a selection of graded exercises ranging from the simple to problems that in some cases would be considered research areas. An outline of the answers to problems is provided in the back of the book. Working the problems will certainly give your powers of reasoning a real workout.

I am not particularly skilled at mathematics, however, I found the discussion relatively easy to follow although most topics require serious study if a full understanding is to be had. I would think that this book would certainly appeal to the math hobbyist, but could easily be the basis for a semester seminar for the advanced undergraduate.

Five stars for this gem!

4.0 out of 5 stars Really like it, but cost is a bit high, November 12, 2010

By 

Stephen Desalvo "Shakey" (Los Angeles, CA USA) - See all my reviews
(REAL NAME)   

This review is from: Integer Partitions (Paperback)

If you like to dabble in combinatorics, this is a very nice self-contained book on integer partitions, written at the undergraduate level. There is a lot of expository material and examples, with exercises as well, and the proofs are easy to read and follow.

The book is pretty thin, which in my opinion isn't a bad thing since they do a very good concise treatment of all the major topics. My only problem with this book is the cost on Amazon right now. I can access a university library so that's how I found it but I would like to have a copy for myself but wouldn't pay more than $10 or $15 for it, and if you ever see it I think you will agree. It should be a Dover book.